Hardware Experiments¶

Patent notice: The underlying methods are covered by pending patent applications.

TSVF Algorithm Experiments (IBM Quantum, Feb–Mar 2026)¶

These experiments extend qgate's trajectory filtering beyond Bell-pair conditioning to four canonical quantum algorithms. The TSVF (Two-State Vector Formalism) approach injects a mild chaotic perturbation and uses an ancilla-based probe to create a post-selectable quality signal — then filters for high-fidelity execution trajectories.

Methodology¶

Standard Algorithm:  H → Algorithm Gates → Measure
                          ↓
TSVF Variant:       H → Algorithm Gates → Chaotic Perturbation → Probe Ancilla → Measure
                                                                        ↓
                                                              Post-select on ancilla |1⟩

The chaotic perturbation is deliberately mild — small random rotations scaled as \(\pi / (c \cdot \sqrt{d})\) where \(d\) is the circuit depth parameter. The probe ancilla applies controlled rotations that reward bitstrings consistent with the expected solution structure. Post-selection on the ancilla measuring \(|1\rangle\) retains only trajectories that survived both the hardware noise and the perturbation.

Results Summary¶

Algorithm	Backend	Metric	Standard	TSVF	Advantage
Grover (iter=4)	IBM Fez	Success probability	0.0830	0.6105	7.3×
QAOA (p=1)	IBM Torino	Approximation ratio	0.4268	0.8029	1.88×
VQE (L=3)	IBM Fez	Energy gap to ground	2.398	1.291	1.86× closer
QPE (t=7)	IBM Fez	Phase fidelity	0.1569	0.0076	N/A
Utility-Scale (133Q)	IBM Torino	Cooling delta	−4.108	−4.188	Δ = −0.080

IBM hardware probe heatmap showing ancilla signal strength across qubit configurations — Probe ancilla signal heatmap across qubit configurations on IBM Quantum hardware. Stronger signal (brighter regions) indicates higher-fidelity trajectory subsets selected by TSVF post-selection.

Score fusion alpha parameter sweep showing optimal blending between low-frequency and high-frequency signals — Score fusion parameter sweep: optimal alpha blending between low-frequency (LF) and high-frequency (HF) parity signals. The fusion mechanism adaptively weights signal channels for maximum discrimination.

Why TSVF Works for Some Algorithms but Not Others¶

The critical distinction is between amplitude-encoded and phase-coherence-encoded information:

Property	Grover / QAOA / VQE	QPE
Answer encoding	Amplitude pattern in computational basis	Phase coherence across precision register
Perturbation effect	Slightly scrambles amplitudes	Destroys inverse QFT interference
Post-selection recovers?	Yes — filters trajectories where signal survives	No — destroyed phase info is unrecoverable
Depth sensitivity	Moderate — noise accumulates gradually	High — single perturbation collapses peak

Amplitude-encoded algorithms (Grover, QAOA, VQE)

The answer is spread across computational basis state amplitudes. A mild perturbation slightly degrades these amplitudes, but the probe ancilla can detect which trajectories retained the signal. Post-selection filters out noise-corrupted paths, yielding a smaller but higher-fidelity sample.

Phase-coherence algorithms (QPE)

The answer is encoded in the relative phases between precision qubits, which the inverse QFT converts to a sharp probability peak. Any perturbation disrupts this phase coherence, and the inverse QFT produces a diffuse rather than peaked distribution. Post-selection cannot reconstruct the destroyed phase information.

Reproduction¶

All experiments can be reproduced with a .secrets.json file containing your IBM Quantum token:

{
  "ibmq_token": "your-ibm-quantum-token-here"
}

See each experiment page for specific commands.

Acceptance rate vs circuit depth across IBM Quantum experiments showing stable post-selection rates — Acceptance rate versus transpiled circuit depth across all IBM Quantum experiments. Post-selection rates remain stable (25–50%) even as circuit depth grows, confirming the probe ancilla selects a meaningful trajectory subset.

Statistical Validation: Bias Study (Mar 2026)¶

Beyond the real-hardware TSVF experiments above, we conducted a rigorous 4-part statistical validation of qgate's Galton trajectory filter under controlled, reproducible conditions — 15 independent trials × 100,000 shots with an IBM Heron-class noise model.

Experiment	Key Finding	Significance
Noise Robustness	MSE reduction grows from 13.6% → 20.7% as noise increases	All \(p < 10^{-23}\)
Qubit Scaling	Stable 14–17% MSE reduction; variance collapse up to 5,360×	All \(p < 10^{-46}\)
Cross-Algorithm	Algorithm-agnostic: VQE +14.8%, QAOA +48.8%, Grover +24.4%	All \(p < 10^{-17}\)
Train/Test Split	Frozen threshold generalises: 14.7% MSE↓ on blind test set	\(p = 0.001\) ***

The Anti-Decoherence Property

Unlike most error mitigation techniques that degrade under heavy noise, qgate's filter improves with noise — the noisier the environment, the better the filter discriminates between the coherent subset and the thermalized bulk.

NEW: Calibrate Once, Deploy Forever

Experiment 4 proves the Galton threshold is a stable physical constant for a given circuit depth and noise environment. Run a cheap calibration circuit to find θ, freeze it, and apply it to massive production runs — with full filtering benefit and zero adaptive overhead.

Full bias study results, methodology, and reproduction steps →