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

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.

23 pages, 9 figures; v5 conforms to journal specifications

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• Scaling and logic in the color code on a superconducting quantum processor
• Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes
• A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
• Synchronization for Fault-Tolerant Quantum Computers