A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing

TL;DR

This paper introduces LaSsynth, a SAT-based synthesizer that optimizes lattice-surgery subroutines in surface-code quantum computing, significantly reducing their spacetime volume and improving fault-tolerance efficiency.

Contribution

It formulates LaS design as a SAT problem and develops LaSsynth, enabling exhaustive search for optimal, minimal-volume lattice-surgery subroutines in surface-code quantum computing.

Findings

Achieves 8% volume reduction over existing designs.

Achieves 18% volume reduction over existing designs.

Enables exhaustive exploration for optimal LaS designs.

Abstract

Quantum error correction is necessary for large-scale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to minimize the overall spacetime volume of FTQC. In this study, we define the variables to represent LaS and the constraints on these variables. Leveraging this formulation, we develop a synthesizer for LaS, LaSsynth, that encodes a LaS construction problem into a SAT instance, subsequently querying SAT solvers for a solution. Starting from a baseline design, we can gradually invoke the solver with shrinking spacetime volume to derive more compact designs. Due to our foundational formulation and the use of SAT solvers, LaSsynth can exhaustively explore the design space, yielding optimal designs in volume. For example, it achieves 8% and 18% volume reduction respectively over two states-of-the-art human designs for the 15-to-1 T-factory, a bottleneck in FTQC.