Python Simulator Backend

The Python Simulator backend provides a pure Python implementation of quantum circuit simulation that doesn't require external quantum computing libraries. This backend is ideal for testing, educational purposes, and as a fallback when other quantum backends are unavailable.

Overview

The Simulator backend in SuperQuantX offers:

• Pure Python Implementation: No external quantum computing dependencies
• Educational Value: Clear, readable quantum simulation code
• Rapid Development: Fast prototyping without backend setup
• Statevector Access: Direct access to quantum state amplitudes
• Feature Maps: Built-in quantum machine learning encoding circuits
• Variational Ansätze: Common parameterized circuit templates
• Gradient Support: Numerical differentiation for optimization

Performance Considerations

This backend is optimized for clarity and simplicity rather than performance. For larger quantum circuits, consider using specialized quantum simulators.

Installation

The Simulator backend is included with SuperQuantX and requires no additional dependencies:

# Install SuperQuantX (simulator included)
pip install superquantx

Verify Installation

import superquantx as sqx

# Initialize simulator backend
backend = sqx.get_backend('simulator')
print(f"Simulator backend loaded: {backend.is_available()}")
print(f"Max qubits: {backend.max_qubits}")

Quick Start

Basic Quantum Circuit

import superquantx as sqx
import numpy as np

# Initialize simulator backend
backend = sqx.get_backend('simulator', max_qubits=5, shots=1024)

# Create a simple Bell state circuit
circuit = backend.create_circuit(2)

# Add quantum gates
circuit = backend.add_gate(circuit, 'H', 0)  # Hadamard on qubit 0
circuit = backend.add_gate(circuit, 'CX', [0, 1])  # CNOT gate

# Execute the circuit
result = backend.execute_circuit(circuit, shots=1000)
print("Bell state results:", result['counts'])

# Expected output: roughly equal probabilities for '00' and '11'

Parameterized Circuit

# Create circuit with rotation gates
circuit = backend.create_circuit(3)

# Add parameterized gates
circuit = backend.add_gate(circuit, 'RY', 0, [np.pi/4])  # π/4 rotation
circuit = backend.add_gate(circuit, 'RX', 1, [np.pi/3])  # π/3 rotation
circuit = backend.add_gate(circuit, 'RZ', 2, [np.pi/2])  # π/2 rotation

# Add entangling gates
circuit = backend.add_gate(circuit, 'CX', [0, 1])
circuit = backend.add_gate(circuit, 'CX', [1, 2])

# Get statevector
statevector = backend.get_statevector(circuit)
print(f"Statevector shape: {statevector.shape}")
print(f"Statevector norm: {np.linalg.norm(statevector):.6f}")

Configuration

Backend Initialization

# Basic configuration
backend = sqx.SimulatorBackend(
    device='simulator',
    max_qubits=10,     # Maximum qubits to simulate
    shots=1024         # Default measurement shots
)

# High-precision simulation
backend_precise = sqx.SimulatorBackend(
    max_qubits=8,
    shots=10000  # More shots for better statistics
)

# Development/testing configuration
backend_dev = sqx.SimulatorBackend(
    max_qubits=4,
    shots=100   # Fast execution for testing
)

Simulator Capabilities

# Check simulator capabilities
capabilities = backend.capabilities

print("Simulator capabilities:")
for capability, supported in capabilities.items():
    print(f"  {capability}: {supported}")

# Output includes:
# supports_gradient: True
# supports_parameter_shift: True  
# supports_finite_diff: True
# supports_backprop: False (not implemented)
# supports_hardware: False
# supports_noise_models: False

Gate Operations

Single-Qubit Gates

circuit = backend.create_circuit(3)

# Pauli gates
circuit = backend.add_gate(circuit, 'X', 0)  # Pauli-X (NOT)
circuit = backend.add_gate(circuit, 'Y', 1)  # Pauli-Y
circuit = backend.add_gate(circuit, 'Z', 2)  # Pauli-Z

# Hadamard gate
circuit = backend.add_gate(circuit, 'H', 0)

# Phase gates
circuit = backend.add_gate(circuit, 'S', 1)  # S gate (√Z)
circuit = backend.add_gate(circuit, 'T', 2)  # T gate (⁴√Z)

# Rotation gates
circuit = backend.add_gate(circuit, 'RX', 0, [np.pi/2])  # X-rotation
circuit = backend.add_gate(circuit, 'RY', 1, [np.pi/3])  # Y-rotation  
circuit = backend.add_gate(circuit, 'RZ', 2, [np.pi/4])  # Z-rotation

# Available single-qubit gates
available_gates = backend.gates.keys()
print("Available gates:", list(available_gates))

Two-Qubit Gates

circuit = backend.create_circuit(4)

# CNOT gate (Controlled-X)
circuit = backend.add_gate(circuit, 'CNOT', [0, 1])
circuit = backend.add_gate(circuit, 'CX', [0, 1])  # Same as CNOT

# Controlled-Z gate
circuit = backend.add_gate(circuit, 'CZ', [1, 2])

# SWAP gate
circuit = backend.add_gate(circuit, 'SWAP', [2, 3])

# Execute and measure
result = backend.execute_circuit(circuit)
print("Two-qubit circuit results:", result['counts'])

Multi-Qubit Gates

# Toffoli gate (CCX - simplified implementation)
circuit = backend.create_circuit(4)
circuit = backend.add_gate(circuit, 'H', 0)
circuit = backend.add_gate(circuit, 'H', 1)  
circuit = backend.add_gate(circuit, 'CCX', [0, 1, 2])  # Control qubits 0,1, target 2

# Note: Toffoli implementation is simplified in the current backend
print("Toffoli circuit executed (simplified implementation)")

Advanced Features

Statevector Analysis

def analyze_quantum_state(backend, circuit):
    """Analyze quantum state properties."""

    # Get statevector
    statevector = backend.get_statevector(circuit)
    n_qubits = backend._get_n_qubits(circuit)

    # Calculate probabilities
    probabilities = np.abs(statevector)**2

    # Find dominant basis states
    dominant_indices = np.where(probabilities > 0.01)[0]

    print(f"Quantum State Analysis ({n_qubits} qubits):")
    print(f"Statevector dimension: {len(statevector)}")
    print(f"Normalization: {np.linalg.norm(statevector):.6f}")
    print(f"Entropy: {-np.sum(probabilities * np.log2(probabilities + 1e-16)):.4f}")

    print("\nDominant basis states:")
    for idx in dominant_indices:
        basis_state = format(idx, f'0{n_qubits}b')
        amplitude = statevector[idx]
        probability = probabilities[idx]
        print(f"|{basis_state}⟩: amplitude = {amplitude:.4f}, probability = {probability:.4f}")

    return {
        'statevector': statevector,
        'probabilities': probabilities,
        'entropy': -np.sum(probabilities * np.log2(probabilities + 1e-16))
    }

# Example: Analyze GHZ state
circuit = backend.create_circuit(3)
circuit = backend.add_gate(circuit, 'H', 0)
circuit = backend.add_gate(circuit, 'CX', [0, 1])
circuit = backend.add_gate(circuit, 'CX', [1, 2])

analysis = analyze_quantum_state(backend, circuit)

Quantum Feature Maps

def demonstrate_feature_maps():
    """Demonstrate quantum feature maps for machine learning."""

    # Generate sample data
    X = np.random.random((5, 3))  # 5 samples, 3 features

    # Create ZZ feature map
    zz_map = backend.create_feature_map(
        n_features=3, 
        feature_map='ZZFeatureMap', 
        reps=2
    )

    # Apply feature map to first data point
    encoded_circuit = zz_map(X[0])
    statevector = backend.get_statevector(encoded_circuit)

    print("ZZ Feature Map Encoding:")
    print(f"Input data: {X[0]}")
    print(f"Encoded statevector norm: {np.linalg.norm(statevector):.6f}")

    # Pauli feature map
    pauli_map = backend.create_feature_map(
        n_features=3,
        feature_map='PauliFeatureMap',
        reps=1
    )

    pauli_circuit = pauli_map(X[0])
    pauli_statevector = backend.get_statevector(pauli_circuit)

    print(f"Pauli feature map statevector norm: {np.linalg.norm(pauli_statevector):.6f}")

demonstrate_feature_maps()

Quantum Kernel Computation

def compute_quantum_kernel_example():
    """Compute quantum kernel matrix."""

    # Sample training data
    X_train = np.array([
        [0.1, 0.2],
        [0.4, 0.8], 
        [0.7, 0.3],
        [0.9, 0.6]
    ])

    # Sample test data
    X_test = np.array([
        [0.2, 0.3],
        [0.5, 0.7]
    ])

    # Compute kernel matrix
    kernel_matrix = backend.compute_kernel_matrix(
        X_train, X_test, 
        feature_map='ZZFeatureMap',
        shots=1000
    )

    print("Quantum Kernel Matrix:")
    print(kernel_matrix)
    print(f"Matrix shape: {kernel_matrix.shape}")

    return kernel_matrix

kernel_matrix = compute_quantum_kernel_example()

Variational Ansätze

def demonstrate_ansatz_circuits():
    """Demonstrate different ansatz circuits for VQE/QAOA."""

    n_qubits = 4

    # Real Amplitudes ansatz
    params_ra = np.random.random(8)  # 2 layers × 4 qubits
    ra_ansatz = backend.create_ansatz('RealAmplitudes', n_qubits, params_ra)
    ra_circuit = ra_ansatz()

    print("Real Amplitudes Ansatz:")
    print(f"Parameters: {params_ra}")
    print(f"Circuit qubits: {backend._get_n_qubits(ra_circuit)}")

    # EfficientSU2 ansatz  
    params_su2 = np.random.random(12)  # 1 layer × 4 qubits × 3 params
    su2_ansatz = backend.create_ansatz('EfficientSU2', n_qubits, params_su2)
    su2_circuit = su2_ansatz()

    print("\nEfficientSU2 Ansatz:")
    print(f"Parameters: {params_su2}")
    print(f"Circuit qubits: {backend._get_n_qubits(su2_circuit)}")

    # Compare statevectors
    ra_state = backend.get_statevector(ra_circuit)
    su2_state = backend.get_statevector(su2_circuit)

    print(f"\nRA statevector entropy: {-np.sum(np.abs(ra_state)**2 * np.log2(np.abs(ra_state)**2 + 1e-16)):.4f}")
    print(f"SU2 statevector entropy: {-np.sum(np.abs(su2_state)**2 * np.log2(np.abs(su2_state)**2 + 1e-16)):.4f}")

demonstrate_ansatz_circuits()

Expectation Value Calculations

def hamiltonian_expectation_example():
    """Calculate expectation values with different Hamiltonians."""

    # Create test circuit (Bell state)
    circuit = backend.create_circuit(2)
    circuit = backend.add_gate(circuit, 'H', 0)
    circuit = backend.add_gate(circuit, 'CX', [0, 1])

    # Simple Hamiltonian: σ_z ⊗ I
    H_z = np.array([
        [1, 0, 0, 0],
        [0, -1, 0, 0], 
        [0, 0, 1, 0],
        [0, 0, 0, -1]
    ])

    expectation_z = backend.compute_expectation(circuit, H_z)
    print(f"⟨ψ|σ_z ⊗ I|ψ⟩ = {expectation_z:.6f}")

    # Hamiltonian: σ_x ⊗ σ_x
    H_xx = np.array([
        [0, 0, 0, 1],
        [0, 0, 1, 0],
        [0, 1, 0, 0], 
        [1, 0, 0, 0]
    ])

    expectation_xx = backend.compute_expectation(circuit, H_xx)
    print(f"⟨ψ|σ_x ⊗ σ_x|ψ⟩ = {expectation_xx:.6f}")

    # For Bell state |00⟩ + |11⟩, expect:
    # ⟨σ_z ⊗ I⟩ = 0 (equal superposition)  
    # ⟨σ_x ⊗ σ_x⟩ = 1 (maximally correlated)

    return expectation_z, expectation_xx

exp_z, exp_xx = hamiltonian_expectation_example()

Quantum Machine Learning Examples

VQE Implementation

def simple_vqe_h2():
    """Simple VQE implementation for H2 molecule."""

    # H2 Hamiltonian (simplified)
    # H = -1.0523 I + 0.3979 Z_0 - 0.3979 Z_1 - 0.0113 Z_0*Z_1 + 0.1809 X_0*X_1

    def h2_energy(params):
        """Calculate H2 energy for given parameters."""
        # Create ansatz circuit
        ansatz = backend.create_ansatz('RealAmplitudes', 2, params)
        circuit = ansatz()

        # Compute expectation values for each Pauli term
        statevector = backend.get_statevector(circuit)

        # Identity term
        energy = -1.0523

        # Z_0 term (σ_z ⊗ I)
        H_z0 = np.diag([1, -1, 1, -1])
        energy += 0.3979 * backend.compute_expectation(circuit, H_z0)

        # Z_1 term (I ⊗ σ_z)  
        H_z1 = np.diag([1, 1, -1, -1])
        energy -= 0.3979 * backend.compute_expectation(circuit, H_z1)

        # Z_0*Z_1 term
        H_zz = np.diag([1, -1, -1, 1])
        energy -= 0.0113 * backend.compute_expectation(circuit, H_zz)

        # X_0*X_1 term
        H_xx = np.array([[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]])
        energy += 0.1809 * backend.compute_expectation(circuit, H_xx)

        return energy

    # Optimize parameters
    from scipy.optimize import minimize

    initial_params = np.random.random(4) * 2 * np.pi
    result = minimize(h2_energy, initial_params, method='COBYLA')

    print("VQE H2 Results:")
    print(f"Optimal energy: {result.fun:.6f} Ha")
    print(f"Optimal parameters: {result.x}")
    print(f"Expected ground state: ≈ -1.137 Ha")

    return result

# Run VQE example
vqe_result = simple_vqe_h2()

QAOA Implementation

def simple_qaoa_maxcut():
    """Simple QAOA for Max-Cut problem."""

    # Define graph edges (triangle + additional edge)
    edges = [(0, 1), (1, 2), (2, 0), (0, 3)]
    n_nodes = 4

    def qaoa_circuit(gamma, beta, p_layers=1):
        """Create QAOA circuit."""
        circuit = backend.create_circuit(n_nodes)

        # Initial superposition
        for i in range(n_nodes):
            circuit = backend.add_gate(circuit, 'H', i)

        # QAOA layers
        for layer in range(p_layers):
            # Cost Hamiltonian (ZZ interactions)
            for i, j in edges:
                circuit = backend.add_gate(circuit, 'CZ', [i, j])
                circuit = backend.add_gate(circuit, 'RZ', j, [2 * gamma[layer]])

            # Mixer Hamiltonian (X rotations)
            for i in range(n_nodes):
                circuit = backend.add_gate(circuit, 'RX', i, [2 * beta[layer]])

        return circuit

    def qaoa_cost(params):
        """QAOA cost function."""
        p_layers = len(params) // 2
        gamma = params[:p_layers]
        beta = params[p_layers:]

        circuit = qaoa_circuit(gamma, beta, p_layers)
        result = backend.execute_circuit(circuit, shots=1000)

        # Calculate cut value expectation
        total_cut = 0
        total_counts = sum(result['counts'].values())

        for bitstring, count in result['counts'].items():
            # Count edges crossing the cut
            cut_value = 0
            for i, j in edges:
                if bitstring[i] != bitstring[j]:
                    cut_value += 1

            total_cut += (count / total_counts) * cut_value

        return -total_cut  # Minimize negative cut (maximize cut)

    # Optimize QAOA
    from scipy.optimize import minimize

    p_layers = 2
    initial_params = np.random.random(2 * p_layers) * np.pi
    result = minimize(qaoa_cost, initial_params, method='COBYLA')

    print("QAOA Max-Cut Results:")
    print(f"Optimal cut value: {-result.fun:.4f}")
    print(f"Optimal parameters: {result.x}")
    print(f"Maximum possible cut: {len(edges)} edges")

    return result

# Run QAOA example  
qaoa_result = simple_qaoa_maxcut()

Quantum Neural Network

def simple_qnn_classifier():
    """Simple quantum neural network for binary classification."""

    # Generate synthetic 2D classification data
    np.random.seed(42)
    n_samples = 20
    X = np.random.random((n_samples, 2)) * 2 - 1  # [-1, 1] range
    y = (X[:, 0] + X[:, 1] > 0).astype(int)  # Simple linear separation

    def qnn_circuit(x, params):
        """Quantum neural network circuit."""
        # Data encoding
        feature_map = backend.create_feature_map(2, 'ZZFeatureMap', reps=1)
        circuit = feature_map(x)

        # Variational layers
        ansatz = backend.create_ansatz('EfficientSU2', 2, params)
        variational_circuit = ansatz()

        # Combine encoding and variational parts (simplified)
        # In practice, you'd need to compose the circuits properly
        return circuit

    def qnn_predict(X_batch, params):
        """Make predictions with QNN."""
        predictions = []

        for x in X_batch:
            circuit = qnn_circuit(x, params)

            # Measure expectation value of Z_0 for classification
            statevector = backend.get_statevector(circuit)

            # Simple measurement probability
            prob_0 = np.abs(statevector[0])**2 + np.abs(statevector[2])**2
            prediction = 1 if prob_0 > 0.5 else 0
            predictions.append(prediction)

        return np.array(predictions)

    def qnn_loss(params):
        """QNN training loss."""
        predictions = qnn_predict(X, params)

        # Binary cross-entropy loss (simplified)
        loss = np.mean((predictions - y)**2)
        return loss

    # Train QNN
    initial_params = np.random.random(6) * 2 * np.pi  # 6 parameters

    print("Training simple QNN...")
    print(f"Initial accuracy: {np.mean(qnn_predict(X, initial_params) == y):.4f}")

    # Note: For real training, you'd use proper gradient descent
    # This is a simplified demonstration

    return initial_params

# Run QNN example
qnn_params = simple_qnn_classifier()

Performance and Limitations

Performance Characteristics

def performance_analysis():
    """Analyze simulator performance."""
    import time

    qubit_counts = [2, 4, 6, 8]
    execution_times = []

    print("Performance Analysis:")
    print("Qubits | Time (ms) | State Dimension")
    print("-------|-----------|----------------")

    for n_qubits in qubit_counts:
        if n_qubits <= backend.max_qubits:
            # Create test circuit
            start_time = time.time()

            circuit = backend.create_circuit(n_qubits)

            # Add gates
            for i in range(n_qubits):
                circuit = backend.add_gate(circuit, 'H', i)

            for i in range(n_qubits - 1):
                circuit = backend.add_gate(circuit, 'CX', [i, i + 1])

            # Execute
            result = backend.execute_circuit(circuit, shots=100)

            end_time = time.time()
            execution_time = (end_time - start_time) * 1000

            execution_times.append(execution_time)
            state_dim = 2**n_qubits

            print(f"   {n_qubits}   |   {execution_time:.2f}   |    {state_dim}")

    print(f"\nSimulator limits:")
    print(f"Max qubits: {backend.max_qubits}")
    print(f"Max state dimension: {2**backend.max_qubits:,}")

performance_analysis()

Memory Usage Estimation

def memory_usage_analysis():
    """Estimate memory usage for different qubit counts."""

    print("Memory Usage Estimates:")
    print("Qubits | State Vector | Memory (MB)")
    print("-------|--------------|------------")

    for n_qubits in range(1, 16):
        state_dim = 2**n_qubits
        # Complex128: 16 bytes per complex number
        memory_bytes = state_dim * 16
        memory_mb = memory_bytes / (1024**2)

        if memory_mb < 1000:  # Only show reasonable sizes
            print(f"   {n_qubits:2d}  |  {state_dim:8,} |   {memory_mb:8.2f}")
        else:
            print(f"   {n_qubits:2d}  |  {state_dim:8,} |   {memory_mb:8.0f}")

        if n_qubits >= 20:  # Stop at very large sizes
            break

memory_usage_analysis()

Error Handling and Debugging

Comprehensive Error Handling

def robust_simulation_example():
    """Demonstrate robust simulation with error handling."""

    import logging

    # Setup logging for debugging
    logging.basicConfig(level=logging.INFO)
    logger = logging.getLogger(__name__)

    def safe_circuit_execution(backend, circuit_builder, max_retries=3):
        """Execute circuit with error handling."""

        for attempt in range(max_retries):
            try:
                # Build circuit
                circuit = circuit_builder()

                # Validate circuit
                n_qubits = backend._get_n_qubits(circuit)
                if n_qubits > backend.max_qubits:
                    raise ValueError(f"Circuit has {n_qubits} qubits, max is {backend.max_qubits}")

                # Execute circuit
                result = backend.execute_circuit(circuit)

                # Validate result
                if 'counts' not in result:
                    raise RuntimeError("Invalid execution result")

                logger.info(f"Circuit execution successful on attempt {attempt + 1}")
                return result

            except Exception as e:
                logger.warning(f"Attempt {attempt + 1} failed: {e}")

                if attempt == max_retries - 1:
                    logger.error("All retry attempts failed")
                    return None

        return None

    # Example circuit builder that might fail
    def problematic_circuit():
        circuit = backend.create_circuit(3)

        # Add gates that might cause issues
        circuit = backend.add_gate(circuit, 'H', 0)
        circuit = backend.add_gate(circuit, 'UNKNOWN_GATE', 1)  # Will cause warning
        circuit = backend.add_gate(circuit, 'RX', 2, [np.pi/4])

        return circuit

    # Test robust execution
    result = safe_circuit_execution(backend, problematic_circuit)

    if result:
        print("Robust execution successful:")
        print(f"Results: {result['counts']}")
    else:
        print("Robust execution failed after all retries")

robust_simulation_example()

Circuit Validation

def validate_circuit_construction():
    """Validate circuit construction steps."""

    def validate_gate_application(backend, gate, qubits, params=None):
        """Validate individual gate application."""

        validation = {
            'valid': True,
            'warnings': [],
            'errors': []
        }

        # Check qubit indices
        if isinstance(qubits, int):
            qubits = [qubits]

        max_qubit = max(qubits) if qubits else -1
        if max_qubit >= backend.max_qubits:
            validation['errors'].append(f"Qubit index {max_qubit} exceeds max {backend.max_qubits-1}")
            validation['valid'] = False

        # Check gate existence
        if gate.upper() not in backend.gates and not gate.upper().startswith('R'):
            validation['warnings'].append(f"Gate '{gate}' may not be recognized")

        # Check parameter requirements
        rotation_gates = ['RX', 'RY', 'RZ']
        if gate.upper() in rotation_gates:
            if not params or len(params) == 0:
                validation['errors'].append(f"Rotation gate '{gate}' requires angle parameter")
                validation['valid'] = False

        return validation

    # Test various gate validations
    test_cases = [
        ('H', [0], None),
        ('RX', [1], [np.pi/2]),
        ('RY', [2], []),  # Missing parameter - should warn
        ('CX', [0, 1], None),
        ('UNKNOWN', [0], None),  # Unknown gate
        ('H', [15], None),  # Invalid qubit index
    ]

    print("Gate Validation Results:")
    for gate, qubits, params in test_cases:
        validation = validate_gate_application(backend, gate, qubits, params)

        status = "✓" if validation['valid'] else "✗"
        print(f"{status} {gate} on {qubits} with params {params}")

        for warning in validation['warnings']:
            print(f"    ⚠ {warning}")
        for error in validation['errors']:
            print(f"    ✗ {error}")

validate_circuit_construction()

Best Practices

Simulation Guidelines

1. Qubit Limits: Keep circuits under 12 qubits for reasonable performance
2. Gate Decomposition: Use basic gates (H, X, Y, Z, CX) when possible
3. Statevector Access: Use statevector operations for debugging
4. Parameter Optimization: Use numerical gradients for parameter optimization

Code Organization

# Example: Well-structured quantum algorithm
class QuantumAlgorithmSimulator:
    """Template for quantum algorithm implementation."""

    def __init__(self, backend, n_qubits):
        self.backend = backend
        self.n_qubits = n_qubits
        self.circuit = None

    def initialize_circuit(self):
        """Initialize quantum circuit."""
        self.circuit = self.backend.create_circuit(self.n_qubits)
        return self.circuit

    def add_initialization(self):
        """Add state initialization."""
        for i in range(self.n_qubits):
            self.circuit = self.backend.add_gate(self.circuit, 'H', i)

    def add_algorithm_gates(self, parameters):
        """Add algorithm-specific gates."""
        # Override in subclasses
        pass

    def execute(self, parameters=None, shots=1000):
        """Execute the quantum algorithm."""
        self.initialize_circuit()
        self.add_initialization()

        if parameters:
            self.add_algorithm_gates(parameters)

        return self.backend.execute_circuit(self.circuit, shots=shots)

    def get_statevector(self):
        """Get current statevector."""
        if self.circuit is None:
            raise ValueError("Circuit not initialized")
        return self.backend.get_statevector(self.circuit)

# Example usage
algorithm = QuantumAlgorithmSimulator(backend, n_qubits=3)
result = algorithm.execute(shots=1000)
print("Algorithm result:", result['counts'])

Troubleshooting

Common Issues

Circuit Size Too Large

# Check qubit limits
if n_qubits > backend.max_qubits:
    print(f"Reducing circuit size from {n_qubits} to {backend.max_qubits} qubits")
    n_qubits = backend.max_qubits

Unknown Gate Error

# Check available gates
available_gates = list(backend.gates.keys())
print("Available gates:", available_gates)

# Use alternative gates
if 'CNOT' not in available_gates and 'CX' in available_gates:
    circuit = backend.add_gate(circuit, 'CX', [0, 1])  # Use CX instead of CNOT

Memory Issues

# Reduce circuit size or use shot-based simulation
if n_qubits > 10:
    print("Large circuit detected - consider using shot-based approaches")
    shots = 10000  # More shots for better statistics with smaller circuits

Numerical Precision

# Check statevector normalization
statevector = backend.get_statevector(circuit)
norm = np.linalg.norm(statevector)
if abs(norm - 1.0) > 1e-10:
    print(f"Warning: Statevector norm = {norm:.12f} (should be 1.0)")

Performance Optimization

Optimize for Small Circuits

# Use statevector operations for analysis
def efficient_small_circuit_analysis(circuit):
    """Efficient analysis for small circuits."""

    # Direct statevector computation
    statevector = backend.get_statevector(circuit)

    # Calculate all probabilities at once
    probabilities = np.abs(statevector)**2

    # Find most likely outcomes
    top_indices = np.argsort(probabilities)[-5:]  # Top 5

    n_qubits = backend._get_n_qubits(circuit)
    results = {}

    for idx in top_indices:
        bitstring = format(idx, f'0{n_qubits}b')
        results[bitstring] = float(probabilities[idx])

    return results

# Use for small circuits instead of shot-based simulation
small_circuit = backend.create_circuit(3)
small_circuit = backend.add_gate(small_circuit, 'H', 0)
small_circuit = backend.add_gate(small_circuit, 'CX', [0, 1])

efficient_results = efficient_small_circuit_analysis(small_circuit)
print("Efficient analysis:", efficient_results)

API Reference

The Simulator backend provides these key methods:

• create_circuit(n_qubits): Create quantum circuit
• add_gate(circuit, gate, qubits, params): Add quantum gate
• execute_circuit(circuit, shots): Execute circuit with measurements
• get_statevector(circuit): Get quantum statevector
• create_feature_map(n_features, type, reps): Create quantum feature map
• create_ansatz(type, n_qubits, params): Create parameterized ansatz
• compute_expectation(circuit, hamiltonian): Calculate expectation values
• compute_kernel_matrix(X1, X2, feature_map): Compute quantum kernel matrix

Gate Library

Available quantum gates: - Single-qubit: I, X, Y, Z, H, S, T - Rotations: RX, RY, RZ (require angle parameter) - Two-qubit: CNOT, CX, CZ, SWAP - Multi-qubit: CCX (Toffoli, simplified implementation)

For complete API documentation, see the API Reference section.

---

The Python Simulator backend is ideal for learning quantum computing concepts, prototyping algorithms, and testing quantum code without external dependencies.