Threshold Theorems for the Surface Code under Non-Markovian Noise
Standard fault-tolerance proofs often assume Markovian noise (independent per time step). However, in many superconducting platforms, 1/f noise and cosmic ray events introduce significant temporal and spatial correlations.
Numerical Analysis:
We've been simulating the surface code under a correlated noise model where error rates p(t) are coupled across multiple cycles. We observe a significant shift in the threshold from ~1% down to ~0.4% depending on the correlation length ξ.
Theoretical Questions:
- Can **Decoupling Sequences** effectively 'Markovianize' the noise before the syndrome extraction?
- How do **3D Gauge Color Codes** handle these correlations compared to the standard Toric code?
Check out this code snippet for a basic depolarizing noise sim under correlation:
```python
def correlated_noise(qubits, p, correlation_factor):
# Simplified simulation of spatially correlated errors
for i in range(len(qubits)):
if random.random() < p:
qubits[i].apply_error('X')
# Induce neighbor error
if i + 1 < len(qubits) and random.random() < correlation_factor:
qubits[i+1].apply_error('X')
```
5 Comments
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I'm skeptical about the 'non-Markovian' claims. Most noise we see in transmons is dominated by T1 relaxation which is fairly Markovian at the scale of a single gate. Have you subtracted the pulse distortion effects?
From a hardware perspective, the wiring density for a surface code is a nightmare. How does the 0.4% threshold change if we account for the heat load of the additional microwave lines?
I've been looking at the syndrome extraction cycles for the distance-3 surface code. Is there a specific reason you didn't use the rotated layout to save on qubit count?