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Grover vs TSVF-Grover (IBM Fez)

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

Objective

Test whether TSVF trajectory filtering can rescue Grover search from hardware noise degradation at higher iteration counts, where standard Grover's success probability collapses on real NISQ devices.

Setup

Parameter Value
Backend IBM Fez (156 qubits)
Algorithm 5-qubit Grover search (marked state \(\lvert10101\rangle\))
Iterations 1–10
Shots 8,192 per configuration
TSVF variant Chaotic perturbation + parity probe ancilla
Date February 2026

TSVF Approach

  1. Standard Grover: Oracle + Diffusion operator, iterated 1–10 times
  2. TSVF-Grover: Same + chaotic layer (random Rz/Ry/CX) + ancilla parity probe (controlled rotations rewarding marked-state bit pattern)
  3. Post-selection: Accept only shots where ancilla measures \(\lvert1\rangle\)

Key Results

Iteration P(success) std P(success) TSVF Ratio Accept%
1 0.2131 0.1953 0.92× 29.1%
2 0.4329 0.3618 0.84× 31.4%
3 0.1801 0.4764 2.65× 28.7%
4 0.0830 0.6105 7.36× 25.3%
5 0.0552 0.4318 7.82× 22.8%

Headline: 7.3× TSVF advantage at iteration 4

At low iterations (1–2), standard Grover still has strong signal and TSVF adds overhead. At iteration 3+, hardware noise degrades the Grover amplitude pattern, and TSVF post-selection filters for trajectories where the marked-state amplitude survived — yielding dramatic improvement.

TSVF vs standard Grover success probability across iterations on IBM Fez showing 7.3x improvement at iteration 4
Success probability (Pacc) versus Grover iteration count on IBM Fez. Standard Grover (blue) collapses after iteration 2 due to hardware noise accumulation, while TSVF-Grover (orange) maintains high success probability through post-selection — peaking at 7.3× advantage at iteration 4.
Grover circuit depth versus fidelity comparison between standard and TSVF variants
Transpiled circuit depth versus measured fidelity. As depth increases, standard Grover's fidelity degrades exponentially, while TSVF post-selection rescues high-fidelity trajectories even at depth 946.

Analysis

  • Crossover point at iteration 3: TSVF begins outperforming standard Grover
  • Peak advantage at iterations 4–5: Standard success drops below 10% while TSVF maintains 40–60%
  • Acceptance rate stays ~25–30%, confirming the probe ancilla selects a meaningful subset
Grover TSVF acceptance rate across iterations showing stable 25-30% post-selection
Post-selection acceptance rate across Grover iterations. The stable 25–30% rate confirms the ancilla probe is selecting a meaningful subset of trajectories rather than randomly filtering.
Galton adaptive threshold evolution during Grover TSVF experiment
Galton adaptive threshold evolution during the Grover experiment. The Galton board mechanism automatically adjusts the acceptance threshold based on the observed score distribution.

Reproduction

python simulations/grover_tsvf/run_grover_tsvf_experiment.py \
    --mode ibm --max-iter 10 --shots 8192

python simulations/grover_tsvf/run_grover_tsvf_experiment.py \
    --mode aer --max-iter 10 --shots 8192

Requirements

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

Using the qgate Adapter

from qgate.adapters.grover_adapter import GroverTSVFAdapter
from qgate.config import GateConfig, ConditioningVariant, FusionConfig
from qgate.filter import TrajectoryFilter

# Initialize the Grover TSVF adapter
adapter = GroverTSVFAdapter(
    backend=backend,          # AerSimulator() or IBM Runtime backend
    algorithm_mode="tsvf",    # "standard" or "tsvf"
    marked_state="10101",
    seed=42,
)

# Build and run
circuit = adapter.build_circuit(n_qubits=5, n_cycles=4)
raw_results = adapter.run(circuit, shots=8192)

# Parse results into ParityOutcome objects
outcomes = adapter.parse_results(raw_results, n_subsystems=5, n_cycles=4)

# Feed into qgate's trajectory filter pipeline
config = GateConfig(
    conditioning=ConditioningVariant.SCORE_FUSION,
    fusion=FusionConfig(alpha=0.5),
)
filt = TrajectoryFilter(config)
accepted, rejected, stats = filt.filter(outcomes)

# Extract success probability
prob, n_accepted = adapter.extract_target_probability(raw_results, postselect=True)
print(f"TSVF success probability: {prob:.4f} ({n_accepted} accepted shots)")