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

Published 29 Apr 2024 in quant-ph and cs.ET | (2404.18369v3)

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.

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Citations (9)
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Summary

  • The paper introduces LaSsynth, which encodes lattice surgery designs into SAT problems to systematically optimize quantum computing subroutines.
  • The paper demonstrates notable spacetime volume reductions—up to 18%—compared to conventional human-crafted designs for T-factories.
  • The paper paves the way for automated, scalable design improvements in fault-tolerant quantum computing, bridging theory and practical hardware implementation.

Optimizing Lattice Surgery Subroutines Using LaSsynth and SAT Solvers

Introduction

Lattice surgery is a prevalent scheme for fault-tolerant quantum computing (FTQC) due to its comparatively low resource overhead. Traditionally, lattice surgery operations, such as merges and splits of code patches, have been graphically represented and manually optimized by researchers. This method, although intuitive at smaller scales, becomes less feasible as system complexity increases. The presented paper introduces a systematic approach for synthesizing and optimizing lattice surgery subroutines (LaS) using a custom tool, LaSsynth, which fully leverages the power of satisfiability (SAT) solvers to explore the vast design space systematically.

LaSsynth: A Scalpel for Lattice Surgery Designs

LaSsynth encodes the design of lattice surgery subroutines into a SAT problem, transforming optimization into a query for SAT solvers. The tool starts with a reference design, iteratively shrinking its spacetime volume until an optimal volume is achieved, provided that the instances remain satisfiable. This approach avoids heuristic human-design biases, uncovering counterintuitive, optimal designs that might be overlooked otherwise.

Key Contributions

  • Representation and Formulation: LaSsynth uses a novel representation, LaSre, allowing intricate operations between any adjacent patches in the plane at any time. This flexibility surpasses traditional lattice surgery operations represented by fixed, simplistic graphical models (tiles and bridges).
  • Functional Implementation: LaSsynth efficiently transforms the LaS synthesis problem into a SAT instance. This encompasses creating constraints for both structural validity and correct implementation of specified stabilizers, dictated through correlation surfaces.
  • Results: Utilizing this approach, LaSsynth has demonstrated a significant reduction in both spacetime volumes and design complexity over existing human-crafted solutions. For instance, it achieved volume reductions of 8\% and 18\% over two state-of-the-art designs for the 15-to-1 T-factory.

Implications and Future Prospects

The development of LaSsynth signifies a pivotal move towards fully automated, optimizable designs in quantum computing hardware. By offloading the cognitive burden of design onto computationally efficient algorithms, researchers can scale operations more effectively, increasing both the reliability and feasibility of larger quantum systems. This approach is particularly beneficial in optimizing frequently used subroutines, which compounds the overall efficiency in larger FTQC protocols.

The broader adoption of tools like LaSsynth could stimulate further exploration into different quantum computing paradigms and architectures, including testing the efficiency of quasi-1D architectures or small footprint quantum chips. Furthermore, ongoing improvements to the underlying SAT solvers or integration with higher-level quantum compilers could enhance the scalability and appeal of this method.

Concluding Thoughts

In sum, the study encapsulates a significant advance in quantum compiler technology by introducing an innovative, scalable tool for optimizing lattice surgery subroutines through SAT solvers. As the quantum computing field moves towards more complex and large-scale implementations, tools like LaSsynth will be crucial in bridging the gap between theoretical models and practical, deployable quantum systems. The reduction in spacetime volume not only improves resource efficiency but also paves the way for more sophisticated designs and optimizations in fault-tolerant quantum computing.

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