NeuralBlitz 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
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
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
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
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
)