spiking-phase-quantum-encoding

name

spiking-phase-quantum-encoding

description

SPATE methodology for quantum machine learning — spiking-phase adaptive temporal encoding. Converts real-valued features into leaky integrate-and-fire spike trains and maps spike statistics to quantum rotations, augmented with temporal qubits via controlled phase operations. Use when: (1) designing QML pipelines for temporal data, (2) encoding time-series/tabular data into quantum feature spaces, (3) comparing spike-based vs angle/amplitude encoding quality, (4) building hybrid quantum neural networks under constrained qubit budgets, (5) evaluating quantum feature representation quality. Triggers: SPATE, spiking encoding quantum, temporal quantum encoding, spike-to-phase, quantum feature encoding, LIF quantum.

SPATE: Spiking-Phase Adaptive Temporal Encoding for QML

Overview

SPATE (arXiv:2604.11022) addresses a key limitation of QML: static encodings (angle, amplitude) cannot handle temporal information. SPATE uses spike-based data representation to incorporate temporal structure into quantum feature preparation.

Core Pipeline

Real-valued features → LIF spike trains → Spike statistics → Quantum rotations + Temporal qubits → Quantum classifier

Step 1: LIF Spike Train Generation

def lif_spike_train(x, tau=1.0, threshold=1.0, dt=0.01, T=1.0):
    """Generate spike train from input using Leaky Integrate-and-Fire model."""
    spikes = []
    v = 0.0
    for t in range(int(T/dt)):
        v += (dt/tau) * (x - v)  # leaky integration
        if v >= threshold:
            spikes.append(t * dt)
            v = 0.0  # reset
    return spikes

Step 2: Spike Statistics → Quantum Rotations

Extract spike count, inter-spike intervals, and phase information. Map to quantum rotations:

• Spike count → RY rotation angle: θ = π × count / max_count
• Inter-spike interval → RZ phase: φ = 2π × ISI / T
• Phase locking → RX rotation for temporal qubits

Step 3: Temporal Qubits

Add controlled phase operations on dedicated temporal qubits:

# For each temporal feature dimension
for i, (spike_times, phase) in enumerate(zip(spike_trains, phases)):
    circuit.ry(phase, qubit[i])
    if len(spike_times) > 1:
        circuit.cp(phase * 0.5, qubit[i], qubit[i+1])  # temporal entanglement

Encoding Quality Evaluation Protocol

Use these metrics to compare encodings independently of the classifier:

Metric	What it measures	Good range
CKTA (Centered Kernel Target Alignment)	Feature alignment with labels	> 0.5
Fisher score	Inter/intra-class separability	> 1.0
Silhouette score	Cluster cohesion	> 0.3
Normalized entropy	Feature informativeness	Low
TV-pair collapse	Representation collapse detection	< 0.1

Performance Benchmarks

SPATE vs Angle encoding (from paper):

Dataset	SPATE CKTA	Angle CKTA	SPATE Fisher	Angle Fisher
Blobs	0.966	0.632	7.37	0.70
Moons	0.506	0.015	—	—

Hybrid QNN results (fixed qubit budget):

• Wine: Accuracy 0.826, AUC 0.978
• Moons: Accuracy 0.840, AUC 0.923

When to Use

• Time-series classification with quantum circuits
• Tabular data where temporal ordering matters
• Low qubit budget scenarios requiring efficient encoding
• When static encodings (angle/amplitude) underperform

Pitfalls

• LIF parameters (tau, threshold) need tuning per dataset
• Spike train length trades off temporal resolution vs circuit depth
• Always evaluate encoding quality BEFORE training the classifier