Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories

TL;DR

This paper introduces a method using SMT solvers to automate the design of fault-tolerant Clifford circuits and develops a decoding algorithm for merged color-surface codes, advancing quantum error correction techniques.

Contribution

It presents a novel approach employing SMT solvers for constructing fault-tolerant Clifford circuits and introduces a decoding algorithm for merged color-surface codes in quantum computing.

Findings

Successfully automates Clifford circuit construction with fault-tolerance properties

Develops a decoding algorithm for merged color-surface codes

Demonstrates application to magic-state-preparation protocols

Abstract

Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how solvers for satisfiability modulo theories (SMT solvers) can be used to automate the construction of Clifford circuits with certain fault-tolerance properties and we apply our techniques to a fault-tolerant magic-state-preparation protocol. Part of the protocol requires converting magic states encoded in the color code to magic states encoded in the surface code. Since the teleportation step involves decoding a color code merged with a surface code, we develop a decoding algorithm that is applicable to such codes.