UXEB Decay Fitting

---
name: uXEB-decay-fitting
description: Evaluates the capability to characterize and quantify correlated noise in near-term quantum processors by measuring the exponential decay of average fidelity under random quantum circuits. Use when the user has predictions and gold and needs to compute uXEB decay fitting (ENR extraction).
metadata:
  skill_kind: metric
  source_arxiv: 2105.05232
  bibtex_key: liu2021benchmarking
  confidence: high
---

# uXEB-decay-fitting

> Benchmarking near-term quantum computers via random circuit sampling — Liu et al. (2021) (arXiv:2105.05232, 2021)

## What this evaluates

Evaluates the capability to characterize and quantify correlated noise in near-term quantum processors by measuring the exponential decay of average fidelity under random quantum circuits.

## Datasets

- **Virtual 10-qubit ring noise simulation** — total ?; splits: test (-1); repo https://github.com/0tt3r/QuaC

## Metrics

- `uXEB decay fitting (ENR extraction)` **(primary)** — range: other
  - Fits the unnormalized Cross Entropy Benchmarking (uXEB) score as a function of circuit depth to an exponential decay curve to extract the total Exponential Noise Rate (λ). Combined with T1 and Ramsey decay rates (Γ1, Γ2) to solve for the correlated ZZ noise rate γ3 = Γ1/4 + Γ2/4 - λ/n.

## Input / output format

**Input**: Two-qubit Haar random quantum circuits of varying depths (typically 12 to 40) executed on a 10-qubit ring topology under a known Lindblad noise model (T1, T_phi, correlated ZZ).

**Output**: Measured bitstring sampling frequencies from circuit executions, used to compute uXEB scores and fit the exponential decay curve.

## Scoring recipe

```python
# 1. Execute Haar random circuits at depths d = 12..40
# 2. Compute uXEB score for each depth
# 3. Fit uXEB decay to extract total ENR lambda
# 4. Measure T1 decay rate (Gamma1) and Ramsey decay rate (Gamma2)
# 5. Compute correlated noise rate: gamma3 = Gamma1/4 + Gamma2/4 - lambda/n
# Note: For high noise (alpha=1.0), fit depth range is restricted to 12..22
```

## Common pitfalls

- Fitting range must be shortened for high noise regimes (e.g., alpha=1.0 uses depths 12-22 instead of 12-40) to avoid saturation effects.
- Assumes uniform noise rates within each channel type across all qubits, which may not hold in real hardware.
- Ramsey decay (Gamma2) conflates T1, T_phi, and correlated ZZ noise, requiring careful decoupling via the RCS-derived lambda.

## Evidence (verbatim from paper)

> We extract the total ENR by using two-qubit Haar random circuits, fitting the resulting uXEB curve from depths 12 to 40, except in the case of α = 1.0, where we fit from 12 to 22, due to the large total ENR of 0.4. The result of performing this extraction is shown in Figure 8.

## Citation

```bibtex
@misc{liu2021benchmarking,
  title={Benchmarking near-term quantum computers via random circuit sampling},
  author={Liu et al. (2021)},
  year={2021},
  note={arXiv:2105.05232}
}
```

- arXiv: 2105.05232