Error correction of transversal CNOT gates for scalable surface code computation

TL;DR

This paper evaluates and benchmarks decoding strategies for transversal CNOT gates in surface codes, crucial for scalable fault-tolerant quantum computing, highlighting a low-complexity decoder with comparable thresholds to existing methods.

Contribution

It introduces a low-complexity MWPM-based decoder for transversal CNOT gates that matches the performance of standard surface code decoders and compares different decoding strategies for scalable quantum computation.

Findings

The MWPM-based decoder achieves the same threshold as the standard decoder.

Tailored decoding improves performance for transversal teleportation circuits.

Comparison shows differences between lattice surgery and transversal operations under noise models.

Abstract

Recent experimental advances have made it possible to implement logical multi-qubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-NOT (tCNOT) gate on two surface codes introduces correlated errors across the code blocks and thus requires modified decoding strategies compared to established methods of decoding surface code quantum memory (SCQM) or lattice surgery operations. In this work, we examine and benchmark the performance of three different decoding strategies for the tCNOT for scalable, fault-tolerant quantum computation. In particular, we present a low-complexity decoder based on minimum-weight perfect matching (MWPM) that achieves the same threshold as the SCQM MWPM decoder. We extend our analysis with a study of tailored decoding of a transversal teleportation circuit, along with a comparison between the performance of lattice surgery and transversal operations under Pauli and erasure noise models. Our investigation works towards systematic estimation of the cost of implementing large-scale quantum algorithms based on transversal gates in the surface code.