Non-Hermitian Quantum Adiabatic Algorithm

Zi-Bo Jin; Yi Zhang

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arXiv · 2607.15343

Non-Hermitian Quantum Adiabatic Algorithm

Zi-Bo Jin·Yi Zhang

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Abstract

Non-Hermitian systems offer new opportunities for quantum optimization and computation. Here, we show that non-Hermitian quantum adiabatic algorithms require not only a real, gapped spectrum, but also a stable pseudospectrum. We propose a novel framework by mapping non-unitary quantum circuits to local Hamiltonian paths, thereby preserving their optimization advantages and shallow depth. While a direct non-Hermitian extension of the Feynman-Kitaev construction suffers severe pseudospectral instability, our history-decoupled construction yields both a controlled pseudospectrum and a real, gapped spectrum. Using the CK benchmark family of maximum independent set problems, we demonstrate polynomial-evolution-time non-Hermitian adiabatic computation that remains robust against perturbations. We further discuss a feasible optical implementation using coupled waveguides with an auxiliary lossy channel. Our work establishes pseudospectral stability, alongside real, gapped spectra, as key principles and a practical route for non-Hermitian quantum adiabatic computation.

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Zi-Bo Jin, Yi Zhang. 2026-07-16. Non-Hermitian Quantum Adiabatic Algorithm. https://arxiv.org/abs/2607.15343

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