quantum-computing

## What I do - Implement quantum-inspired neural networks - Model quantum spiking neurons - Handle quantum state evolution - Manage superposition and entanglement - Implement quantum tunneling behavior - Handle coherence and decoherence - Work with multi-reality networks - Optimize quantum circuit simulation ## When to use me When working with the NeuralBlitz quantum computing components or implementing quantum-inspired algorithms. ## Quantum State Representation ```python import numpy as np from typing import Optional, Tuple from scipy.linalg import expm class QuantumState: """ Quantum state vector in Hilbert space. The state is represented as a normalized complex vector. For n qubits, the state space has dimension 2^n. """ def __init__(self, num_qubits: int) -> None: """ Initialize quantum state to |0⟩^n. Args: num_qubits: Number of qubits (must be positive integer) """ self.num_qubits = num_qubits self.dim = 2 ** num_qubits self.state = np.zeros(self.dim, dtype=complex) self.state[0] = 1.0 # |0⟩ state @property def data(self) -> np.ndarray: """Return the state vector (read-only view).""" return self.state.copy() def normalize(self) -> None: """Normalize state vector to unit length.""" norm = np.linalg.norm(self.state) if norm > 0: self.state /= norm def measure(self) -> int: """ Measure state in computational basis. Returns: Measured basis state index with probability = |<x|ψ⟩|² """ probs = np.abs(self.state) ** 2 probs /= probs.sum() return np.random.choice(len(self.state), p=probabilities) def fidelity(self, other: 'QuantumState') -> float: """ Calculate fidelity between two quantum states. Fidelity = |⟨ψ|φ⟩|² for pure states. Args: other: Another quantum state to compare Returns: Fidelity value between 0 and 1 """ overlap = np.vdot(self.state, other.state) return np.abs(overlap) ** 2 ``` ## Quantum Gates ```python class QuantumGate: """Quantum gate operations on state vectors.""" @staticmethod def hadamard(num_qubits: int, target: int) -> np.ndarray: """ Create Hadamard gate for superposition. H|0⟩ = (|0⟩ + |1⟩)/√2 H|1⟩ = (|0⟩ - |1⟩)/√2 """ H = np.array([[1, 1], [1, -1]]) / np.sqrt(2) return QuantumGate.expand_gate(H, num_qubits, target) @staticmethod def pauli_x(num_qubits: int, target: int) -> np.ndarray: """Pauli-X (NOT) gate: |0⟩→|1⟩, |1⟩→|0⟩""" X = np.array([[0, 1], [1, 0]]) return QuantumGate.expand_gate(X, num_qubits, target) @staticmethod def pauli_z(num_qubits: int, target: int) -> np.ndarray: """Pauli-Z gate: |1⟩→-|1⟩, |0⟩→|0⟩""" Z = np.array([[1, 0], [0, -1]]) return QuantumGate.expand_gate(Z, num_qubits, target) @staticmethod def cnot(num_qubits: int, control: int, target: int) -> np.ndarray: """Controlled-NOT gate (CNOT).""" dim = 2 ** num_qubits matrix = np.eye(dim, dtype=complex) for i in range(dim): if (i >> control) & 1 and not (i >> target) & 1: j = i | (1 << target) k = i & ~(1 << target) matrix[j, i] = 1 matrix[k, i] = 0 return matrix @staticmethod def rz(angle: float, num_qubits: int, target: int) -> np.ndarray: """ Rotation around Z-axis by angle. Rz(θ) = exp(-iθZ/2) """ RZ = np.array([ [np.exp(-1j * angle / 2), 0], [0, np.exp(1j * angle / 2)] ]) return QuantumGate.expand_gate(RZ, num_qubits, target) @staticmethod def expand_gate( gate: np.ndarray, num_qubits: int, target: int ) -> np.ndarray: """ Expand single-qubit gate to full operator. Uses tensor product to embed single-qubit operation into larger Hilbert space. """ dim = 2 ** num_qubits if target < 0 or target >= num_qubits: raise ValueError(f"Invalid target qubit: {target}") result = np.eye(1, dtype=complex) for i in range(num_qubits): if i == target: result = np.kron(result, gate) else: result = np.kron(result, np.eye(2, dtype=complex)) return result ``` ## Quantum Spiking Neuron ```python class QuantumSpikingNeuron: """ Quantum-inspired spiking neuron model. Combines quantum mechanics with spiking neural network principles: - Quantum superposition for input integration - Quantum tunneling for spike generation - Coherence time limiting neural activity """ def __init__( self, num_qubits: int = 4, coherence_time: float = 100.0, tunneling: float = 0.1, threshold: float = 0.5, ) -> None: self.num_qubits = num_qubits self.coherence_time = coherence_time self.tunneling = tunneling self.threshold = threshold self.state = QuantumState(num_qubits) self.weights = np.random.randn(num_qubits) * 0.1 self.spike_history: list[float] = [] self.last_update: float = 0.0 def evolve( self, inputs: np.ndarray, dt: float, hamiltonian: Optional[np.ndarray] = None ) -> Tuple[np.ndarray, bool]: """ Evolve quantum state and potentially spike. Args: inputs: Input currents from connected neurons dt: Time step in milliseconds hamiltonian: Optional custom Hamiltonian matrix Returns: Tuple of (output_state, did_spike) """ if len(inputs) != self.num_qubits: raise ValueError(f"Expected {self.num_qubits} inputs, got {len(inputs)}") self.last_update = dt # Create Hamiltonian from inputs (H = -Σ w_i |i⟩⟨i|) if hamiltonian is None: hamiltonian = np.diag(-self.weights * inputs) # Time evolution operator: U(t) = exp(-iHt) evolution = expm(-1j * hamiltonian * dt) # Apply evolution self.state.state = evolution @ self.state.state # Apply tunneling (stochastic spike mechanism) spike_probability = self._calculate_spike_probability() should_spike = np.random.random() < spike_probability if should_spike: self._emit_spike() return self.state.state, True return self.state.state, False def _calculate_spike_probability(self) -> float: """ Calculate spike probability based on quantum state. Uses probability amplitude in excited states modulated by tunneling rate. """ excited_prob = np.sum(np.abs(self.state.state[2 ** (self.num_qubits - 1):]) ** 2) coherence_factor = np.exp(-self.last_update / self.coherence_time) return excited_prob * self.tunneling * coherence_factor def _emit_spike(self) -> None: """Reset state after spike emission.""" self.spike_history.append(self.last_update) # Collapse to ground state (reset) self.state = QuantumState(self.num_qubits) # Keep last spike time for refractory period self._refractory_timer = 5.0 # ms def get_membrane_potential(self) -> float: """Estimate membrane potential from state vector.""" return np.sum( np.arange(2 ** self.num_qubits) * np.abs(self.state.state) ** 2 ) ``` ## Multi-Reality Network ```python class MultiRealityNetwork: """ Network that spans multiple parallel realities. Each reality maintains its own quantum state, and entanglement allows correlation between realities. """ def __init__( self, num_realities: int = 4, neurons_per_reality: int = 20, entanglement_strength: float = 0.1, ) -> None: self.num_realities = num_realities self.neurons_per_reality = neurons_per_reality self.entanglement_strength = entanglement_strength self.neurons: list[list[QuantumSpikingNeuron]] = [] self.entanglement_matrix: np.ndarray self._initialize_network() def _initialize_network(self) -> None: """Initialize neurons in each reality.""" for r in range(self.num_realities): reality_neurons = [ QuantumSpikingNeuron( num_qubits=4, coherence_time=100.0, tunneling=0.1, ) for _ in range(self.neurons_per_reality) ] self.neurons.append(reality_neurons) self.entanglement_matrix = np.eye(self.num_realities) def evolve_cycle(self, dt: float) -> list[list[bool]]: """ Evolve all neurons across all realities. Returns: Matrix of spike events (reality × neuron) """ spike_matrix = [] for r in range(self.num_realities): reality_spikes = [] for neuron in self.neurons[r]: inputs = self._get_inputs(r, neuron) _, spiked = neuron.evolve(inputs, dt) reality_spikes.append(spiked) spike_matrix.append(reality_spikes) self._apply_entanglement(spike_matrix) return spike_matrix def _get_inputs( self, reality: int, target_neuron: QuantumSpikingNeuron ) -> np.ndarray: """Get inputs from neurons in same reality.""" inputs = np.zeros(target_neuron.num_qubits) for i, neuron in enumerate(self.neurons[reality]): if neuron is not target_neuron: inputs[i] = neuron.get_membrane_potential() return inputs def _apply_entanglement(self, spike_matrix: list[list[bool]]) -> None: """ Apply quantum entanglement between realities. Correlates activity across realities based on entanglement matrix. """ spike_array = np.array(spike_matrix) for i in range(self.num_realities): for j in range(i + 1, self.num_realities): correlation = self.entanglement_matrix[i, j] if correlation > 0: self._entangle_realities( spike_array[i], spike_array[j], correlation ) def _entangle_realities( self, spikes_a: np.ndarray, spikes_b: np.ndarray, strength: float ) -> None: """ Entangle activity between two realities. Adjusts spike probabilities based on correlated activity patterns. """ agreement = np.sum(spikes_a == spikes_b) / len(spikes_a) if agreement > 0.8: # Strong correlation - reinforce adjustment = strength * (1 - agreement) elif agreement < 0.2: # Strong anti-correlation adjustment = -strength * (0.5 - agreement) else: adjustment = 0 self.entanglement_matrix = np.clip( self.entanglement_matrix + adjustment * 0.01, 0, 1 ) ```