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Quantum Monte Carlo methods and stabilizer states

Bhilahari Jeevanesan*

  • *Contact author: billa.j@gmail.com
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Phys. Rev. A 112, 012603 – Published 2 July, 2025

DOI: https://doi.org/10.1103/8jmy-sj3f

Abstract

The quantum Monte Carlo technique known as the stochastic series expansion (SSE) relies on a crucial no-branching condition: the SSE sampling is carried out in the computational basis, and the no-branching assumption ensures that superpositions of basis states do not appear when operators are applied. Without this proviso, the number of complex amplitudes would grow exponentially with the number of qubits and would eventually overwhelm the memory and processing power of a classical computer. However, the action of Clifford group elements on stabilizer states can be very efficiently described without resorting to an amplitude description. We explore how stabilizer states allow an extension of the SSE technique, and we give an example of a toy model that can be studied in this way. The method is also illustrated using the transverse-field Ising model.

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Phys. Rev. A 112, 012603– Published 2 July, 2025
  • Received 1 November 2024
  • Revised 5 May 2025
  • Accepted 13 June 2025
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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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