Quantum Information Utilities

# Quantum information
from braket.quantum_information import PauliString

# Circuit registers and qubits (from circuits module)
from braket.circuits import Qubit, QubitInput, QubitSet, QubitSetInput  

# Parametric circuits and free parameters (from circuits module)
from braket.circuits import FreeParameter, FreeParameterExpression, Parameterizable

# Program sets for batch execution
from braket.program_sets import CircuitBinding, ParameterSets, ParameterSetsLike, ProgramSet

# Timing data structures
from braket.timings import TimeSeries, TimeSeriesItem

from braket.quantum_information import PauliString
import numpy as np

class PauliString:
    """Representation and manipulation of Pauli strings."""
    
    def __init__(self, pauli_dict: dict = None):
        """
        Initialize Pauli string from dictionary representation.
        
        Args:
            pauli_dict: Dictionary mapping qubit indices to Pauli operators
                       {'X': [0, 2], 'Y': [1], 'Z': [3]} represents X₀Y₁X₂Z₃
        """
        self.pauli_dict = pauli_dict or {}
    
    @classmethod
    def from_string(cls, pauli_string: str) -> 'PauliString':
        """
        Create PauliString from string representation.
        
        Args:
            pauli_string: String like 'XIYIZ' or 'X0 Y1 Z2'
            
        Returns:
            PauliString: Parsed Pauli string
        """
        pass
    
    def __str__(self) -> str:
        """
        String representation of Pauli string.
        
        Returns:
            str: Human-readable Pauli string
        """
        pass
    
    def __mul__(self, other) -> 'PauliString':
        """
        Multiply two Pauli strings.
        
        Args:
            other: Another PauliString or scalar
            
        Returns:
            PauliString: Product of Pauli strings
        """
        pass
    
    def __add__(self, other) -> 'PauliSum':
        """
        Add Pauli strings to create Pauli sum (Hamiltonian).
        
        Args:
            other: Another PauliString
            
        Returns:
            PauliSum: Sum of Pauli strings
        """
        pass
    
    def commutes_with(self, other: 'PauliString') -> bool:
        """
        Check if this Pauli string commutes with another.
        
        Args:
            other: Another Pauli string
            
        Returns:
            bool: True if strings commute
        """
        pass
    
    def expectation_value(self, state_vector: np.ndarray) -> complex:
        """
        Compute expectation value of Pauli string in given state.
        
        Args:
            state_vector: Quantum state vector
            
        Returns:
            complex: Expectation value ⟨ψ|P|ψ⟩
        """
        pass
    
    def to_matrix(self) -> np.ndarray:
        """
        Convert Pauli string to matrix representation.
        
        Returns:
            np.ndarray: Matrix representation of Pauli string
        """
        pass
    
    @property
    def qubits(self) -> list[int]:
        """Get list of qubits involved in Pauli string."""
        pass
    
    @property
    def weight(self) -> int:
        """Get weight (number of non-identity Paulis)."""
        pass

# Pauli string examples
def create_pauli_hamiltonians() -> dict:
    """
    Create common Pauli string Hamiltonians for quantum algorithms.
    
    Returns:
        dict: Collection of important Hamiltonians
    """
    hamiltonians = {}
    
    # Ising model Hamiltonian: H = -J∑ZᵢZⱼ - h∑Xᵢ
    # 1D chain with 4 qubits
    ising_terms = []
    J = 1.0  # Coupling strength
    h = 0.5  # Transverse field
    
    # ZZ interactions
    for i in range(3):  # 0-1, 1-2, 2-3 pairs
        zz_string = PauliString({'Z': [i, i+1]})
        ising_terms.append((-J, zz_string))
    
    # X transverse field
    for i in range(4):
        x_string = PauliString({'X': [i]})
        ising_terms.append((-h, x_string))
    
    hamiltonians['ising_1d'] = ising_terms
    
    # Heisenberg model: H = J∑(XᵢXⱼ + YᵢYⱼ + ZᵢZⱼ)
    heisenberg_terms = []
    J_heis = 1.0
    
    for i in range(3):
        # XX interaction
        xx_string = PauliString({'X': [i, i+1]})
        heisenberg_terms.append((J_heis, xx_string))
        
        # YY interaction
        yy_string = PauliString({'Y': [i, i+1]})
        heisenberg_terms.append((J_heis, yy_string))
        
        # ZZ interaction
        zz_string = PauliString({'Z': [i, i+1]})
        heisenberg_terms.append((J_heis, zz_string))
    
    hamiltonians['heisenberg'] = heisenberg_terms
    
    # H₂ molecule Hamiltonian (simplified)
    h2_terms = [
        (-1.0523732, PauliString({})),  # Identity term
        (0.39793742, PauliString({'Z': [0]})),  # Z₀
        (-0.39793742, PauliString({'Z': [1]})),  # Z₁
        (-0.01128010, PauliString({'Z': [0, 1]})),  # Z₀Z₁
        (0.18093119, PauliString({'X': [0, 1]}))   # X₀X₁
    ]
    
    hamiltonians['h2_molecule'] = h2_terms
    
    return hamiltonians

def analyze_pauli_string_properties(pauli_string: PauliString) -> dict:
    """
    Analyze mathematical properties of Pauli string.
    
    Args:
        pauli_string: Pauli string to analyze
        
    Returns:
        dict: Comprehensive property analysis
    """
    analysis = {
        'basic_properties': {
            'weight': pauli_string.weight,
            'qubits': pauli_string.qubits,
            'qubit_count': len(pauli_string.qubits),
            'string_representation': str(pauli_string)
        },
        'algebraic_properties': {
            'is_hermitian': True,  # All Pauli strings are Hermitian
            'eigenvalues': [-1, 1],  # All Pauli operators have eigenvalues ±1
            'trace': 0 if pauli_string.weight > 0 else 2**len(pauli_string.qubits)
        },
        'computational_complexity': {
            'matrix_size': 2**(2 * len(pauli_string.qubits)),
            'measurement_complexity': 'O(1)',  # Single measurement setting
            'classical_simulation': 'Exponential' if len(pauli_string.qubits) > 20 else 'Feasible'
        }
    }
    
    return analysis

def find_commuting_pauli_groups(pauli_strings: list[PauliString]) -> list[list[PauliString]]:
    """
    Group Pauli strings by commutation relations.
    
    Args:
        pauli_strings: List of Pauli strings to group
        
    Returns:
        list[list[PauliString]]: Groups of mutually commuting Pauli strings
    """
    groups = []
    unassigned = pauli_strings.copy()
    
    while unassigned:
        # Start new group with first unassigned string
        current_group = [unassigned.pop(0)]
        
        # Find all strings that commute with all strings in current group
        i = 0
        while i < len(unassigned):
            string = unassigned[i]
            
            # Check if string commutes with all in current group
            if all(string.commutes_with(group_string) for group_string in current_group):
                current_group.append(unassigned.pop(i))
            else:
                i += 1
        
        groups.append(current_group)
    
    return groups

def optimize_pauli_measurement_grouping(pauli_strings: list[PauliString]) -> dict:
    """
    Optimize measurement grouping for Pauli string expectation values.
    
    Args:
        pauli_strings: Pauli strings requiring expectation value measurement
        
    Returns:
        dict: Optimized measurement strategy
    """
    # Group by commutation relations
    commuting_groups = find_commuting_pauli_groups(pauli_strings)
    
    optimization = {
        'original_measurements': len(pauli_strings),
        'optimized_measurements': len(commuting_groups),
        'reduction_factor': len(pauli_strings) / len(commuting_groups),
        'measurement_groups': [],
        'measurement_circuits': []
    }
    
    for i, group in enumerate(commuting_groups):
        group_info = {
            'group_id': i,
            'pauli_strings': [str(ps) for ps in group],
            'measurement_basis': determine_measurement_basis(group),
            'simultaneous_measurements': len(group)
        }
        optimization['measurement_groups'].append(group_info)
        
        # Create measurement circuit for this group
        measurement_circuit = create_pauli_measurement_circuit(group)
        optimization['measurement_circuits'].append(measurement_circuit)
    
    return optimization

def determine_measurement_basis(pauli_group: list[PauliString]) -> dict:
    """
    Determine optimal measurement basis for commuting Pauli group.
    
    Args:
        pauli_group: Group of commuting Pauli strings
        
    Returns:
        dict: Measurement basis transformations needed
    """
    # Analyze required basis rotations for each qubit
    qubit_basis = {}
    
    for pauli_string in pauli_group:
        for pauli_op, qubits in pauli_string.pauli_dict.items():
            for qubit in qubits:
                if qubit not in qubit_basis:
                    qubit_basis[qubit] = pauli_op
                elif qubit_basis[qubit] != pauli_op:
                    # Conflict - this should not happen in commuting group
                    raise ValueError(f"Non-commuting Pauli operations on qubit {qubit}")
    
    return qubit_basis

def create_pauli_measurement_circuit(pauli_group: list[PauliString]):
    """
    Create quantum circuit for measuring commuting Pauli group.
    
    Args:
        pauli_group: Commuting Pauli strings to measure
        
    Returns:
        Circuit: Quantum circuit with appropriate basis rotations
    """
    from braket.circuits import Circuit
    from braket.circuits.gates import H, S, Si
    
    circuit = Circuit()
    measurement_basis = determine_measurement_basis(pauli_group)
    
    # Add basis rotation gates
    for qubit, pauli_op in measurement_basis.items():
        if pauli_op == 'X':
            circuit.h(qubit)  # Rotate to X basis
        elif pauli_op == 'Y':
            circuit.si(qubit)  # S† gate
            circuit.h(qubit)   # Then Hadamard for Y basis
        # Z basis needs no rotation
    
    # Add measurements
    measured_qubits = list(measurement_basis.keys())
    circuit.measure(measured_qubits)
    
    return circuit

from braket.circuits import Qubit, QubitInput, QubitSet, QubitSetInput

class Qubit:
    """Individual qubit representation."""
    
    def __init__(self, index: int):
        """
        Initialize qubit with index.
        
        Args:
            index: Qubit index identifier
        """
        self.index = index
    
    def __eq__(self, other) -> bool:
        """Check equality with another qubit."""
        return isinstance(other, Qubit) and self.index == other.index
    
    def __hash__(self) -> int:
        """Hash for use in sets and dictionaries."""
        return hash(self.index)
    
    def __str__(self) -> str:
        """String representation."""
        return f"Qubit({self.index})"

class QubitSet:
    """Set of qubits with set operations."""
    
    def __init__(self, qubits: QubitSetInput = None):
        """
        Initialize qubit set.
        
        Args:
            qubits: Initial qubits (int, Qubit, list, or range)
        """
        self._qubits = set()
        if qubits is not None:
            self.add(qubits)
    
    def add(self, qubits: QubitSetInput) -> 'QubitSet':
        """
        Add qubits to set.
        
        Args:
            qubits: Qubits to add
            
        Returns:
            QubitSet: Self for method chaining
        """
        pass
    
    def union(self, other: 'QubitSet') -> 'QubitSet':
        """
        Union with another qubit set.
        
        Args:
            other: Another qubit set
            
        Returns:
            QubitSet: Union of qubit sets
        """
        pass
    
    def intersection(self, other: 'QubitSet') -> 'QubitSet':
        """
        Intersection with another qubit set.
        
        Args:
            other: Another qubit set
            
        Returns:
            QubitSet: Intersection of qubit sets
        """
        pass
    
    def __len__(self) -> int:
        """Number of qubits in set."""
        return len(self._qubits)
    
    def __iter__(self):
        """Iterate over qubits in set."""
        return iter(sorted(self._qubits, key=lambda q: q.index))
    
    def __contains__(self, qubit: QubitInput) -> bool:
        """Check if qubit is in set."""
        pass

# Register management examples
def create_quantum_register_layout(n_qubits: int, connectivity: str = 'all_to_all') -> dict:
    """
    Create quantum register layout with connectivity constraints.
    
    Args:
        n_qubits: Number of qubits in register
        connectivity: Connectivity type ('all_to_all', 'linear', 'grid')
        
    Returns:
        dict: Register layout with connectivity information
    """
    qubits = QubitSet(range(n_qubits))
    
    layout = {
        'qubits': list(qubits),
        'qubit_count': len(qubits),
        'connectivity_type': connectivity,
        'adjacency_list': {},
        'coupling_map': []
    }
    
    # Generate connectivity based on type
    if connectivity == 'all_to_all':
        for i in range(n_qubits):
            layout['adjacency_list'][i] = list(range(n_qubits))
            layout['adjacency_list'][i].remove(i)  # Remove self
            
            for j in range(i+1, n_qubits):
                layout['coupling_map'].append((i, j))
    
    elif connectivity == 'linear':
        for i in range(n_qubits):
            neighbors = []
            if i > 0:
                neighbors.append(i-1)
            if i < n_qubits - 1:
                neighbors.append(i+1)
            layout['adjacency_list'][i] = neighbors
            
            if i < n_qubits - 1:
                layout['coupling_map'].append((i, i+1))
    
    elif connectivity == 'grid':
        # Assume square grid for simplicity
        grid_size = int(n_qubits ** 0.5)
        if grid_size * grid_size != n_qubits:
            raise ValueError(f"Grid connectivity requires perfect square number of qubits, got {n_qubits}")
        
        for i in range(n_qubits):
            row = i // grid_size
            col = i % grid_size
            neighbors = []
            
            # Add neighbors (up, down, left, right)
            if row > 0:  # Up
                neighbors.append((row-1) * grid_size + col)
            if row < grid_size - 1:  # Down
                neighbors.append((row+1) * grid_size + col)
            if col > 0:  # Left
                neighbors.append(row * grid_size + (col-1))
            if col < grid_size - 1:  # Right
                neighbors.append(row * grid_size + (col+1))
            
            layout['adjacency_list'][i] = neighbors
            
            # Add coupling map entries
            for neighbor in neighbors:
                if i < neighbor:  # Avoid duplicates
                    layout['coupling_map'].append((i, neighbor))
    
    return layout

def optimize_qubit_allocation(circuit, device_layout: dict) -> dict:
    """
    Optimize qubit allocation for circuit on device with limited connectivity.
    
    Args:
        circuit: Quantum circuit requiring qubit allocation
        device_layout: Device connectivity layout
        
    Returns:
        dict: Optimized qubit mapping and routing information
    """
    # Extract two-qubit gates from circuit
    two_qubit_operations = []
    for instruction in circuit.instructions:
        if len(instruction.target) == 2:
            two_qubit_operations.append(tuple(instruction.target))
    
    # Build circuit connectivity graph
    circuit_connectivity = {}
    for qubit in range(circuit.qubit_count):
        circuit_connectivity[qubit] = []
    
    for q1, q2 in two_qubit_operations:
        if q2 not in circuit_connectivity[q1]:
            circuit_connectivity[q1].append(q2)
        if q1 not in circuit_connectivity[q2]:
            circuit_connectivity[q2].append(q1)
    
    # Simple greedy mapping (more sophisticated algorithms exist)
    qubit_mapping = {}
    used_physical_qubits = set()
    
    # Start with most connected circuit qubit
    start_qubit = max(circuit_connectivity.keys(), key=lambda q: len(circuit_connectivity[q]))
    
    # Map to most connected device qubit
    start_physical = max(device_layout['adjacency_list'].keys(), 
                        key=lambda q: len(device_layout['adjacency_list'][q]))
    
    qubit_mapping[start_qubit] = start_physical
    used_physical_qubits.add(start_physical)
    
    # Iteratively map remaining qubits
    remaining_circuit_qubits = set(range(circuit.qubit_count)) - {start_qubit}
    
    while remaining_circuit_qubits:
        best_score = -1
        best_mapping = None
        
        for circuit_qubit in remaining_circuit_qubits:
            for physical_qubit in device_layout['adjacency_list'].keys():
                if physical_qubit in used_physical_qubits:
                    continue
                
                # Score based on adjacency to already mapped qubits
                score = 0
                for neighbor in circuit_connectivity[circuit_qubit]:
                    if neighbor in qubit_mapping:
                        mapped_neighbor = qubit_mapping[neighbor]
                        if physical_qubit in device_layout['adjacency_list'][mapped_neighbor]:
                            score += 1
                
                if score > best_score:
                    best_score = score
                    best_mapping = (circuit_qubit, physical_qubit)
        
        if best_mapping:
            circuit_qubit, physical_qubit = best_mapping
            qubit_mapping[circuit_qubit] = physical_qubit
            used_physical_qubits.add(physical_qubit)
            remaining_circuit_qubits.remove(circuit_qubit)
        else:
            # Fallback: use any available physical qubit
            circuit_qubit = remaining_circuit_qubits.pop()
            for physical_qubit in device_layout['adjacency_list'].keys():
                if physical_qubit not in used_physical_qubits:
                    qubit_mapping[circuit_qubit] = physical_qubit
                    used_physical_qubits.add(physical_qubit)
                    break
    
    # Calculate routing overhead
    swap_gates_needed = 0
    for q1, q2 in two_qubit_operations:
        p1, p2 = qubit_mapping[q1], qubit_mapping[q2]
        if p2 not in device_layout['adjacency_list'][p1]:
            swap_gates_needed += 1  # Simplified - actual routing more complex
    
    return {
        'qubit_mapping': qubit_mapping,
        'routing_overhead': swap_gates_needed,
        'mapping_efficiency': (len(two_qubit_operations) - swap_gates_needed) / max(len(two_qubit_operations), 1),
        'physical_qubits_used': len(used_physical_qubits)
    }

from braket.circuits import FreeParameter, FreeParameterExpression, Parameterizable

class FreeParameter(Parameterizable):
    """Free parameter for parameterized quantum circuits."""
    
    def __init__(self, name: str):
        """
        Initialize free parameter.
        
        Args:
            name: Parameter name identifier
        """
        self.name = name
    
    def __str__(self) -> str:
        """String representation."""
        return self.name
    
    def __add__(self, other) -> 'FreeParameterExpression':
        """Addition with another parameter or number."""
        return FreeParameterExpression(f"({self.name} + {other})")
    
    def __sub__(self, other) -> 'FreeParameterExpression':
        """Subtraction with another parameter or number."""
        return FreeParameterExpression(f"({self.name} - {other})")
    
    def __mul__(self, other) -> 'FreeParameterExpression':
        """Multiplication with another parameter or number."""
        return FreeParameterExpression(f"({self.name} * {other})")
    
    def __truediv__(self, other) -> 'FreeParameterExpression':
        """Division with another parameter or number."""
        return FreeParameterExpression(f"({self.name} / {other})")

class FreeParameterExpression(Parameterizable):
    """Mathematical expressions with free parameters."""
    
    def __init__(self, expression: str):
        """
        Initialize parameter expression.
        
        Args:
            expression: Mathematical expression string
        """
        self.expression = expression
    
    def substitute(self, substitutions: dict) -> float:
        """
        Substitute parameter values and evaluate expression.
        
        Args:
            substitutions: Dictionary mapping parameter names to values
            
        Returns:
            float: Evaluated expression value
        """
        pass
    
    def get_free_parameters(self) -> set[str]:
        """
        Get all free parameters in expression.
        
        Returns:
            set[str]: Set of parameter names
        """
        pass
    
    def __add__(self, other) -> 'FreeParameterExpression':
        """Addition with another expression or number."""
        return FreeParameterExpression(f"({self.expression} + {other})")
    
    def __mul__(self, other) -> 'FreeParameterExpression':
        """Multiplication with another expression or number."""
        return FreeParameterExpression(f"({self.expression} * {other})")

# Parametric computation examples
def create_parametric_ansatz(n_qubits: int, n_layers: int) -> dict:
    """
    Create parametric quantum ansatz with systematic parameter naming.
    
    Args:
        n_qubits: Number of qubits in ansatz
        n_layers: Number of parametric layers
        
    Returns:
        dict: Parametric ansatz information and parameter structure
    """
    from braket.circuits import Circuit
    from braket.circuits.gates import Ry, Rz, CNot
    
    circuit = Circuit()
    parameters = {}
    parameter_count = 0
    
    # Initialize with Hadamard gates
    for qubit in range(n_qubits):
        circuit.h(qubit)
    
    # Parametric layers
    for layer in range(n_layers):
        # Single-qubit rotations
        for qubit in range(n_qubits):
            # Y rotation parameter
            theta_param = FreeParameter(f"theta_{layer}_{qubit}")
            parameters[f"theta_{layer}_{qubit}"] = theta_param
            circuit.ry(qubit, theta_param)
            parameter_count += 1
            
            # Z rotation parameter
            phi_param = FreeParameter(f"phi_{layer}_{qubit}")
            parameters[f"phi_{layer}_{qubit}"] = phi_param
            circuit.rz(qubit, phi_param)
            parameter_count += 1
        
        # Entangling gates
        for qubit in range(n_qubits - 1):
            circuit.cnot(qubit, (qubit + 1) % n_qubits)
    
    ansatz_info = {
        'circuit': circuit,
        'parameters': parameters,
        'parameter_count': parameter_count,
        'parameter_names': list(parameters.keys()),
        'layers': n_layers,
        'qubits': n_qubits,
        'structure': 'Hardware-efficient ansatz'
    }
    
    return ansatz_info

def optimize_parameter_expressions(expressions: list[FreeParameterExpression]) -> dict:
    """
    Optimize parameter expressions for efficient evaluation.
    
    Args:
        expressions: List of parameter expressions to optimize
        
    Returns:
        dict: Optimization analysis and recommendations
    """
    optimization = {
        'original_expressions': [expr.expression for expr in expressions],
        'common_subexpressions': {},
        'parameter_dependencies': {},
        'evaluation_order': [],
        'computational_complexity': {}
    }
    
    # Find common subexpressions
    subexpr_count = {}
    for expr in expressions:
        # Simplified parsing - would need proper expression tree analysis
        subexprs = expr.expression.split()
        for subexpr in subexprs:
            if subexpr.startswith('(') and ')' in subexpr:
                subexpr_count[subexpr] = subexpr_count.get(subexpr, 0) + 1
    
    # Identify reusable subexpressions
    optimization['common_subexpressions'] = {
        subexpr: count for subexpr, count in subexpr_count.items() if count > 1
    }
    
    # Analyze parameter dependencies
    all_parameters = set()
    for expr in expressions:
        params = expr.get_free_parameters()
        all_parameters.update(params)
        optimization['parameter_dependencies'][expr.expression] = list(params)
    
    optimization['total_unique_parameters'] = len(all_parameters)
    
    return optimization

def generate_parameter_sweep_ranges(ansatz_info: dict, sweep_type: str = 'random') -> dict:
    """
    Generate parameter value ranges for ansatz optimization.
    
    Args:
        ansatz_info: Ansatz information from create_parametric_ansatz
        sweep_type: Type of parameter sweep ('random', 'grid', 'adaptive')
        
    Returns:
        dict: Parameter sweep configuration
    """
    import numpy as np
    
    parameter_names = ansatz_info['parameter_names']
    n_params = len(parameter_names)
    
    sweep_config = {
        'sweep_type': sweep_type,
        'parameter_count': n_params,
        'parameter_ranges': {},
        'suggested_values': {},
        'optimization_hints': []
    }
    
    if sweep_type == 'random':
        # Random sampling in [0, 2π] for rotation angles
        for param_name in parameter_names:
            sweep_config['parameter_ranges'][param_name] = (0, 2*np.pi)
            sweep_config['suggested_values'][param_name] = np.random.random(10) * 2 * np.pi
        
        sweep_config['optimization_hints'] = [
            "Use random search for initial exploration",
            "Consider Bayesian optimization for refinement",
            f"Total parameter space size: {n_params} dimensions"
        ]
    
    elif sweep_type == 'grid':
        # Grid search with reasonable resolution
        points_per_dim = max(3, int(10**(1/max(n_params, 1))))  # Adaptive grid resolution
        
        for param_name in parameter_names:
            sweep_config['parameter_ranges'][param_name] = (0, 2*np.pi)
            sweep_config['suggested_values'][param_name] = np.linspace(0, 2*np.pi, points_per_dim)
        
        total_evaluations = points_per_dim ** n_params
        sweep_config['optimization_hints'] = [
            f"Grid search with {points_per_dim} points per parameter",
            f"Total evaluations needed: {total_evaluations}",
            "Consider reducing parameters if grid is too large"
        ]
    
    elif sweep_type == 'adaptive':
        # Adaptive ranges based on parameter sensitivity
        for param_name in parameter_names:
            if 'theta' in param_name:  # Y rotations - typically more sensitive
                sweep_config['parameter_ranges'][param_name] = (0, np.pi)
            else:  # Z rotations - full range
                sweep_config['parameter_ranges'][param_name] = (0, 2*np.pi)
            
            # Initial sampling points
            sweep_config['suggested_values'][param_name] = np.random.random(5) * sweep_config['parameter_ranges'][param_name][1]
        
        sweep_config['optimization_hints'] = [
            "Adaptive sampling based on parameter types",
            "Y rotations limited to [0, π] for efficiency",
            "Use gradient-based methods when possible"
        ]
    
    return sweep_config

from braket.timings import TimeSeries, TimeSeriesItem

class TimeSeriesItem:
    """Individual time series data item."""
    
    def __init__(self, time: float, value: float):
        """
        Initialize time series item.
        
        Args:
            time: Time point
            value: Value at time point
        """
        self.time = time
        self.value = value

class TimeSeries:
    """Time series data representation."""
    
    def __init__(self, values: list[TimeSeriesItem] = None):
        """
        Initialize time series.
        
        Args:
            values: List of time series items
        """
        self.values = values or []
    
    def add_point(self, time: float, value: float) -> 'TimeSeries':
        """
        Add data point to time series.
        
        Args:
            time: Time coordinate
            value: Value at time
            
        Returns:
            TimeSeries: Self for method chaining
        """
        self.values.append(TimeSeriesItem(time, value))
        return self
    
    def interpolate(self, time: float) -> float:
        """
        Interpolate value at given time.
        
        Args:
            time: Time point for interpolation
            
        Returns:
            float: Interpolated value
        """
        pass
    
    def resample(self, new_times: list[float]) -> 'TimeSeries':
        """
        Resample time series at new time points.
        
        Args:
            new_times: New time sampling points
            
        Returns:
            TimeSeries: Resampled time series
        """
        pass

### Program Set Management

```python { .api }
from braket.program_sets import CircuitBinding, ParameterSets, ProgramSet

class CircuitBinding:
    """Circuit parameter binding for program sets."""
    
    def __init__(self, circuit, parameter_values: dict):
        """
        Initialize circuit binding.
        
        Args:
            circuit: Parameterized circuit
            parameter_values: Parameter value assignments
        """
        self.circuit = circuit
        self.parameter_values = parameter_values
    
    def bind_parameters(self):
        """
        Create bound circuit with parameter values substituted.
        
        Returns:
            Circuit: Circuit with parameters bound
        """
        pass

class ParameterSets:
    """Parameter set management for optimization."""
    
    def __init__(self, parameter_names: list[str]):
        """
        Initialize parameter sets.
        
        Args:
            parameter_names: Names of parameters to manage
        """
        self.parameter_names = parameter_names
        self.parameter_sets = []
    
    def add_parameter_set(self, values: list[float]) -> 'ParameterSets':
        """
        Add parameter value set.
        
        Args:
            values: Parameter values in order of parameter_names
            
        Returns:
            ParameterSets: Self for method chaining
        """
        if len(values) != len(self.parameter_names):
            raise ValueError(f"Expected {len(self.parameter_names)} values, got {len(values)}")
        
        param_dict = dict(zip(self.parameter_names, values))
        self.parameter_sets.append(param_dict)
        return self
    
    def generate_grid(self, ranges: dict, resolution: int = 10) -> 'ParameterSets':
        """
        Generate grid of parameter values.
        
        Args:
            ranges: Parameter ranges {param_name: (min, max)}
            resolution: Grid resolution per parameter
            
        Returns:
            ParameterSets: Self with grid parameter sets
        """
        import itertools
        import numpy as np
        
        grid_values = []
        for param_name in self.parameter_names:
            if param_name in ranges:
                min_val, max_val = ranges[param_name]
                param_grid = np.linspace(min_val, max_val, resolution)
                grid_values.append(param_grid)
            else:
                grid_values.append([0.0])  # Default value
        
        # Generate all combinations
        for combination in itertools.product(*grid_values):
            self.add_parameter_set(list(combination))
        
        return self

class ProgramSet:
    """Collection of parameterized programs for batch execution."""
    
    def __init__(self, base_program, parameter_sets: ParameterSets):
        """
        Initialize program set.
        
        Args:
            base_program: Base parameterized program
            parameter_sets: Parameter sets for batch execution
        """
        self.base_program = base_program
        self.parameter_sets = parameter_sets
    
    def create_bindings(self) -> list[CircuitBinding]:
        """
        Create circuit bindings for all parameter sets.
        
        Returns:
            list[CircuitBinding]: Bound circuits for execution
        """
        bindings = []
        for param_set in self.parameter_sets.parameter_sets:
            binding = CircuitBinding(self.base_program, param_set)
            bindings.append(binding)
        return bindings
    
    def execute_all(self, device, shots: int = 1000) -> list:
        """
        Execute all programs in set on device.
        
        Args:
            device: Quantum device for execution
            shots: Number of shots per program
            
        Returns:
            list: Results from all program executions
        """
        bindings = self.create_bindings()
        bound_circuits = [binding.bind_parameters() for binding in bindings]
        
        # Execute batch
        batch_task = device.run_batch(bound_circuits, shots=shots)
        return batch_task.results()

# Program set example
def create_optimization_program_set(ansatz_info: dict, optimization_config: dict) -> ProgramSet:
    """
    Create program set for variational quantum optimization.
    
    Args:
        ansatz_info: Ansatz circuit information
        optimization_config: Optimization configuration
        
    Returns:
        ProgramSet: Program set for batch optimization
    """
    base_circuit = ansatz_info['circuit']
    parameter_names = ansatz_info['parameter_names']
    
    # Create parameter sets based on optimization strategy
    parameter_sets = ParameterSets(parameter_names)
    
    if optimization_config.get('method') == 'grid_search':
        ranges = optimization_config.get('parameter_ranges', {})
        resolution = optimization_config.get('resolution', 5)
        parameter_sets.generate_grid(ranges, resolution)
        
    elif optimization_config.get('method') == 'random_search':
        import numpy as np
        n_samples = optimization_config.get('n_samples', 100)
        
        for _ in range(n_samples):
            random_values = []
            for param_name in parameter_names:
                if param_name in optimization_config.get('parameter_ranges', {}):
                    min_val, max_val = optimization_config['parameter_ranges'][param_name]
                    random_val = np.random.uniform(min_val, max_val)
                else:
                    random_val = np.random.uniform(0, 2*np.pi)
                random_values.append(random_val)
            
            parameter_sets.add_parameter_set(random_values)
    
    return ProgramSet(base_circuit, parameter_sets)