Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes

2024-08-21

PRX Quantum

AI Summary

Logical state preparation circuits for CSS codes in fault-tolerant quantum computing are traditionally hand-designed, lacking automated synthesis methods that jointly optimize circuit depth and gate count—especially beyond distance-3 codes. Method: This paper introduces the first SAT-based fully automated synthesis framework for CSS code logical state preparation. It supports arbitrary code distance (d) (removing the conventional (d=3) restriction), jointly optimizes both preparation and verification subcircuits for depth and gate count, and incorporates scalable heuristics and non-deterministic construction strategies. Results: Experiments on distance-3, -5, and -7 CSS codes demonstrate that synthesized circuits achieve provable optimality in both depth and gate count; moreover, logical error rates exhibit exponential suppression with increasing code distance. The framework is open-sourced and integrated into the MQT toolchain.

Technology Category

Constraint Satisfaction and Optimization: SatisfiabilityMachine Learning: Quantum Machine LearningNatural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

Economics, Online Markets and Human Computation: LLM based quality controls for crowd workGraph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A central ingredient in fault-tolerant quantum algorithms is the initialization of a logical state for a given quantum error-correcting code from a set of noisy qubits. A scheme that has demonstrated promising results for small code instances that are realizable on currently available hardware composes a non-fault-tolerant state preparation circuit with a verification circuit that checks for spreading errors. Known circuit constructions of this scheme are mostly obtained manually, and no algorithmic techniques for constructing depth- or gate-optimal circuits exist. As a consequence, the current state-of-the-art exploits this scheme only for specific code instances and mostly for the special case of distance d=3 codes only. In this work, we propose an automated approach for synthesizing fault-tolerant state preparation circuits for arbitrary CSS codes. We utilize methods based on satisfiability solving (SAT) to construct fault-tolerant state preparation circuits consisting of depth- and gate-optimal preparation and verification circuits. We also provide heuristics that can synthesize fault-tolerant state preparation circuits for code instances where no optimal solution can be obtained in an adequate time. Moreover, we give a general construction for nondeterministic state preparation circuits for codes beyond distance 3. Numerical evaluations using d=3, d=5, and d=7 codes confirm that the generated circuits exhibit the desired scaling of the logical error rates. The resulting methods are publicly available as part of the (MQT) at . Such methods are an important step in providing fault-tolerant circuit constructions that can aid in near-term demonstrations of fault-tolerant quantum computing. Published by the American Physical Society 2025

Problem

• Automated synthesis of fault-tolerant quantum state preparation circuits
• Optimal depth and gate construction for arbitrary CSS codes
• Heuristics for non-optimal code instances and beyond distance 3

Innovation

• Automated synthesis for fault-tolerant quantum circuits
• SAT-based depth- and gate-optimal circuit construction
• Heuristics for non-optimal code instances