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  • Open Access

Emulation of self-consistent non-Hermitian quantum formalisms

Mario Gonzalez, Karin Sim*, and R. Chitra†

  • Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland

  • *Contact author: simkarin@phys.ethz.ch
  • †Contact author: chitrar@ethz.ch
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Phys. Rev. Research 8, 023271 – Published 10 June, 2026

DOI: https://doi.org/10.1103/h2ls-9b5b

Abstract

Hermiticity has long been a cornerstone of quantum theory, ensuring the conservation of probability and real energy spectra. Recent advances in non-Hermitian physics have revealed that this requirement can be relaxed, giving rise to richer dynamics where the Hilbert space is endowed with a time-dependent inner product defined by a metric operator ρ(t). This dynamical metric fundamentally reshapes quantum predictions, yet direct access to it on physical devices has remained elusive. Here, we bridge this gap by presenting general, platform-agnostic operator-dilation schemes that embed the metric formalism into closed Hermitian systems. Our proposed framework converts any time-dependent non-Hermitian Hamiltonian into a larger unitary evolution, bringing the theory from a purely mathematical curiosity into the experimentally testable realm. This permits the first controlled study of PT-symmetric and symmetry-broken regimes at arbitrarily long timescales. We demonstrate the power of this approach on a digital quantum simulator, showing that cutting-edge questions about non-Hermiticity are already within reach of today's noisy intermediate-scale quantum processors. Our results provide the first direct evidence of a dynamically evolving metric in a single qubit, establishing a new paradigm for simulating non-Hermitian quantum mechanics and opening the door to its realization in the laboratory.

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Phys. Rev. Research 8, 023271– Published 10 June, 2026
  • Received 17 July 2025
  • Accepted 9 May 2026
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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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