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  • Open Access

Optimizing fault-tolerant cat state preparation

Tom Peham1,*, Erik Weilandt1,†, and Robert Wille1,2,‡

  • *Contact author: tom.peham@tum.de
  • †Contact author: erik.weilandt@tum.de
  • ‡Contact author: robert.wille@tum.de
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Phys. Rev. A 113, 062426 – Published 9 June, 2026

DOI: https://doi.org/10.1103/13v7-n843

Abstract

Cat states are an important resource for fault-tolerant quantum computing, where they serve as building blocks for a variety of fault-tolerant primitives. Consequently, the ability to prepare high-quality cat states at large fault distances is essential. While optimizations for low fault distances or small numbers of qubits exist, higher fault distances can be achieved via generalized constructions with potentially suboptimal circuit sizes. In this work, we propose a cat state preparation scheme based on preparing two cat states with low-depth circuits, followed by a transversal cnot and measurement of one of the states. This scheme prepares w-qubit cat states fault tolerantly up to fault distances of 9 using ⌈log2w⌉+1 depth and at most 3w−2 cnots and 2w qubits. We discuss that the combinatorially challenging aspect of this construction is the precise wiring of the transversal cnot and propose three methods for finding these: two based on Satisfiability Modulo Theory solving and one heuristic search based on a local repair strategy. Numerical evaluations show that our circuits achieve a high fault distance while requiring fewer resources than generalized constructions.

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Outline

Information

Phys. Rev. A 113, 062426– Published 9 June, 2026
  • Received 10 January 2026
  • Revised 20 April 2026
  • Accepted 29 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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