Exceptional-Point-Anchored Variational Quantum Eigensolver for Non-Hermitian Many-Body Phase Diagrams: Bridging Skin-Effect Topology and Entanglement Criticality on NISQ Hardware

• URL: http://arxiv.org/abs/2606.18916v1
• Date: Wed, 17 Jun 2026 10:43:26 GMT
• Title: Exceptional-Point-Anchored Variational Quantum Eigensolver for Non-Hermitian Many-Body Phase Diagrams: Bridging Skin-Effect Topology and Entanglement Criticality on NISQ Hardware
• Abstract summary: We introduce the Biorthogonal Variational Quantum Eigensolver (B-VQE), a quantum algorithm for simulating non-Hermitian many-body systems.<n>Non-Hermitian quantum matter exhibits exceptional points, parity-time symmetry breaking, and non-Hermitian skin effects.
• Score: 5.006594927582348
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce the Biorthogonal Variational Quantum Eigensolver (B-VQE), a quantum algorithm for simulating non-Hermitian many-body systems on noisy intermediate-scale quantum (NISQ) hardware. Non-Hermitian quantum matter exhibits exceptional points, parity-time symmetry breaking, and non-Hermitian skin effects, yet existing quantum algorithms often rely on costly post-selection procedures and are not designed to capture biorthogonal eigenstates. B-VQE employs independent variational circuits to represent the left and right eigenstates of a non-Hermitian Hamiltonian and optimizes a biorthogonal objective function that directly tracks non-Hermitian phase transitions. The framework incorporates an Exceptional-Point Detector (EPD) that identifies exceptional points through a hardware-native coalescence metric and a Non-Hermitian Quantum Geometric Tensor (NH-QGT) readout that distinguishes state-topological and band-topological signatures in interacting many-body systems. To overcome the exponential overhead associated with conventional non-Hermitian simulation, we develop an importance-sampling mitigation strategy that removes the need for ancilla-based post-selection while retaining polynomial computational scaling. We validate the approach on three representative models: a non-Hermitian Hubbard chain, a non-Hermitian XXZ spin chain, and a two-dimensional non-Hermitian (t)-(J) model. B-VQE achieves relative energy errors below (5\times10^{-3}) and locates exceptional points with high accuracy on noise-free simulations while resolving phase boundaries associated with localization, quantum scars, and skin-effect physics. These results establish B-VQE as a scalable NISQ methodology for constructing non-Hermitian many-body phase diagrams and exploring topological and critical phenomena in open quantum systems.

Related papers

• Detecting quantum phase transitions via shallow variational quantum circuits [0.0]
  A variational quantum eigensolver (VQE) determines critical points by contrasting variational energies optimized from reference states of distinct phases.<n>We demonstrate that, whenever dual anstze are employed, Delta-VQE invariably detects the self-dual points rather than the true criticality.<n>Our results establish that, while Delta-VQE provides a resource-efficient probe of quantum criticality without requiring precise ground-state preparation, its diagnostic power is fundamentally contingent upon the judicious selection of physically representative anstze.
  arXiv  Detail & Related papers  (2026-07-28T06:47:35Z)
• SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians [42.007194397302825]
  Ground state search is central to quantum computing.<n>We present SpinGQE, an extension of the Generative Quantum Eigensolver framework to spin Hamiltonians.<n>We employ a transformer-based decoder to learn over quantum circuits that produce low-energy states.
  arXiv  Detail & Related papers  (2026-03-25T13:38:15Z)
• Digital Quantum Simulation of the Holstein-Primakoff Transformation on Noisy Qubits [40.8066152850216]
  We study the digital quantum simulation of bosonic modes on a cloud-based superconducting quantum processor.<n>We examine the interplay between algorithmic and hardware-induced errors to identify optimal simulation parameters.
  arXiv  Detail & Related papers  (2026-02-19T20:14:04Z)
• Symmetry-Preserving Variational Quantum Simulation of the Heisenberg Spin Chain on Noisy Quantum Hardware [0.0]
  We investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed variational circuits.<n>Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior.
  arXiv  Detail & Related papers  (2025-12-28T17:17:24Z)
• Path integral approach to quantum thermalization [39.25860941747971]
  We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems.<n>We show that it is capable of describing a wide range of system classes and disorder models.<n>We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems.
  arXiv  Detail & Related papers  (2025-09-07T12:10:48Z)
• Engineering Non-Hermitian Quantum Evolution Using a Hermitian Bath Environment [31.392358417707825]
  Engineering quantum bath networks through non-Hermitian subsystem Hamiltonians has emerged as a promising strategy for qubit cooling, state stabilization, and fault-tolerant quantum computation.<n>We introduce a systematic framework for constructing non-Hermitian subsystems within entirely Hermitian photonic platforms.<n>In particular, controlled exponential decay absorption without actual loss is realized in finite 1-D waveguide chains through discrete-to-continuum coupling and Lanczos transformations.
  arXiv  Detail & Related papers  (2025-07-22T07:14:05Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations [44.13836547616739]
  Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers.<n> choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.<n>Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem.
  arXiv  Detail & Related papers  (2025-06-04T08:30:35Z)
• Robust Simulations of Many-Body Symmetry-Protected Topological Phase Transitions on a Quantum Processor [7.515748475237134]
  Topology and symmetry play critical roles in characterizing quantum phases of matter.<n>Recent advancements have unveiled symmetry-protected topological (SPT) phases in many-body systems.<n>We demonstrate the robust simulation of many-body ground states of an Ising-cluster model on a quantum computer.
  arXiv  Detail & Related papers  (2025-03-11T18:00:02Z)
• Eigenstate solutions of the Fermi-Hubbard model via symmetry-enhanced variational quantum eigensolver [7.079422962805218]
  Variational Quantum Eigensolver (VQE) is an important tool for effective quantum computing.<n>By incorporating symmetries into the quantum circuits and loss function, we find that both the ground state and excited state calculations are improved greatly.
  arXiv  Detail & Related papers  (2025-01-27T09:55:18Z)
• Exponential quantum advantages for practical non-Hermitian eigenproblems [9.59420259768862]
  We develop a quantum algorithm to address general non-Hermitian eigenvalue problems.<n>Our method combines a fuzzy quantum eigenvalue detector with a divide-and-conquer strategy to efficiently isolate relevant eigenvalues.<n>We discuss the broad applications in detecting spontaneous $PT$-symmetry breaking, estimating Liouvillian gaps, and analyzing classical Markov processes.
  arXiv  Detail & Related papers  (2024-01-22T16:29:08Z)
• Non-adiabatic holonomies as photonic quantum gates [36.136619420474766]
  We present the quantum-optical realization of non-adiabatic holonomies that can be used as single-qubit quantum gates. The inherent non-adiabaticity of the structures paves the way for unprecedented miniaturization.
  arXiv  Detail & Related papers  (2024-01-08T16:44:45Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences [0.0]
  We show the usefulness of multiple quantum coherences for probing equilibrium phase transitions in non-Hermitian systems. Our results have applications to non-Hermitian quantum sensing, quantum thermodynamics, and in the study of the non-Hermitian skin effect.
  arXiv  Detail & Related papers  (2021-09-06T14:30:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.