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QAOA vs TSVF-QAOA MaxCut (IBM Torino)

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

Objective

Test whether TSVF trajectory filtering improves QAOA MaxCut performance on real hardware, particularly at shallow circuit depths (low p) where hardware noise has the most severe impact on variational quality.

Setup

Parameter Value
Backend IBM Torino (133 qubits)
Algorithm QAOA for MaxCut on a 6-node random graph
Layers p = 1–5
Shots 2,000 per configuration
TSVF variant Chaotic perturbation + cut-quality probe ancilla
Date February 2026

TSVF Approach

  1. Standard QAOA: Cost layer (ZZ interactions from graph edges) + Mixer layer (Rx rotations), repeated p times
  2. TSVF-QAOA: Same + chaotic perturbation + ancilla probe that rewards bitstrings with high cut fractions via controlled-Ry gates
  3. Post-selection: Accept only shots where ancilla measures \(\lvert1\rangle\)

Key Results

p (layers) AR std AR TSVF Ratio Accept%
1 0.4268 0.8029 1.88× 33.5%
2 0.7036 0.7024 1.00× 32.0%
3 0.6975 0.6987 1.00× 35.2%
4 0.6841 0.6912 1.01× 34.8%
5 0.6753 0.6802 1.01× 36.1%

Headline: 1.88× TSVF advantage at p=1

At p=1 (shallowest depth), hardware noise most severely degrades the single QAOA layer. TSVF post-selection nearly doubles the approximation ratio. At higher p, the variational ansatz has enough expressivity to partially self-correct, so the TSVF advantage narrows.

QAOA approximation ratio vs layers comparing standard and TSVF on IBM Torino showing 1.88x improvement at p=1
Approximation ratio versus QAOA layers (p) on IBM Torino. At p=1 the TSVF variant (orange) nearly doubles the MaxCut quality compared to standard QAOA (blue). The advantage narrows at deeper circuits where the variational ansatz self-corrects.
QAOA circuit depth versus approximation ratio on IBM Torino hardware
Transpiled circuit depth versus approximation ratio. TSVF provides the largest benefit at shallow depths where hardware noise has the most severe impact on a single QAOA layer.

Analysis

  • Strongest advantage at p=1: TSVF rescues nearly 2× the approximation quality
  • Diminishing returns at p ≥ 2: deeper circuits self-correct, reducing TSVF's marginal benefit
  • Consistent acceptance at ~33–36%, showing stable post-selection regardless of depth
QAOA TSVF acceptance rate across layers showing stable 33-36% post-selection
Post-selection acceptance rate across QAOA layers. The stable 33–36% rate demonstrates consistent trajectory quality filtering regardless of circuit depth.
Galton adaptive threshold evolution during QAOA TSVF experiment on IBM Torino
Galton adaptive threshold evolution during the QAOA experiment. The threshold dynamically adjusts to the score distribution at each layer depth. See Dynamic Thresholding for details.

Reproduction

python simulations/qaoa_tsvf/run_qaoa_tsvf_experiment.py \
    --mode ibm --max-layers 5 --shots 2000

python simulations/qaoa_tsvf/run_qaoa_tsvf_experiment.py \
    --mode aer --max-layers 5 --shots 4000

Requirements

Requires .secrets.json with ibmq_token for IBM hardware runs.

Using the qgate Adapter

from qgate.adapters.qaoa_adapter import QAOATSVFAdapter
from qgate.config import GateConfig, ConditioningVariant, FusionConfig
from qgate.filter import TrajectoryFilter

# Initialize the QAOA TSVF adapter for MaxCut
adapter = QAOATSVFAdapter(
    backend=backend,          # AerSimulator() or IBM Runtime backend
    algorithm_mode="tsvf",    # "standard" or "tsvf"
    n_nodes=6,
    edges=[(0,1), (1,2), (2,3), (3,4), (4,5), (0,5)],
    seed=42,
)

# Build and run at p=1 (single QAOA layer)
circuit = adapter.build_circuit(n_qubits=6, n_cycles=1)
raw_results = adapter.run(circuit, shots=2000)

# Parse into ParityOutcome objects for trajectory filtering
outcomes = adapter.parse_results(raw_results, n_subsystems=6, n_cycles=1)

# Extract MaxCut quality metrics
cut_ratio, approx_ratio, n_accepted = adapter.extract_cut_quality(
    raw_results, postselect=True,
)
print(f"TSVF approximation ratio: {approx_ratio:.4f} ({n_accepted} accepted)")