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Quantum Optimization Open Quantum Systems Decoherence

Decoder-Consistent Hamiltonians for POVM-Based Quantum Relaxations

arXiv

Authors: Takayuki Suzuki

Year

2026

Paper ID

67817

Status

Preprint

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Abstract

In compression-based quantum relaxations like QRAO, classical variables are encoded into qubits and decoded after optimization. We formalize that the choice of the quantum Hamiltonian is fundamentally determined by this decoder. By representing the decoder as a POVM, we define a unique decoder-consistent Hamiltonian via the pullback of the post-decoding expected objective value. Using this framework, we reveal that standard QRAO Hamiltonians are inconsistent for certain mixed-degree quadratic functions, and we provide new approximation guarantees for the MaxCut problem based directly on POVM decoder design.

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This paper contributes to the Quantum Optimization research area in the Quantum Articles archive.
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In compression-based quantum relaxations like QRAO, classical variables are encoded into qubits and decoded after optimization.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2606.05604 [2] arXiv https://arxiv.org/abs/2606.05604 [3] Publisher https://arxiv.org/abs/2606.05604

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External citation index: OpenAlex citation signal • updated 2026-06-14 05:53:04

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