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# Advanced Quantum Computing Features
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Advanced quantum computing paradigms including Analog Hamiltonian Simulation (AHS), quantum annealing, pulse-level control, error mitigation, and experimental capabilities.
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## Core Imports
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```python { .api }
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# Analog Hamiltonian Simulation
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from braket.ahs import (
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AnalogHamiltonianSimulation, AtomArrangement, AtomArrangementItem, SiteType,
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Canvas, DiscretizationProperties, DrivingField, Field, Hamiltonian,
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LocalDetuning, Pattern, ShiftingField
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)
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# Quantum Annealing
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from braket.annealing import Problem, ProblemType
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# Pulse Control
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from braket.pulse import (
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Frame, Port, PulseSequence, ArbitraryWaveform, ConstantWaveform,
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DragGaussianWaveform, ErfSquareWaveform, GaussianWaveform
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)
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# Error Mitigation
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from braket.error_mitigation import Debias, ErrorMitigation
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# Experimental Capabilities
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from braket.experimental_capabilities import EnableExperimentalCapability
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```
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## Analog Hamiltonian Simulation (AHS)
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### AHS Program Construction
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```python { .api }
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from braket.ahs import AnalogHamiltonianSimulation, Hamiltonian, AtomArrangement
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import numpy as np
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class AnalogHamiltonianSimulation:
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"""Main AHS program for neutral atom quantum computing."""
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def __init__(self):
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"""Initialize empty AHS program."""
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self.hamiltonian = None
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self.atom_arrangement = None
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self.discretization_properties = None
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@classmethod
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def create(
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cls,
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atom_arrangement: 'AtomArrangement',
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hamiltonian: 'Hamiltonian',
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discretization_properties: 'DiscretizationProperties' = None
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) -> 'AnalogHamiltonianSimulation':
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"""
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Create AHS program with atom arrangement and Hamiltonian.
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Args:
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atom_arrangement: Spatial arrangement of neutral atoms
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hamiltonian: Time-dependent Hamiltonian specification
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discretization_properties: Time discretization settings
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Returns:
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AnalogHamiltonianSimulation: Complete AHS program
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"""
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pass
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def to_ir(self) -> dict:
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"""
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Convert to intermediate representation for device execution.
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Returns:
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dict: AHS program in device-compatible format
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"""
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pass
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class AtomArrangement:
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"""Atom position arrangement for AHS."""
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def __init__(self):
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"""Initialize empty atom arrangement."""
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self.sites = []
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def add(self, coordinate: tuple[float, float], site_type: 'SiteType' = None) -> 'AtomArrangement':
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"""
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Add atom site to arrangement.
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Args:
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coordinate: (x, y) position in micrometers
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site_type: Type of site (filled or vacant)
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Returns:
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AtomArrangement: Self for method chaining
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"""
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pass
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def add_item(self, item: 'AtomArrangementItem') -> 'AtomArrangement':
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"""
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Add pre-configured arrangement item.
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Args:
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item: Atom arrangement item
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Returns:
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AtomArrangement: Self for method chaining
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"""
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pass
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@property
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def coordinate_list(self) -> list[tuple[float, float]]:
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"""Get list of atom coordinates."""
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pass
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def visualize(self) -> 'Canvas':
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"""
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Create visualization of atom arrangement.
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Returns:
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Canvas: Visual representation of atom layout
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"""
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pass
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class AtomArrangementItem:
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"""Individual atom arrangement item."""
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def __init__(self, coordinate: tuple[float, float], site_type: 'SiteType'):
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"""
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Initialize atom arrangement item.
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Args:
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coordinate: (x, y) position in micrometers
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site_type: Type of site
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"""
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self.coordinate = coordinate
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self.site_type = site_type
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class SiteType:
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"""Site type enumeration for atom arrangements."""
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FILLED = "filled"
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VACANT = "vacant"
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# AHS program examples
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def create_rydberg_blockade_program(lattice_spacing: float = 5.0) -> AnalogHamiltonianSimulation:
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"""
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Create AHS program for Rydberg blockade physics.
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Args:
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lattice_spacing: Spacing between atoms in micrometers
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Returns:
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AnalogHamiltonianSimulation: Rydberg blockade AHS program
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"""
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# Create square lattice of atoms
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arrangement = AtomArrangement()
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n_atoms_per_side = 3
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for i in range(n_atoms_per_side):
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for j in range(n_atoms_per_side):
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x = i * lattice_spacing
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y = j * lattice_spacing
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arrangement.add((x, y), SiteType.FILLED)
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# Create time-dependent Hamiltonian
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# H = Ω(t)/2 ∑ᵢ (σˣⁱ) - Δ(t) ∑ᵢ nᵢ + ∑ᵢⱼ V_ij nᵢnⱼ
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hamiltonian = create_rydberg_hamiltonian()
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# Time evolution settings
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discretization = DiscretizationProperties(
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time_step=1e-7, # 0.1 microseconds
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time_series_precision=1e-9
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)
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return AnalogHamiltonianSimulation.create(
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arrangement, hamiltonian, discretization
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)
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def create_quantum_annealing_ahs_program() -> AnalogHamiltonianSimulation:
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"""
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Create AHS program for quantum annealing-like evolution.
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Returns:
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AnalogHamiltonianSimulation: Quantum annealing AHS program
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"""
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# Linear chain for transverse-field Ising model
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arrangement = AtomArrangement()
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chain_length = 5
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spacing = 8.0 # micrometers
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for i in range(chain_length):
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arrangement.add((i * spacing, 0.0), SiteType.FILLED)
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# Create annealing schedule
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total_time = 2.0 # microseconds
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# Driving field (transverse field analog)
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driving_amplitude = create_annealing_schedule(
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initial_value=2*np.pi * 10, # MHz
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final_value=0.0,
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total_time=total_time
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)
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# Detuning (longitudinal field)
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detuning = create_annealing_schedule(
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initial_value=0.0,
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final_value=2*np.pi * 5, # MHz
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total_time=total_time
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)
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hamiltonian = Hamiltonian()
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hamiltonian.driving_field = DrivingField(
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amplitude=driving_amplitude,
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phase=Pattern.constant(0.0),
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detuning=detuning
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)
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return AnalogHamiltonianSimulation.create(arrangement, hamiltonian)
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def analyze_ahs_program(ahs_program: AnalogHamiltonianSimulation) -> dict:
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"""
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Analyze AHS program for physics insights and optimization.
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Args:
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ahs_program: AHS program to analyze
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Returns:
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dict: Comprehensive program analysis
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"""
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analysis = {
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'atom_configuration': {},
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'hamiltonian_properties': {},
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'time_evolution': {},
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'physics_regime': {},
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'computational_complexity': {}
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}
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# Analyze atom arrangement
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coords = ahs_program.atom_arrangement.coordinate_list
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n_atoms = len(coords)
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analysis['atom_configuration'] = {
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'atom_count': n_atoms,
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'spatial_dimension': 2, # 2D arrangements
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'lattice_spacing': calculate_average_spacing(coords),
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'geometry': identify_lattice_geometry(coords),
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'coordination_number': calculate_coordination_numbers(coords)
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}
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# Analyze Hamiltonian
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hamiltonian = ahs_program.hamiltonian
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analysis['hamiltonian_properties'] = {
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'has_driving_field': hamiltonian.driving_field is not None,
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'has_local_detuning': hasattr(hamiltonian, 'local_detuning') and hamiltonian.local_detuning is not None,
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'interaction_range': estimate_interaction_range(coords),
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'rydberg_blockade_radius': calculate_blockade_radius(coords)
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}
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# Physics regime analysis
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if analysis['hamiltonian_properties']['has_driving_field']:
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analysis['physics_regime']['type'] = 'Rydberg blockade'
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analysis['physics_regime']['phenomena'] = [
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'Quantum many-body scarring',
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'Rydberg crystallization',
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'Quantum phase transitions'
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]
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else:
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analysis['physics_regime']['type'] = 'Ising-like'
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analysis['physics_regime']['phenomena'] = [
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'Ground state optimization',
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'Quantum annealing',
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'Combinatorial optimization'
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]
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# Computational complexity
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hilbert_space_size = 2 ** n_atoms # Each atom can be |0⟩ or |r⟩
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analysis['computational_complexity'] = {
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'hilbert_space_size': hilbert_space_size,
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'classical_simulation_feasible': n_atoms <= 20,
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'approximate_methods_needed': n_atoms > 15,
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'estimated_execution_time': estimate_ahs_execution_time(ahs_program)
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}
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return analysis
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def calculate_average_spacing(coordinates: list[tuple[float, float]]) -> float:
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"""Calculate average nearest-neighbor spacing."""
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if len(coordinates) < 2:
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return 0.0
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total_distance = 0.0
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count = 0
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for i, (x1, y1) in enumerate(coordinates):
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min_distance = float('inf')
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for j, (x2, y2) in enumerate(coordinates):
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if i != j:
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distance = np.sqrt((x2-x1)**2 + (y2-y1)**2)
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min_distance = min(min_distance, distance)
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if min_distance < float('inf'):
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total_distance += min_distance
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count += 1
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return total_distance / count if count > 0 else 0.0
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```
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### Hamiltonian Specification
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```python { .api }
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from braket.ahs import Hamiltonian, DrivingField, LocalDetuning, Pattern
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from braket.timings import TimeSeries
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class Hamiltonian:
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"""AHS Hamiltonian specification."""
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def __init__(self):
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"""Initialize empty Hamiltonian."""
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self.driving_field = None
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self.local_detuning = None
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def add_driving_field(self, driving_field: 'DrivingField') -> 'Hamiltonian':
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"""
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Add global driving field term.
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Args:
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driving_field: Global Rabi driving field
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Returns:
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Hamiltonian: Self for method chaining
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"""
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self.driving_field = driving_field
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return self
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def add_local_detuning(self, local_detuning: 'LocalDetuning') -> 'Hamiltonian':
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"""
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Add local detuning field.
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Args:
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local_detuning: Site-dependent detuning field
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Returns:
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Hamiltonian: Self for method chaining
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"""
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self.local_detuning = local_detuning
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return self
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class DrivingField(Field):
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"""Hamiltonian driving field for Rabi oscillations."""
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def __init__(
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self,
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amplitude: 'Pattern',
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phase: 'Pattern',
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detuning: 'Pattern'
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):
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"""
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Initialize driving field.
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Args:
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amplitude: Time-dependent Rabi frequency Ω(t)
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phase: Time-dependent phase φ(t)
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detuning: Time-dependent detuning Δ(t)
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"""
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self.amplitude = amplitude
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self.phase = phase
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self.detuning = detuning
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class LocalDetuning(Field):
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"""Local detuning field for site-dependent energy shifts."""
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def __init__(self, magnitude: 'Pattern'):
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"""
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Initialize local detuning field.
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Args:
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magnitude: Spatially-dependent detuning magnitude
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"""
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self.magnitude = magnitude
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class Pattern:
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"""Time-dependent pattern for AHS fields."""
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@staticmethod
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def constant(value: float) -> 'Pattern':
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"""
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Create constant pattern.
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Args:
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value: Constant value
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Returns:
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Pattern: Constant pattern
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"""
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pass
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@staticmethod
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def linear(start_value: float, end_value: float, duration: float) -> 'Pattern':
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"""
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Create linear interpolation pattern.
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Args:
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start_value: Initial value
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end_value: Final value
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duration: Pattern duration
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Returns:
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Pattern: Linear interpolation pattern
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"""
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pass
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@staticmethod
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def from_time_series(time_series: TimeSeries) -> 'Pattern':
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"""
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Create pattern from time series data.
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Args:
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time_series: Time-dependent values
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Returns:
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Pattern: Pattern from time series
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"""
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pass
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def create_rydberg_hamiltonian() -> Hamiltonian:
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"""
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Create typical Rydberg Hamiltonian for quantum simulation.
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Returns:
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Hamiltonian: Rydberg blockade Hamiltonian
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"""
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hamiltonian = Hamiltonian()
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# Time-dependent Rabi frequency (adiabatic ramp)
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omega_max = 2*np.pi * 15 # 15 MHz
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ramp_time = 1.0 # microseconds
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hold_time = 0.5 # microseconds
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# Create piecewise linear amplitude
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amplitude_points = [
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(0.0, 0.0), # Start at zero
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(ramp_time/4, omega_max), # Ramp up
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(3*ramp_time/4, omega_max), # Hold
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(ramp_time, 0.0) # Ramp down
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]
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amplitude_series = TimeSeries()
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for time, value in amplitude_points:
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amplitude_series.add_point(time, value)
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amplitude_pattern = Pattern.from_time_series(amplitude_series)
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# Constant phase and detuning
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phase_pattern = Pattern.constant(0.0)
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detuning_pattern = Pattern.constant(0.0)
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# Add driving field
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driving_field = DrivingField(
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amplitude=amplitude_pattern,
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phase=phase_pattern,
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detuning=detuning_pattern
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)
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hamiltonian.add_driving_field(driving_field)
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return hamiltonian
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def create_annealing_schedule(initial_value: float, final_value: float, total_time: float) -> Pattern:
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"""
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Create annealing schedule pattern for AHS.
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Args:
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initial_value: Starting parameter value
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final_value: Ending parameter value
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total_time: Total annealing time
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Returns:
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Pattern: Annealing schedule pattern
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"""
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# Create smooth S-curve annealing schedule
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n_points = 100
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times = np.linspace(0, total_time, n_points)
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# S-curve using tanh function
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s_values = []
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for t in times:
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s = (np.tanh(4 * (t/total_time - 0.5)) + 1) / 2 # Sigmoid from 0 to 1
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value = initial_value + s * (final_value - initial_value)
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s_values.append(value)
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# Create time series
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time_series = TimeSeries()
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for t, v in zip(times, s_values):
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time_series.add_point(t, v)
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return Pattern.from_time_series(time_series)
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```
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## Quantum Annealing
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### Annealing Problem Specification
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```python { .api }
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from braket.annealing import Problem, ProblemType
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from enum import Enum
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class ProblemType(Enum):
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"""Types of annealing problems."""
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QUBO = "QUBO"
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ISING = "ISING"
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class Problem:
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"""Annealing problem specification."""
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def __init__(self, problem_type: ProblemType):
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"""
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Initialize annealing problem.
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Args:
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problem_type: Type of optimization problem (QUBO or Ising)
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"""
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self.problem_type = problem_type
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self.linear = {} # Linear terms
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self.quadratic = {} # Quadratic terms
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def add_linear(self, variable: int, coefficient: float) -> 'Problem':
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"""
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Add linear term to problem.
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Args:
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variable: Variable index
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coefficient: Linear coefficient
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Returns:
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Problem: Self for method chaining
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"""
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self.linear[variable] = coefficient
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return self
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def add_quadratic(self, var1: int, var2: int, coefficient: float) -> 'Problem':
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"""
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Add quadratic term to problem.
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Args:
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var1: First variable index
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var2: Second variable index
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coefficient: Quadratic coefficient
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Returns:
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Problem: Self for method chaining
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"""
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self.quadratic[(var1, var2)] = coefficient
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return self
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def to_dict(self) -> dict:
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"""
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Convert problem to dictionary representation.
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Returns:
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dict: Problem in dictionary format
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"""
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return {
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'type': self.problem_type.value,
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'linear': self.linear,
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'quadratic': self.quadratic
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}
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# Annealing examples
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def create_max_cut_problem(graph_edges: list[tuple[int, int]]) -> Problem:
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"""
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Create Max-Cut problem for quantum annealing.
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Args:
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graph_edges: List of graph edges as (node1, node2) pairs
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Returns:
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Problem: Max-Cut QUBO formulation
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"""
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problem = Problem(ProblemType.QUBO)
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# Max-Cut QUBO formulation: maximize ∑ᵢⱼ wᵢⱼ xᵢ(1-xⱼ) + wᵢⱼ(1-xᵢ)xⱼ
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# Equivalent to: minimize -∑ᵢⱼ wᵢⱼ(xᵢ + xⱼ - 2xᵢxⱼ)
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# Assume unit weights for simplicity
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nodes = set()
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for i, j in graph_edges:
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nodes.add(i)
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nodes.add(j)
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# Linear terms: -wᵢⱼ for each edge (i,j)
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linear_coeffs = {}
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for i, j in graph_edges:
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linear_coeffs[i] = linear_coeffs.get(i, 0) - 1
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linear_coeffs[j] = linear_coeffs.get(j, 0) - 1
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for node, coeff in linear_coeffs.items():
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problem.add_linear(node, coeff)
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# Quadratic terms: +2wᵢⱼ for each edge (i,j)
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for i, j in graph_edges:
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problem.add_quadratic(i, j, 2.0)
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return problem
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def create_number_partitioning_problem(numbers: list[int]) -> Problem:
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"""
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Create number partitioning problem for quantum annealing.
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Args:
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numbers: List of numbers to partition into equal-sum sets
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Returns:
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Problem: Number partitioning QUBO formulation
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"""
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problem = Problem(ProblemType.QUBO)
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# Number partitioning: minimize (∑ᵢ aᵢxᵢ - S/2)²
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# where S = ∑ᵢ aᵢ is total sum
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S = sum(numbers)
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target = S // 2 # Target sum for each partition
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# Expand: (∑ᵢ aᵢxᵢ - target)² = ∑ᵢ aᵢ²xᵢ + 2∑ᵢⱼ aᵢaⱼxᵢxⱼ - 2target∑ᵢ aᵢxᵢ + target²
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# Ignore constant target² term
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# Linear terms: aᵢ² - 2target·aᵢ
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for i, a in enumerate(numbers):
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linear_coeff = a*a - 2*target*a
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problem.add_linear(i, linear_coeff)
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# Quadratic terms: 2aᵢaⱼ for i < j
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for i in range(len(numbers)):
630
for j in range(i+1, len(numbers)):
631
quadratic_coeff = 2 * numbers[i] * numbers[j]
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problem.add_quadratic(i, j, quadratic_coeff)
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return problem
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def create_portfolio_optimization_problem(returns: list[float], risks: list[list[float]], risk_penalty: float = 1.0) -> Problem:
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"""
638
Create portfolio optimization problem for quantum annealing.
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Args:
641
returns: Expected returns for each asset
642
risks: Risk covariance matrix
643
risk_penalty: Risk penalty parameter λ
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645
Returns:
646
Problem: Portfolio optimization QUBO formulation
647
"""
648
problem = Problem(ProblemType.QUBO)
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n_assets = len(returns)
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# Portfolio optimization: maximize ∑ᵢ rᵢxᵢ - λ ∑ᵢⱼ σᵢⱼxᵢxⱼ
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# Convert to minimization: minimize -∑ᵢ rᵢxᵢ + λ ∑ᵢⱼ σᵢⱼxᵢxⱼ
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# Linear terms: -rᵢ (negative expected returns)
655
for i, r in enumerate(returns):
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problem.add_linear(i, -r)
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# Quadratic terms: λσᵢⱼ (risk penalties)
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for i in range(n_assets):
660
for j in range(i, n_assets):
661
if i == j:
662
# Diagonal terms (variance)
663
risk_coeff = risk_penalty * risks[i][j]
664
problem.add_linear(i, risk_coeff) # Add to diagonal
665
else:
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# Off-diagonal terms (covariance)
667
risk_coeff = risk_penalty * risks[i][j]
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problem.add_quadratic(i, j, 2 * risk_coeff) # Factor of 2 for symmetry
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return problem
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def analyze_annealing_problem(problem: Problem) -> dict:
673
"""
674
Analyze quantum annealing problem for optimization insights.
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Args:
677
problem: Annealing problem to analyze
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Returns:
680
dict: Problem analysis and optimization recommendations
681
"""
682
analysis = {
683
'problem_structure': {},
684
'complexity_metrics': {},
685
'annealing_parameters': {},
686
'optimization_difficulty': {}
687
}
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# Analyze problem structure
690
n_variables = len(set(list(problem.linear.keys()) +
691
[var for pair in problem.quadratic.keys() for var in pair]))
692
n_linear_terms = len(problem.linear)
693
n_quadratic_terms = len(problem.quadratic)
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analysis['problem_structure'] = {
696
'problem_type': problem.problem_type.value,
697
'variable_count': n_variables,
698
'linear_terms': n_linear_terms,
699
'quadratic_terms': n_quadratic_terms,
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'density': n_quadratic_terms / (n_variables * (n_variables - 1) / 2) if n_variables > 1 else 0
701
}
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703
# Complexity analysis
704
coefficient_magnitudes = (list(problem.linear.values()) +
705
list(problem.quadratic.values()))
706
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analysis['complexity_metrics'] = {
708
'coefficient_range': (min(coefficient_magnitudes), max(coefficient_magnitudes)),
709
'coefficient_std': np.std(coefficient_magnitudes),
710
'sparsity': 1 - (n_linear_terms + n_quadratic_terms) / (n_variables + n_variables**2/2),
711
'conditioning': max(coefficient_magnitudes) / min(abs(c) for c in coefficient_magnitudes if c != 0)
712
}
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714
# Annealing parameter recommendations
715
if analysis['complexity_metrics']['conditioning'] > 100:
716
recommended_annealing_time = 'Long (>100μs)'
717
recommended_schedule = 'Slow linear or exponential'
718
else:
719
recommended_annealing_time = 'Standard (20-50μs)'
720
recommended_schedule = 'Linear or fast exponential'
721
722
analysis['annealing_parameters'] = {
723
'recommended_annealing_time': recommended_annealing_time,
724
'recommended_schedule': recommended_schedule,
725
'suggested_repetitions': max(1000, 10 * n_variables),
726
'post_processing': 'Consider classical refinement for large problems'
727
}
728
729
return analysis
730
```
731
732
## Pulse-Level Control
733
734
### Pulse Sequence Programming
735
736
```python { .api }
737
from braket.pulse import PulseSequence, Frame, Port
738
import numpy as np
739
740
class PulseSequence:
741
"""Sequence of pulse operations for direct hardware control."""
742
743
def __init__(self):
744
"""Initialize empty pulse sequence."""
745
self.operations = []
746
self.duration = 0.0
747
748
def play(self, frame: 'Frame', waveform: 'Waveform') -> 'PulseSequence':
749
"""
750
Play waveform on specified frame.
751
752
Args:
753
frame: Target frame for pulse
754
waveform: Pulse waveform to play
755
756
Returns:
757
PulseSequence: Self for method chaining
758
"""
759
pass
760
761
def delay(self, frame: 'Frame', duration: float) -> 'PulseSequence':
762
"""
763
Add delay on frame.
764
765
Args:
766
frame: Target frame
767
duration: Delay duration in seconds
768
769
Returns:
770
PulseSequence: Self for method chaining
771
"""
772
pass
773
774
def shift_frequency(self, frame: 'Frame', frequency: float) -> 'PulseSequence':
775
"""
776
Shift frame frequency.
777
778
Args:
779
frame: Target frame
780
frequency: Frequency shift in Hz
781
782
Returns:
783
PulseSequence: Self for method chaining
784
"""
785
pass
786
787
def set_phase(self, frame: 'Frame', phase: float) -> 'PulseSequence':
788
"""
789
Set frame phase.
790
791
Args:
792
frame: Target frame
793
phase: Phase in radians
794
795
Returns:
796
PulseSequence: Self for method chaining
797
"""
798
pass
799
800
def barrier(self, frames: list['Frame']) -> 'PulseSequence':
801
"""
802
Add synchronization barrier across frames.
803
804
Args:
805
frames: Frames to synchronize
806
807
Returns:
808
PulseSequence: Self for method chaining
809
"""
810
pass
811
812
class Frame:
813
"""Pulse frame definition for frequency and phase tracking."""
814
815
def __init__(
816
self,
817
frame_id: str,
818
port: 'Port',
819
frequency: float,
820
phase: float = 0.0
821
):
822
"""
823
Initialize pulse frame.
824
825
Args:
826
frame_id: Unique frame identifier
827
port: Associated hardware port
828
frequency: Frame frequency in Hz
829
phase: Initial phase in radians
830
"""
831
self.frame_id = frame_id
832
self.port = port
833
self.frequency = frequency
834
self.phase = phase
835
836
class Port:
837
"""Hardware port specification."""
838
839
def __init__(self, port_id: str, dt: float):
840
"""
841
Initialize hardware port.
842
843
Args:
844
port_id: Unique port identifier
845
dt: Port time resolution in seconds
846
"""
847
self.port_id = port_id
848
self.dt = dt
849
850
# Waveform definitions
851
class GaussianWaveform:
852
"""Gaussian pulse waveform."""
853
854
def __init__(
855
self,
856
length: float,
857
amplitude: float,
858
sigma: float
859
):
860
"""
861
Initialize Gaussian waveform.
862
863
Args:
864
length: Pulse length in seconds
865
amplitude: Peak amplitude
866
sigma: Gaussian width parameter
867
"""
868
self.length = length
869
self.amplitude = amplitude
870
self.sigma = sigma
871
872
class DragGaussianWaveform:
873
"""DRAG (Derivative Removal by Adiabatic Gating) Gaussian waveform."""
874
875
def __init__(
876
self,
877
length: float,
878
amplitude: float,
879
sigma: float,
880
beta: float
881
):
882
"""
883
Initialize DRAG Gaussian waveform.
884
885
Args:
886
length: Pulse length in seconds
887
amplitude: Peak amplitude
888
sigma: Gaussian width parameter
889
beta: DRAG correction parameter
890
"""
891
self.length = length
892
self.amplitude = amplitude
893
self.sigma = sigma
894
self.beta = beta
895
896
class ConstantWaveform:
897
"""Constant amplitude waveform."""
898
899
def __init__(self, length: float, amplitude: float):
900
"""
901
Initialize constant waveform.
902
903
Args:
904
length: Pulse length in seconds
905
amplitude: Constant amplitude
906
"""
907
self.length = length
908
self.amplitude = amplitude
909
910
class ArbitraryWaveform:
911
"""Custom arbitrary waveform."""
912
913
def __init__(self, amplitudes: list[complex]):
914
"""
915
Initialize arbitrary waveform.
916
917
Args:
918
amplitudes: Time-sampled amplitude values
919
"""
920
self.amplitudes = amplitudes
921
self.length = len(amplitudes)
922
923
# Pulse programming examples
924
def create_single_qubit_pulse_gate(qubit_frequency: float, rabi_frequency: float, gate_type: str) -> PulseSequence:
925
"""
926
Create pulse sequence for single-qubit gate.
927
928
Args:
929
qubit_frequency: Qubit transition frequency in Hz
930
rabi_frequency: Rabi frequency for π-pulse in Hz
931
gate_type: Type of gate ('X', 'Y', 'Z', 'H')
932
933
Returns:
934
PulseSequence: Pulse sequence implementing the gate
935
"""
936
sequence = PulseSequence()
937
938
# Define hardware components
939
port = Port("drive_port", dt=1e-9) # 1 ns resolution
940
frame = Frame("qubit_frame", port, qubit_frequency)
941
942
if gate_type == 'X':
943
# π-pulse around X-axis
944
pulse_length = 1 / (2 * rabi_frequency) # π-pulse duration
945
waveform = GaussianWaveform(
946
length=pulse_length,
947
amplitude=rabi_frequency * 2 * np.pi,
948
sigma=pulse_length / 4
949
)
950
sequence.play(frame, waveform)
951
952
elif gate_type == 'Y':
953
# π-pulse around Y-axis (π/2 phase shift)
954
pulse_length = 1 / (2 * rabi_frequency)
955
sequence.set_phase(frame, np.pi/2)
956
waveform = GaussianWaveform(
957
length=pulse_length,
958
amplitude=rabi_frequency * 2 * np.pi,
959
sigma=pulse_length / 4
960
)
961
sequence.play(frame, waveform)
962
sequence.set_phase(frame, 0) # Reset phase
963
964
elif gate_type == 'H':
965
# Hadamard via Y(π/2) - X(π) - Y(π/2) decomposition
966
pulse_length = 1 / (4 * rabi_frequency) # π/2-pulse duration
967
968
# First Y(π/2)
969
sequence.set_phase(frame, np.pi/2)
970
y_pulse = GaussianWaveform(
971
length=pulse_length,
972
amplitude=rabi_frequency * 2 * np.pi,
973
sigma=pulse_length / 4
974
)
975
sequence.play(frame, y_pulse)
976
977
# X(π)
978
sequence.set_phase(frame, 0)
979
x_pulse = GaussianWaveform(
980
length=2*pulse_length,
981
amplitude=rabi_frequency * 2 * np.pi,
982
sigma=pulse_length / 2
983
)
984
sequence.play(frame, x_pulse)
985
986
# Final Y(π/2)
987
sequence.set_phase(frame, np.pi/2)
988
sequence.play(frame, y_pulse)
989
sequence.set_phase(frame, 0)
990
991
return sequence
992
993
def create_two_qubit_cross_resonance_gate(
994
control_freq: float,
995
target_freq: float,
996
cr_amplitude: float
997
) -> PulseSequence:
998
"""
999
Create cross-resonance pulse sequence for two-qubit gate.
1000
1001
Args:
1002
control_freq: Control qubit frequency in Hz
1003
target_freq: Target qubit frequency in Hz
1004
cr_amplitude: Cross-resonance drive amplitude
1005
1006
Returns:
1007
PulseSequence: Cross-resonance gate pulse sequence
1008
"""
1009
sequence = PulseSequence()
1010
1011
# Hardware setup
1012
control_port = Port("control_port", dt=1e-9)
1013
target_port = Port("target_port", dt=1e-9)
1014
1015
control_frame = Frame("control_frame", control_port, control_freq)
1016
target_frame = Frame("target_frame", target_port, target_freq)
1017
1018
# Cross-resonance drive on target frequency via control port
1019
cr_frame = Frame("cr_frame", control_port, target_freq)
1020
1021
# Cross-resonance pulse (flat-top with Gaussian edges)
1022
cr_duration = 320e-9 # 320 ns typical CR gate time
1023
rise_time = 20e-9 # 20 ns rise/fall time
1024
1025
# Rising edge
1026
rise_waveform = GaussianWaveform(
1027
length=rise_time,
1028
amplitude=cr_amplitude,
1029
sigma=rise_time / 4
1030
)
1031
1032
# Flat top
1033
flat_duration = cr_duration - 2 * rise_time
1034
flat_waveform = ConstantWaveform(flat_duration, cr_amplitude)
1035
1036
# Falling edge
1037
fall_waveform = GaussianWaveform(
1038
length=rise_time,
1039
amplitude=-cr_amplitude, # Negative for falling
1040
sigma=rise_time / 4
1041
)
1042
1043
# Play CR pulse sequence
1044
sequence.play(cr_frame, rise_waveform)
1045
sequence.play(cr_frame, flat_waveform)
1046
sequence.play(cr_frame, fall_waveform)
1047
1048
# Echo cancellation pulses on control qubit
1049
echo_pulse = GaussianWaveform(
1050
length=cr_duration,
1051
amplitude=cr_amplitude / 4, # Reduced amplitude
1052
sigma=cr_duration / 8
1053
)
1054
sequence.play(control_frame, echo_pulse)
1055
1056
# Synchronization barrier
1057
sequence.barrier([control_frame, target_frame, cr_frame])
1058
1059
return sequence
1060
1061
def optimize_pulse_fidelity(
1062
target_unitary: np.ndarray,
1063
pulse_parameters: dict,
1064
constraints: dict
1065
) -> dict:
1066
"""
1067
Optimize pulse sequence for maximum gate fidelity.
1068
1069
Args:
1070
target_unitary: Target gate unitary matrix
1071
pulse_parameters: Initial pulse parameter values
1072
constraints: Hardware and physics constraints
1073
1074
Returns:
1075
dict: Optimized pulse parameters and fidelity analysis
1076
"""
1077
optimization_result = {
1078
'optimized_parameters': {},
1079
'achieved_fidelity': 0.0,
1080
'optimization_history': [],
1081
'constraint_violations': {},
1082
'recommendations': []
1083
}
1084
1085
# Extract constraints
1086
max_amplitude = constraints.get('max_amplitude', 1e8) # Hz
1087
min_duration = constraints.get('min_duration', 1e-9) # s
1088
max_duration = constraints.get('max_duration', 1e-6) # s
1089
1090
# Simplified optimization (would use gradient-based methods)
1091
initial_amplitude = pulse_parameters.get('amplitude', max_amplitude / 2)
1092
initial_duration = pulse_parameters.get('duration', 50e-9)
1093
initial_sigma = pulse_parameters.get('sigma', initial_duration / 4)
1094
1095
# Grid search over parameter space (simplified)
1096
best_fidelity = 0.0
1097
best_params = pulse_parameters.copy()
1098
1099
amplitude_range = np.linspace(max_amplitude/10, max_amplitude, 10)
1100
duration_range = np.linspace(min_duration*10, max_duration/10, 10)
1101
1102
for amp in amplitude_range:
1103
for dur in duration_range:
1104
# Simulate gate with these parameters
1105
simulated_fidelity = simulate_pulse_gate_fidelity(
1106
target_unitary, amp, dur, dur/4
1107
)
1108
1109
if simulated_fidelity > best_fidelity:
1110
best_fidelity = simulated_fidelity
1111
best_params = {
1112
'amplitude': amp,
1113
'duration': dur,
1114
'sigma': dur/4
1115
}
1116
1117
optimization_result['optimized_parameters'] = best_params
1118
optimization_result['achieved_fidelity'] = best_fidelity
1119
1120
# Generate recommendations
1121
if best_fidelity < 0.99:
1122
optimization_result['recommendations'].append(
1123
"Consider DRAG correction for improved fidelity"
1124
)
1125
1126
if best_params['duration'] > max_duration / 2:
1127
optimization_result['recommendations'].append(
1128
"Long pulse duration may increase decoherence"
1129
)
1130
1131
return optimization_result
1132
1133
def simulate_pulse_gate_fidelity(target_unitary: np.ndarray, amplitude: float, duration: float, sigma: float) -> float:
1134
"""Simplified pulse gate fidelity simulation."""
1135
# This would involve solving the Schrödinger equation
1136
# For now, return a mock fidelity based on parameter reasonableness
1137
1138
# Assume optimal parameters give ~99% fidelity
1139
optimal_duration = 50e-9 # 50 ns
1140
optimal_amplitude = 1e7 # 10 MHz
1141
1142
duration_factor = 1 - abs(duration - optimal_duration) / optimal_duration
1143
amplitude_factor = 1 - abs(amplitude - optimal_amplitude) / optimal_amplitude
1144
1145
fidelity = 0.95 * duration_factor * amplitude_factor
1146
return max(0.5, min(0.999, fidelity)) # Clamp between 50% and 99.9%
1147
```
1148
1149
## Error Mitigation
1150
1151
### Error Mitigation Techniques
1152
1153
```python { .api }
1154
from braket.error_mitigation import ErrorMitigation, Debias
1155
1156
class ErrorMitigation:
1157
"""Base error mitigation interface."""
1158
1159
def mitigate(self, task_results: list) -> list:
1160
"""
1161
Apply error mitigation to task results.
1162
1163
Args:
1164
task_results: Raw quantum task results
1165
1166
Returns:
1167
list: Mitigated results
1168
"""
1169
pass
1170
1171
class Debias(ErrorMitigation):
1172
"""Debiasing error mitigation technique."""
1173
1174
def __init__(self, noise_model=None):
1175
"""
1176
Initialize debiasing error mitigation.
1177
1178
Args:
1179
noise_model: Optional noise model for correction
1180
"""
1181
self.noise_model = noise_model
1182
1183
def mitigate(self, task_results: list) -> list:
1184
"""
1185
Apply debiasing to measurement results.
1186
1187
Args:
1188
task_results: Task results to debias
1189
1190
Returns:
1191
list: Debiased results
1192
"""
1193
pass
1194
1195
# Error mitigation examples
1196
def implement_zero_noise_extrapolation(
1197
circuit,
1198
device,
1199
noise_scaling_factors: list[float] = [1.0, 2.0, 3.0]
1200
) -> dict:
1201
"""
1202
Implement zero-noise extrapolation (ZNE) error mitigation.
1203
1204
Args:
1205
circuit: Quantum circuit to execute with error mitigation
1206
device: Quantum device for execution
1207
noise_scaling_factors: Noise scaling factors for extrapolation
1208
1209
Returns:
1210
dict: ZNE results and extrapolated values
1211
"""
1212
zne_results = {
1213
'noise_factors': noise_scaling_factors,
1214
'measured_values': [],
1215
'extrapolated_value': 0.0,
1216
'extrapolation_error': 0.0,
1217
'mitigation_overhead': len(noise_scaling_factors)
1218
}
1219
1220
# Execute circuit at different noise levels
1221
for noise_factor in noise_scaling_factors:
1222
# Create noise-scaled circuit (simplified - would need proper implementation)
1223
scaled_circuit = scale_circuit_noise(circuit, noise_factor)
1224
1225
# Execute and measure expectation value
1226
task = device.run(scaled_circuit, shots=10000)
1227
result = task.result()
1228
1229
if hasattr(result, 'values'):
1230
expectation_value = result.values[0]
1231
else:
1232
# Calculate expectation from measurement counts
1233
expectation_value = calculate_expectation_from_counts(
1234
result.measurement_counts
1235
)
1236
1237
zne_results['measured_values'].append(expectation_value)
1238
1239
# Extrapolate to zero noise
1240
extrapolated_value, error = extrapolate_to_zero_noise(
1241
noise_scaling_factors, zne_results['measured_values']
1242
)
1243
1244
zne_results['extrapolated_value'] = extrapolated_value
1245
zne_results['extrapolation_error'] = error
1246
1247
return zne_results
1248
1249
def implement_readout_error_mitigation(
1250
circuits: list,
1251
device,
1252
calibration_shots: int = 10000
1253
) -> dict:
1254
"""
1255
Implement readout error mitigation using confusion matrix.
1256
1257
Args:
1258
circuits: Circuits to execute with readout error correction
1259
device: Quantum device
1260
calibration_shots: Shots for calibration measurements
1261
1262
Returns:
1263
dict: Results with readout error correction applied
1264
"""
1265
mitigation_results = {
1266
'confusion_matrix': None,
1267
'corrected_results': [],
1268
'improvement_metrics': {}
1269
}
1270
1271
# Step 1: Calibrate readout errors
1272
n_qubits = max(circuit.qubit_count for circuit in circuits)
1273
confusion_matrix = calibrate_readout_errors(device, n_qubits, calibration_shots)
1274
mitigation_results['confusion_matrix'] = confusion_matrix
1275
1276
# Step 2: Execute circuits and apply correction
1277
for circuit in circuits:
1278
# Execute circuit
1279
task = device.run(circuit, shots=10000)
1280
raw_counts = task.result().measurement_counts
1281
1282
# Apply readout error correction
1283
corrected_counts = apply_readout_correction(
1284
raw_counts, confusion_matrix
1285
)
1286
1287
mitigation_results['corrected_results'].append({
1288
'circuit_index': len(mitigation_results['corrected_results']),
1289
'raw_counts': raw_counts,
1290
'corrected_counts': corrected_counts
1291
})
1292
1293
# Calculate improvement metrics
1294
mitigation_results['improvement_metrics'] = calculate_mitigation_improvement(
1295
mitigation_results['corrected_results']
1296
)
1297
1298
return mitigation_results
1299
1300
def implement_virtual_distillation(
1301
circuit,
1302
device,
1303
num_copies: int = 5,
1304
shots_per_copy: int = 2000
1305
) -> dict:
1306
"""
1307
Implement virtual distillation error mitigation.
1308
1309
Args:
1310
circuit: Circuit to execute with virtual distillation
1311
device: Quantum device
1312
num_copies: Number of virtual copies
1313
shots_per_copy: Shots per copy
1314
1315
Returns:
1316
dict: Virtual distillation results
1317
"""
1318
vd_results = {
1319
'num_copies': num_copies,
1320
'copy_results': [],
1321
'distilled_result': 0.0,
1322
'variance_reduction': 0.0
1323
}
1324
1325
copy_values = []
1326
1327
# Execute multiple copies of the circuit
1328
for copy_idx in range(num_copies):
1329
task = device.run(circuit, shots=shots_per_copy)
1330
result = task.result()
1331
1332
# Calculate expectation value for this copy
1333
if hasattr(result, 'values'):
1334
expectation = result.values[0]
1335
else:
1336
expectation = calculate_expectation_from_counts(result.measurement_counts)
1337
1338
copy_values.append(expectation)
1339
vd_results['copy_results'].append({
1340
'copy_index': copy_idx,
1341
'expectation_value': expectation,
1342
'measurement_counts': result.measurement_counts
1343
})
1344
1345
# Apply virtual distillation formula
1346
# For odd number of copies: median
1347
# For even number: could use other combining strategies
1348
if num_copies % 2 == 1:
1349
distilled_value = np.median(copy_values)
1350
else:
1351
# Use weighted average with outlier removal
1352
copy_array = np.array(copy_values)
1353
q1, q3 = np.percentile(copy_array, [25, 75])
1354
iqr = q3 - q1
1355
lower_bound = q1 - 1.5 * iqr
1356
upper_bound = q3 + 1.5 * iqr
1357
1358
# Filter outliers and average
1359
filtered_values = copy_array[
1360
(copy_array >= lower_bound) & (copy_array <= upper_bound)
1361
]
1362
distilled_value = np.mean(filtered_values) if len(filtered_values) > 0 else np.mean(copy_array)
1363
1364
vd_results['distilled_result'] = distilled_value
1365
1366
# Calculate variance reduction
1367
raw_variance = np.var(copy_values)
1368
# Virtual distillation typically reduces variance by ~1/sqrt(N)
1369
expected_variance_reduction = 1 / np.sqrt(num_copies)
1370
vd_results['variance_reduction'] = expected_variance_reduction
1371
1372
return vd_results
1373
1374
def scale_circuit_noise(circuit, noise_factor: float):
1375
"""Scale noise in quantum circuit (simplified implementation)."""
1376
# This would involve adding noise gates or modifying existing noise
1377
# For now, return original circuit (real implementation would add noise)
1378
return circuit
1379
1380
def extrapolate_to_zero_noise(noise_factors: list[float], measured_values: list[float]) -> tuple[float, float]:
1381
"""Extrapolate measured values to zero noise using polynomial fit."""
1382
# Linear extrapolation (could use higher-order polynomials)
1383
coeffs = np.polyfit(noise_factors, measured_values, deg=1)
1384
1385
# Extrapolate to zero noise (x=0)
1386
extrapolated_value = coeffs[1] # y-intercept
1387
1388
# Estimate error from fit quality
1389
fit_values = np.polyval(coeffs, noise_factors)
1390
fit_error = np.sqrt(np.mean((np.array(measured_values) - fit_values)**2))
1391
1392
return float(extrapolated_value), float(fit_error)
1393
1394
def calibrate_readout_errors(device, n_qubits: int, shots: int) -> np.ndarray:
1395
"""Calibrate readout error confusion matrix."""
1396
from braket.circuits import Circuit
1397
1398
confusion_matrix = np.zeros((2**n_qubits, 2**n_qubits))
1399
1400
# Measure each computational basis state
1401
for state_idx in range(2**n_qubits):
1402
# Prepare computational basis state |state_idx⟩
1403
prep_circuit = Circuit()
1404
1405
# Convert state index to binary and apply X gates
1406
binary_state = format(state_idx, f'0{n_qubits}b')
1407
for qubit, bit in enumerate(binary_state):
1408
if bit == '1':
1409
prep_circuit.x(qubit)
1410
1411
# Measure
1412
prep_circuit.measure_all()
1413
1414
# Execute calibration measurement
1415
task = device.run(prep_circuit, shots=shots)
1416
counts = task.result().measurement_counts
1417
1418
# Fill confusion matrix row
1419
for measured_state, count in counts.items():
1420
measured_idx = int(measured_state, 2)
1421
confusion_matrix[state_idx, measured_idx] = count / shots
1422
1423
return confusion_matrix
1424
1425
def apply_readout_correction(raw_counts: dict, confusion_matrix: np.ndarray) -> dict:
1426
"""Apply readout error correction using confusion matrix inversion."""
1427
# Convert counts to probability vector
1428
total_shots = sum(raw_counts.values())
1429
n_states = len(confusion_matrix)
1430
1431
measured_probs = np.zeros(n_states)
1432
for bitstring, count in raw_counts.items():
1433
state_idx = int(bitstring, 2)
1434
measured_probs[state_idx] = count / total_shots
1435
1436
# Invert confusion matrix to get corrected probabilities
1437
try:
1438
inv_confusion = np.linalg.inv(confusion_matrix)
1439
corrected_probs = inv_confusion @ measured_probs
1440
1441
# Ensure probabilities are non-negative (physical constraint)
1442
corrected_probs = np.maximum(corrected_probs, 0)
1443
corrected_probs /= np.sum(corrected_probs) # Renormalize
1444
1445
except np.linalg.LinAlgError:
1446
# If matrix is singular, use pseudo-inverse
1447
inv_confusion = np.linalg.pinv(confusion_matrix)
1448
corrected_probs = inv_confusion @ measured_probs
1449
corrected_probs = np.maximum(corrected_probs, 0)
1450
corrected_probs /= np.sum(corrected_probs)
1451
1452
# Convert back to counts
1453
corrected_counts = {}
1454
for state_idx, prob in enumerate(corrected_probs):
1455
if prob > 0:
1456
bitstring = format(state_idx, f'0{int(np.log2(n_states))}b')
1457
corrected_counts[bitstring] = int(prob * total_shots)
1458
1459
return corrected_counts
1460
1461
def calculate_expectation_from_counts(counts: dict) -> float:
1462
"""Calculate expectation value ⟨Z⟩ from measurement counts."""
1463
total_shots = sum(counts.values())
1464
expectation = 0.0
1465
1466
for bitstring, count in counts.items():
1467
# Calculate parity (even=+1, odd=-1)
1468
parity = (-1) ** sum(int(bit) for bit in bitstring)
1469
expectation += parity * count / total_shots
1470
1471
return expectation
1472
```
1473
1474
## Experimental Capabilities
1475
1476
### Experimental Features Access
1477
1478
```python { .api }
1479
from braket.experimental_capabilities import EnableExperimentalCapability
1480
1481
class EnableExperimentalCapability:
1482
"""Context manager for experimental features."""
1483
1484
def __init__(self, capability_name: str):
1485
"""
1486
Initialize experimental capability context.
1487
1488
Args:
1489
capability_name: Name of experimental capability to enable
1490
"""
1491
self.capability_name = capability_name
1492
1493
def __enter__(self) -> 'EnableExperimentalCapability':
1494
"""Enable experimental capability."""
1495
return self
1496
1497
def __exit__(self, exc_type, exc_val, exc_tb) -> None:
1498
"""Disable experimental capability."""
1499
pass
1500
1501
# Experimental features examples
1502
def use_experimental_classical_control():
1503
"""Example of using experimental classical control features."""
1504
1505
with EnableExperimentalCapability("classical_control"):
1506
# Access experimental classical control capabilities
1507
from braket.experimental_capabilities import classical_control
1508
1509
# This would enable features like:
1510
# - Mid-circuit measurements with classical feedback
1511
# - Conditional quantum operations
1512
# - Real-time classical processing during quantum execution
1513
1514
experimental_features = {
1515
'mid_circuit_measurement': True,
1516
'classical_feedback': True,
1517
'conditional_gates': True,
1518
'real_time_processing': True
1519
}
1520
1521
return experimental_features
1522
1523
def explore_advanced_noise_modeling():
1524
"""Explore experimental advanced noise modeling capabilities."""
1525
1526
with EnableExperimentalCapability("advanced_noise"):
1527
# Access experimental noise modeling features
1528
experimental_noise_features = {
1529
'correlated_noise': 'Multi-qubit correlated noise channels',
1530
'time_dependent_noise': 'Time-varying noise parameters',
1531
'device_specific_noise': 'Hardware-calibrated noise models',
1532
'non_markovian_effects': 'Memory effects in noise evolution'
1533
}
1534
1535
return experimental_noise_features
1536
1537
def demonstrate_experimental_optimization():
1538
"""Demonstrate experimental optimization capabilities."""
1539
1540
with EnableExperimentalCapability("advanced_optimization"):
1541
1542
optimization_features = {
1543
'adaptive_shot_allocation': 'Dynamic shot count optimization',
1544
'circuit_cutting': 'Large circuit decomposition',
1545
'error_extrapolation': 'Advanced error extrapolation methods',
1546
'hardware_aware_compilation': 'Device-specific circuit optimization'
1547
}
1548
1549
# Example: Adaptive shot allocation
1550
def adaptive_shot_optimization(circuits: list, target_accuracy: float) -> dict:
1551
"""
1552
Experimental adaptive shot allocation for circuit collection.
1553
1554
Args:
1555
circuits: Circuits requiring optimization
1556
target_accuracy: Target measurement accuracy
1557
1558
Returns:
1559
dict: Optimized shot allocation strategy
1560
"""
1561
shot_allocation = {}
1562
1563
for i, circuit in enumerate(circuits):
1564
# Estimate required shots based on circuit properties
1565
estimated_variance = estimate_measurement_variance(circuit)
1566
required_shots = int(estimated_variance / (target_accuracy**2))
1567
1568
# Apply experimental optimization heuristics
1569
if circuit.depth > 50:
1570
required_shots *= 2 # Deeper circuits need more shots
1571
1572
if has_small_angle_rotations(circuit):
1573
required_shots *= 1.5 # Small angles need higher precision
1574
1575
shot_allocation[f'circuit_{i}'] = {
1576
'required_shots': required_shots,
1577
'estimated_variance': estimated_variance,
1578
'optimization_factor': required_shots / 1000 # Compared to baseline
1579
}
1580
1581
return shot_allocation
1582
1583
return {
1584
'features': optimization_features,
1585
'adaptive_optimizer': adaptive_shot_optimization
1586
}
1587
1588
def estimate_measurement_variance(circuit) -> float:
1589
"""Estimate measurement variance for shot optimization."""
1590
# Simplified variance estimation based on circuit properties
1591
base_variance = 0.25 # Maximum variance for uniform distribution
1592
1593
# Adjust based on circuit depth (deeper = more noise = higher variance)
1594
depth_factor = min(2.0, 1 + circuit.depth / 100)
1595
1596
# Adjust based on number of measured qubits
1597
qubit_factor = circuit.qubit_count / 10
1598
1599
return base_variance * depth_factor * qubit_factor
1600
1601
def has_small_angle_rotations(circuit) -> bool:
1602
"""Check if circuit contains small-angle rotations requiring high precision."""
1603
small_angle_threshold = 0.1 # radians
1604
1605
for instruction in circuit.instructions:
1606
gate = instruction.operator
1607
if hasattr(gate, 'angle'):
1608
if abs(gate.angle) < small_angle_threshold:
1609
return True
1610
1611
return False
1612
1613
def demonstrate_quantum_error_correction_experiments():
1614
"""Demonstrate experimental quantum error correction capabilities."""
1615
1616
with EnableExperimentalCapability("quantum_error_correction"):
1617
1618
qec_experiments = {
1619
'surface_codes': {
1620
'description': 'Surface code implementation and testing',
1621
'min_qubits': 17, # Smallest logical qubit
1622
'features': ['syndrome extraction', 'logical operations', 'error correction']
1623
},
1624
'color_codes': {
1625
'description': 'Color code quantum error correction',
1626
'min_qubits': 7, # 7-qubit color code
1627
'features': ['triangular lattice', 'transversal gates', 'fault tolerance']
1628
},
1629
'repetition_codes': {
1630
'description': 'Simple repetition codes for bit-flip errors',
1631
'min_qubits': 3, # 3-qubit repetition code
1632
'features': ['bit flip correction', 'syndrome measurement', 'majority voting']
1633
}
1634
}
1635
1636
def create_simple_qec_circuit(code_type: str = 'repetition') -> dict:
1637
"""Create simple quantum error correction demonstration circuit."""
1638
from braket.circuits import Circuit
1639
1640
if code_type == 'repetition':
1641
# 3-qubit bit-flip repetition code
1642
circuit = Circuit()
1643
1644
# Encode logical |0⟩ or |1⟩
1645
# |0⟩_L = |000⟩, |1⟩_L = |111⟩
1646
1647
# For |+⟩_L state: (|000⟩ + |111⟩)/√2
1648
circuit.h(0) # Create superposition on first qubit
1649
circuit.cnot(0, 1) # Entangle with second qubit
1650
circuit.cnot(0, 2) # Entangle with third qubit
1651
1652
# Syndrome measurement (detect single bit-flip errors)
1653
circuit.cnot(0, 3) # Ancilla 3: measures X₀X₁
1654
circuit.cnot(1, 3)
1655
1656
circuit.cnot(1, 4) # Ancilla 4: measures X₁X₂
1657
circuit.cnot(2, 4)
1658
1659
# Measure syndrome qubits
1660
circuit.measure([3, 4])
1661
1662
qec_info = {
1663
'circuit': circuit,
1664
'logical_qubits': 1,
1665
'physical_qubits': 3,
1666
'ancilla_qubits': 2,
1667
'correctable_errors': ['single bit flip'],
1668
'code_distance': 3
1669
}
1670
1671
return qec_info
1672
1673
return {
1674
'available_codes': qec_experiments,
1675
'circuit_generator': create_simple_qec_circuit
1676
}
1677
```
1678
1679
## Circuit Emulation and Compilation
1680
1681
### Emulator Infrastructure
1682
1683
```python { .api }
1684
from braket.emulation import Emulator, PassManager
1685
1686
class Emulator:
1687
"""Quantum circuit emulator with compilation passes."""
1688
1689
def __init__(
1690
self,
1691
pass_manager: PassManager = None,
1692
target_device = None
1693
):
1694
"""
1695
Initialize quantum circuit emulator.
1696
1697
Args:
1698
pass_manager: Compilation pass manager
1699
target_device: Target device for emulation properties
1700
"""
1701
self.pass_manager = pass_manager or PassManager()
1702
self.target_device = target_device
1703
1704
def emulate(
1705
self,
1706
circuit,
1707
shots: int = 1000,
1708
inputs: dict = None
1709
):
1710
"""
1711
Emulate quantum circuit with compilation.
1712
1713
Args:
1714
circuit: Quantum circuit to emulate
1715
shots: Number of measurement shots
1716
inputs: Input parameters for parameterized circuits
1717
1718
Returns:
1719
EmulationResult: Emulation results with compilation info
1720
"""
1721
pass
1722
1723
def add_pass(self, pass_instance) -> 'Emulator':
1724
"""
1725
Add compilation pass to emulator.
1726
1727
Args:
1728
pass_instance: Compilation pass to add
1729
1730
Returns:
1731
Emulator: Self for method chaining
1732
"""
1733
self.pass_manager.add_pass(pass_instance)
1734
return self
1735
1736
class PassManager:
1737
"""Compilation pass management for quantum circuits."""
1738
1739
def __init__(self):
1740
"""Initialize empty pass manager."""
1741
self.passes = []
1742
1743
def add_pass(self, pass_instance) -> 'PassManager':
1744
"""
1745
Add compilation pass.
1746
1747
Args:
1748
pass_instance: Pass to add
1749
1750
Returns:
1751
PassManager: Self for method chaining
1752
"""
1753
self.passes.append(pass_instance)
1754
return self
1755
1756
def run(self, circuit):
1757
"""
1758
Run all passes on circuit.
1759
1760
Args:
1761
circuit: Input quantum circuit
1762
1763
Returns:
1764
Circuit: Compiled quantum circuit
1765
"""
1766
compiled_circuit = circuit
1767
for pass_instance in self.passes:
1768
compiled_circuit = pass_instance.run(compiled_circuit)
1769
return compiled_circuit
1770
1771
# Emulation examples
1772
def create_optimized_emulator() -> Emulator:
1773
"""
1774
Create emulator with standard optimization passes.
1775
1776
Returns:
1777
Emulator: Configured emulator with optimization
1778
"""
1779
pass_manager = PassManager()
1780
1781
# Add standard optimization passes
1782
# Note: Actual pass implementations would be more complex
1783
# pass_manager.add_pass(GateCommutationPass())
1784
# pass_manager.add_pass(RedundantGateEliminationPass())
1785
# pass_manager.add_pass(CircuitDepthOptimizationPass())
1786
1787
emulator = Emulator(pass_manager=pass_manager)
1788
return emulator
1789
1790
def benchmark_emulation_performance(circuit) -> dict:
1791
"""
1792
Benchmark emulation vs direct simulation performance.
1793
1794
Args:
1795
circuit: Circuit to benchmark
1796
1797
Returns:
1798
dict: Performance comparison results
1799
"""
1800
import time
1801
from braket.devices import LocalSimulator
1802
1803
benchmark_results = {
1804
'circuit_info': {
1805
'qubit_count': circuit.qubit_count,
1806
'depth': circuit.depth,
1807
'gate_count': len(circuit.instructions)
1808
},
1809
'simulation': {},
1810
'emulation': {}
1811
}
1812
1813
# Direct simulation
1814
simulator = LocalSimulator()
1815
start_time = time.time()
1816
sim_task = simulator.run(circuit, shots=1000)
1817
sim_result = sim_task.result()
1818
sim_time = time.time() - start_time
1819
1820
benchmark_results['simulation'] = {
1821
'execution_time': sim_time,
1822
'compilation_time': 0,
1823
'result_counts': sim_result.measurement_counts
1824
}
1825
1826
# Emulation with compilation
1827
emulator = create_optimized_emulator()
1828
start_time = time.time()
1829
compile_start = time.time()
1830
compiled_circuit = emulator.pass_manager.run(circuit)
1831
compile_time = time.time() - compile_start
1832
1833
emu_result = emulator.emulate(compiled_circuit, shots=1000)
1834
total_emu_time = time.time() - start_time
1835
1836
benchmark_results['emulation'] = {
1837
'execution_time': total_emu_time,
1838
'compilation_time': compile_time,
1839
'optimizations_applied': len(emulator.pass_manager.passes),
1840
'compiled_circuit_depth': compiled_circuit.depth if hasattr(compiled_circuit, 'depth') else 'Unknown'
1841
}
1842
1843
# Performance analysis
1844
benchmark_results['analysis'] = {
1845
'speedup_factor': sim_time / total_emu_time if total_emu_time > 0 else float('inf'),
1846
'compilation_overhead': compile_time / total_emu_time if total_emu_time > 0 else 0,
1847
'depth_reduction': (circuit.depth - (compiled_circuit.depth if hasattr(compiled_circuit, 'depth') else circuit.depth)) / circuit.depth if circuit.depth > 0 else 0
1848
}
1849
1850
return benchmark_results
1851
```
1852
1853
## Experimental Capabilities
1854
1855
### Experimental Feature Access
1856
1857
```python { .api }
1858
from braket.experimental_capabilities import EnableExperimentalCapability
1859
1860
class EnableExperimentalCapability:
1861
"""Context manager for enabling experimental features."""
1862
1863
def __init__(self, capability_name: str):
1864
"""
1865
Initialize experimental capability context.
1866
1867
Args:
1868
capability_name: Name of experimental capability to enable
1869
"""
1870
self.capability_name = capability_name
1871
1872
def __enter__(self):
1873
"""Enter experimental capability context."""
1874
pass
1875
1876
def __exit__(self, exc_type, exc_val, exc_tb):
1877
"""Exit experimental capability context."""
1878
pass
1879
1880
# Experimental capabilities examples
1881
def access_experimental_features() -> dict:
1882
"""
1883
Demonstrate access to experimental quantum computing features.
1884
1885
Returns:
1886
dict: Available experimental capabilities
1887
"""
1888
experimental_features = {
1889
'available_capabilities': [
1890
'classical_control',
1891
'adaptive_circuits',
1892
'real_time_feedback',
1893
'advanced_error_correction',
1894
'novel_gate_sets'
1895
],
1896
'usage_examples': {},
1897
'stability_warnings': {
1898
'api_stability': 'Experimental APIs may change without notice',
1899
'result_reliability': 'Results may vary between SDK versions',
1900
'production_readiness': 'Not recommended for production use'
1901
}
1902
}
1903
1904
# Classical control example (IQM-specific)
1905
def classical_control_example():
1906
"""Demonstrate classical control features."""
1907
try:
1908
with EnableExperimentalCapability('classical_control'):
1909
from braket.experimental_capabilities.iqm import classical_control
1910
1911
# This would enable classical control features
1912
# Actual implementation depends on device support
1913
control_config = {
1914
'conditional_gates': True,
1915
'real_time_feedback': True,
1916
'adaptive_measurements': True
1917
}
1918
1919
return {
1920
'status': 'enabled',
1921
'configuration': control_config,
1922
'supported_devices': ['IQM Adonis', 'IQM Apollo']
1923
}
1924
except Exception as e:
1925
return {
1926
'status': 'unavailable',
1927
'error': str(e),
1928
'reason': 'Experimental feature not available in current environment'
1929
}
1930
1931
experimental_features['usage_examples']['classical_control'] = classical_control_example()
1932
1933
# Advanced error correction
1934
def advanced_error_correction_example():
1935
"""Demonstrate advanced error correction features."""
1936
with EnableExperimentalCapability('advanced_error_correction'):
1937
# Experimental error correction protocols
1938
advanced_qec = {
1939
'surface_codes': {
1940
'supported': True,
1941
'min_qubits': 17, # Smallest surface code
1942
'features': ['arbitrary distance', 'custom boundary conditions']
1943
},
1944
'color_codes': {
1945
'supported': True,
1946
'min_qubits': 15, # Color code triangle
1947
'features': ['higher threshold', 'transversal gates']
1948
},
1949
'topological_codes': {
1950
'supported': False,
1951
'reason': 'Requires specific hardware topology'
1952
}
1953
}
1954
1955
return advanced_qec
1956
1957
experimental_features['usage_examples']['advanced_error_correction'] = advanced_error_correction_example()
1958
1959
return experimental_features
1960
1961
def create_experimental_workflow() -> dict:
1962
"""
1963
Create experimental quantum computing workflow.
1964
1965
Returns:
1966
dict: Experimental workflow configuration
1967
"""
1968
workflow = {
1969
'stages': [
1970
'feature_detection',
1971
'capability_enablement',
1972
'experimental_execution',
1973
'result_validation',
1974
'fallback_handling'
1975
],
1976
'implementation': {}
1977
}
1978
1979
def feature_detection_stage():
1980
"""Detect available experimental features."""
1981
available_features = []
1982
1983
# Check for classical control
1984
try:
1985
with EnableExperimentalCapability('classical_control'):
1986
available_features.append('classical_control')
1987
except:
1988
pass
1989
1990
# Check for advanced error correction
1991
try:
1992
with EnableExperimentalCapability('advanced_error_correction'):
1993
available_features.append('advanced_error_correction')
1994
except:
1995
pass
1996
1997
return {
1998
'detected_features': available_features,
1999
'detection_method': 'capability_probing',
2000
'confidence': 'high' if available_features else 'low'
2001
}
2002
2003
def experimental_execution_stage(circuit, experimental_config: dict):
2004
"""Execute circuit with experimental features."""
2005
execution_plan = {
2006
'base_circuit': circuit,
2007
'experimental_modifications': [],
2008
'fallback_strategy': 'standard_execution'
2009
}
2010
2011
# Apply experimental modifications based on config
2012
if 'classical_control' in experimental_config.get('enabled_features', []):
2013
execution_plan['experimental_modifications'].append({
2014
'type': 'classical_control',
2015
'description': 'Enable conditional gate execution',
2016
'impact': 'Allows adaptive circuit behavior'
2017
})
2018
2019
if 'advanced_error_correction' in experimental_config.get('enabled_features', []):
2020
execution_plan['experimental_modifications'].append({
2021
'type': 'advanced_qec',
2022
'description': 'Apply experimental error correction',
2023
'impact': 'Improved fidelity with overhead'
2024
})
2025
2026
return execution_plan
2027
2028
workflow['implementation'] = {
2029
'feature_detection': feature_detection_stage,
2030
'experimental_execution': experimental_execution_stage
2031
}
2032
2033
return workflow
2034
```
2035
2036
This comprehensive advanced features documentation covers all the sophisticated quantum computing capabilities provided by the Amazon Braket SDK, including analog Hamiltonian simulation, quantum annealing, pulse-level control, error mitigation techniques, circuit emulation infrastructure, and experimental features for cutting-edge quantum computing research and development.