Architecture & Methodology¶

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

Overview¶

This repository implements and validates quantum error suppression via post-selection conditioning on Bell-pair subsystems. The approach uses mid-circuit measurements to monitor subsystem fidelity and applies decision rules to accept or reject quantum computation outcomes — thereby suppressing errors without full quantum error correction.

qgate conceptual schematic showing the full trajectory filtering pipeline from Bell-pair preparation through conditioning and decision — Conceptual schematic of the qgate trajectory filtering pipeline. Bell-pair subsystems are prepared, scrambled under noise, and monitored via mid-circuit Z-parity measurements. The conditioning decision rule (global, hierarchical, or score fusion) accepts or rejects each shot based on subsystem fidelity.

Core Concept¶

 ┌─────────────────────────────────────────────────────────┐
 │                    Quantum Circuit                       │
 │                                                          │
 │  ┌──────────┐   ┌───────────┐   ┌─────────────┐        │
 │  │ Bell-pair │──▶│ Scramble  │──▶│ Mid-circuit │──┐     │
 │  │ prep ×N  │   │ layers ×D │   │ Z-parity    │  │     │
 │  └──────────┘   └───────────┘   │ measure     │  │     │
 │                                  └─────────────┘  │     │
 │                                       ▼           │     │
 │                               ┌───────────────┐   │     │
 │                               │ Conditioning  │◀──┘     │
 │                               │ Decision Rule │         │
 │                               └───────┬───────┘         │
 │                                       │                  │
 │                              ┌────────┴────────┐        │
 │                              │                 │        │
 │                          ACCEPT            REJECT       │
 │                        (keep shot)     (discard shot)   │
 └─────────────────────────────────────────────────────────┘

Bell-Pair Subsystems¶

Each subsystem is a 2-qubit Bell pair \((\lvert00\rangle + \lvert11\rangle)/\sqrt{2}\). Under noise, the pair's parity may flip. Mid-circuit Z-parity measurements detect these flips without collapsing the computational state.

Multi-Rate Monitoring¶

HF (high-frequency): Z-parity measured every monitoring cycle
LF (low-frequency): Z-parity measured every 2nd cycle (0, 2, 4, …)
The two rates provide complementary signal: LF captures slow drift, HF catches fast errors

Conditioning Strategies¶

1. Global Conditioning¶

All N subsystems must pass all W monitoring cycles.

\[P_{\text{accept}}^{\text{global}} = \prod_{w=1}^{W} \prod_{i=1}^{N} p_i^{(w)}\]

Limitation

Exponential decay with N — unusable at N ≥ 2 under real noise.

2. Hierarchical k-of-N Conditioning¶

Accept if at least ⌈k·N⌉ subsystems pass each cycle:

\[P_{\text{accept}}^{\text{hier}} = \prod_{w=1}^{W} P\!\left(\sum_{i=1}^{N} X_i^{(w)} \ge \lceil k \cdot N \rceil\right)\]

Advantage

O(1) scaling — maintains high acceptance from N = 1 to N = 64.

3. Score Fusion Conditioning¶

Continuous metric combining LF and HF scores:

\[S_{\text{combined}} = \alpha \cdot \bar{S}_{\text{LF}} + (1 - \alpha) \cdot \bar{S}_{\text{HF}}\]

Accept if \(S_{\text{combined}} \ge \theta\).

Advantage

Soft decision boundary absorbs noise spikes that break logical (hard) fusion. The most robust strategy on real IBM hardware.

Simulation Backends¶

QuTiP (Master-Equation Simulation)¶

The simulation module models a driven qubit with pure dephasing:

\[H = \frac{\Omega}{2}\sigma_x + \frac{\omega}{2}\sigma_z\]

\[\mathcal{L}[\rho] = \gamma \left(\sigma_z \rho \sigma_z - \rho\right)\]

Fidelity is computed as \(F(t) = \langle\psi_0\lvert\rho(t)\lvert\psi_0\rangle\) and evaluated within a trailing time window.

Qiskit (IBM Quantum Hardware)¶

Dynamic circuits with mid-circuit measurements on real IBM processors. Bell pairs are prepared, scrambled with random rotations, and measured via ancilla-based Z-parity checks with reset and reuse.

Project Structure¶

qgate-shots-filter/
├── packages/
│   └── qgate/                    # Pip-installable developer toolkit
│       ├── src/qgate/            # Core library (conditioning + monitors)
│       │   └── adapters/         # Mock, Qiskit, Grover, QAOA, VQE, QPE
│       ├── tests/                # 376 unit tests
│       └── pyproject.toml        # Build configuration
│
├── simulations/
│   ├── qutip_sims/              # QuTiP master-equation simulations
│   ├── ibm_hardware/            # IBM Quantum conditioning experiments
│   ├── grover_tsvf/             # Grover vs TSVF-Grover (IBM Fez)
│   ├── qaoa_tsvf/               # QAOA vs TSVF-QAOA MaxCut (IBM Torino)
│   ├── vqe_tsvf/                # VQE vs TSVF-VQE TFIM (IBM Fez)
│   └── qpe_tsvf/                # QPE vs TSVF-QPE Phase Est. (IBM Fez)
│
├── examples/                    # Usage examples
├── docs/                        # Documentation
└── src/sim.py                   # Core QuTiP simulation engine

Validation Chain¶

The research follows a progression from theory to hardware:

 QuTiP Simulations              IBM Quantum Hardware
 ═══════════════════             ════════════════════════
 1. High-noise sweep      ──▶   5. IBM Marrakesh experiment
    (300 configs, 405K           (120 rows, 5000 shots each,
     trials)                      ≈ 6 min on real hardware)
                                      │
 2. k-of-N follow-up      ──▶   Both confirm:
    (216 configs, N=1-32)        • Global collapses at N≥2
                                 • Hierarchical scales to N=64
 3. Incremental N=64             • Score fusion is most robust
    (6 new configs)                on real hardware
                                      │
 4. Multi-frequency sweep  ──▶   Score fusion absorbs HF noise
    (54 configs, 3 variants)     that destroys logical fusion

Empirical Validation¶

Result	Evidence
Global conditioning collapses exponentially	High-noise sweep: 0% acceptance at N ≥ 2
Hierarchical conditioning scales O(1)	Follow-up + incremental: 100% acceptance N = 1–64
Multi-rate monitoring improves detection	Multi-freq sweep: score fusion at γ = 10
Score fusion outperforms logical fusion	Multi-freq: 50% vs 0% acceptance at extreme noise
Hardware validation on IBM Quantum	IBM Marrakesh: score fusion best on real device

TSVF Algorithm Extensions¶

Beyond Bell-pair conditioning, qgate extends trajectory filtering to canonical quantum algorithms via the TSVF (Two-State Vector Formalism) approach. See Hardware Experiments for full results.

Algorithm	Backend	Advantage
Grover	IBM Fez	7.3× at iteration 4
QAOA	IBM Torino	1.88× at p=1
VQE	IBM Fez	1.86× closer (barren plateau avoidance)
QPE	IBM Fez	N/A (phase-coherence incompatible)