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  • Featured in Physics
  • Open Access

Efficient Simulation of Logical Magic State Preparation Protocols

Samyak Surti1,*, Lucas Daguerre2, and Isaac H. Kim1

  • *Contact author: spsurti@ucdavis.edu
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PRX Quantum 7, 020329 – Published 14 May, 2026

DOI: https://doi.org/10.1103/fby6-xjbm

Abstract

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

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synopsis

A Magic Trick for Simulating Quantum Computers

Published 14 May, 2026

A new technique efficiently simulates a crucial process in a fault-tolerant quantum computer: the preparation of so-called logical magic states.

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Popular Summary

Quantum computers are noisy, however, reliable computation is possible with the aid of quantum error correcting (QEC) codes. General-purpose computation on QEC codes requires supporting gates of two types: Clifford and non-Clifford. While Clifford gates are typically cheap to implement, non-Clifford gates are resource-intensive, since they are often realized by consuming high-quality “magic states.” To this end, various magic state preparation (MSP) protocols have been proposed and experimentally demonstrated at small scale; however, larger protocols are beyond current device capabilities. These protocols contain many non-Clifford gates, which cannot be simulated efficiently, even with the best-known simulation techniques. To address this issue, we propose an efficient classical simulation technique applicable to a large class of MSP protocols, which relies on the propagation of errors to the end of the circuit. Our work provides an efficient method to benchmark MSP protocols that will likely influence the development of large-scale quantum computers.

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PRX Quantum 7, 020329– Published 14 May, 2026
  • Received 22 January 2026
  • Revised 12 March 2026
  • Accepted 26 March 2026
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