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Qudit noisy stabilizer formalism

Paul Aigner, Maria Flors Mor-Ruiz, and Wolfgang Dür

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Phys. Rev. A 112, 022402 – Published 1 August, 2025

DOI: https://doi.org/10.1103/gqfw-x72s

Abstract

We introduce the qudit noisy stabilizer formalism, a framework for efficiently describing the evolution of stabilizer states in prime-power dimensions subject to generalized Pauli-diagonal noise under Clifford operations and generalized Pauli measurements. For arbitrary dimensions, the formalism remains applicable, though restricted to a subset of stabilizer states and operations. The computational complexity scales linearly with the number of qudits in the initial state and exponentially with the number of qudits in the final state. This ensures that when noisy qudit stabilizer states evolve via generalized Pauli measurements and Clifford operations to generate multipartite entangled states of a few qudits, their description remains efficient. We demonstrate this by analyzing the generation of a generalized Bell pair from a noisy linear cluster state subject to two distinct noise sources acting on each of the qudits.

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Phys. Rev. A 112, 022402– Published 1 August, 2025
  • Received 13 May 2025
  • Accepted 9 July 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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