τ-chrono — Bayesian noise tracking for quantum circuits

The Result

We applied the Petz recovery map to predict quantum circuit noise. On QuTech Starmon-5 / Tuna-9 superconducting hardware:

46%

Improvement at depth 50
over independent gate model

60.4%

Bernstein-Vazirani
improvement

0

Training circuits
required

~10 min

Deployment time
from calibration data

Depth Scaling

Improvement grows with circuit depth. Deeper circuits have more correlated noise for the Petz map to exploit.

Why It Works

Independent noise models assume each gate fails independently. In reality, noise saturates — a qubit that’s already noisy can’t get much noisier.

The Petz recovery map (Petz, 1986) provides the mathematically correct way to track this saturation through the circuit. Instead of multiplying error rates, it uses Bayesian retrodiction to update noise estimates conditioned on what has already happened.

Applications

H₂

Molecular Simulation (VQE)

Users can run deeper variational circuits with better noise estimates, leading to more accurate molecular energy calculations.

BV

Bernstein-Vazirani

More accurate success probability prediction for structured quantum algorithms, validated at 60.4% improvement.

?

Circuit Pre-screening

Know before you run — avoid wasting QPU time on circuits that won’t produce useful results at the target depth.

Limitations

We believe in honest reporting. Here is what this approach cannot do.

Tested on small, noisy hardware (QuTech Tuna-9, 5 qubits). Results on larger processors are unverified.
On low-noise hardware (Google Willow), improvement is only ~2.5%. The benefit scales with noise magnitude.
Not a replacement for quantum error correction or error mitigation. This is a noise prediction tool.
Improvement depends on the degree of noise correlation in the hardware. Independent noise yields no benefit.

How to Use

Three lines of code. No training data needed.

      # Install

      pip install tau-chrono

      # Use

      from tau_chrono import PetzPredictor

      predictor = PetzPredictor(backend)

      fidelity = predictor.predict(circuit)