Simple logical quantum computation with concatenated symplectic double codes

TL;DR

This paper introduces concatenated symplectic double codes that enable fault-tolerant quantum gates with simple circuits, showing promising simulation results for quantum error correction at realistic error rates.

Contribution

It presents a novel concatenated symplectic double code construction that simplifies fault-tolerant logical gate implementation using only basic physical operations.

Findings

Achieves full Clifford group with simple circuits and relabeling.

Shows promising error correction performance at near state-of-the-art error rates.

Demonstrates potential for scalable quantum computing applications.

Abstract

There have been significant recent advances in constructing theoretical and practical quantum error correcting codes that function well as quantum memories; however, performing fault-tolerant logical gates on these codes is less studied, and the protocols that do exist often require significant complexity. Building off the symplectic double construction, we investigate concatenated symplectic double codes, which have a rich set of logical gates implementable using only physical single-qubit gates and qubit relabeling. Combined with an injected logical phase gate, the full Clifford group on a single codeblock is achieved through a functionally simple circuit. We perform circuit-level simulations of state preparation and quantum error correction on these codes and show that they have promising performance at near state-of-the-art physical error rates. As such, we argue that concatenated symplectic double codes are strong contenders as the underlying computational code on medium- to large-scale quantum computers.