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  • Open Access

Minimizing classical resources in variational measurement-based quantum computation for generative modeling

Arunava Majumder*, Hendrik Poulsen Nautrup, and Hans J. Briegel

  • *Contact author: arunava.majumder@uibk.ac.at
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Phys. Rev. A 114, 052420 – Published 9 November, 2026

DOI: https://doi.org/10.1103/5hzz-v77n

Abstract

Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared with the unitary model, scaling as N×D, where N is the number of logical qubits (width) and D is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be represented by the corresponding unitary model.

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Outline

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Phys. Rev. A 114, 052420– Published 9 November, 2026
  • Received 19 April 2026
  • Revised 3 August 2026
  • Accepted 20 October 2026
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