An iterative transversal CNOT decoder

TL;DR

This paper introduces an iterative decoder for transversal CNOT gates in quantum computing, effectively managing correlated errors and maintaining logical error rates under circuit-level noise with minimal code cycles.

Contribution

It presents a novel multi-pass iterative decoding method that handles correlated errors in transversal CNOT operations, preserving error thresholds with few code cycles.

Findings

Threshold persists under circuit-level noise with O(1) code cycles.

Logical error rate scales as p^{floor(d/2)} for a distance d rotated surface code.

Decoder effectively mitigates error propagation in transversal CNOT gates.

Abstract

Modern platforms for potential qubit candidates, such as trapped ions or neutral atoms, allow long range connectivity between distant physical qubits through shuttling. This opens up an avenue for transversal logical CNOT gates between distant logical qubits, whereby physical CNOT gates are performed between each corresponding physical qubit on the control and target logical qubits. However, the transversal CNOT can propagate errors from one logical qubit to another, leading to correlated errors between logical qubits. We have developed a multi-pass iterative decoder that decodes each logical qubit separately to deal with this correlated error. We show that under circuit-level noise and only $\mathcal{O}(1)$ code cycles, a threshold can still persist, and the logical error rate will not be significantly degraded, matching the sub-threshold logical error rate scaling of $p^{\lfloor\frac{d}{2}\rfloor}$ for a distance $d$ rotated surface code.