Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation

2026-05-14

AI Summary

This work addresses the high resource overhead of logical state encoding circuits in fault-tolerant quantum computing by presenting the first systematic optimization framework for arbitrary stabilizer codes. The authors formulate encoding synthesis as a stabilizer tableau search problem and integrate greedy and rollout heuristics with exact SMT-based synthesis and a modular encoder composition strategy. This approach substantially reduces both the number of two-qubit gates and circuit depth. Evaluated across multiple stabilizer codes, the method achieves up to a 43% reduction in two-qubit gate count and up to a 70% decrease in circuit depth. The implementation has been incorporated into the open-source Munich Quantum Toolkit.

Abstract

Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.

Problem

• encoding circuits
• fault-tolerant quantum computation
• stabilizer codes
• circuit synthesis
• resource overhead

Innovation

• encoder synthesis
• stabilizer codes
• fault-tolerant quantum computation
• circuit optimization
• SMT-based synthesis