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arxiv: 2606.18916 · v1 · pith:KZRL2ZLRnew · submitted 2026-06-17 · 🪐 quant-ph

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

Akoramurthy B , Surendiran B , Xiaochun Cheng This is my paper

Pith reviewed 2026-06-26 20:27 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-Hermitian systemsvariational quantum eigensolverexceptional pointsNISQ hardwarebiorthogonal eigenstatesskin effectphase diagramsopen quantum systems
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The pith

B-VQE uses separate variational circuits for left and right eigenstates to simulate non-Hermitian many-body systems on NISQ hardware.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Biorthogonal Variational Quantum Eigensolver to simulate non-Hermitian quantum systems that exhibit exceptional points, skin effects, and PT-symmetry breaking. It represents the left and right eigenstates with two independent parameterized circuits and minimizes a biorthogonal objective function instead of the usual Hermitian energy. An importance-sampling technique is added to eliminate the exponential sampling cost of conventional post-selection. The method also supplies an exceptional-point detector based on state coalescence and a non-Hermitian geometric tensor that reads topological features. A sympathetic reader cares because these systems appear in open quantum matter and topological sensors, yet existing quantum algorithms cannot handle their non-Hermitian character at scale.

Core claim

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 that identifies exceptional points through a hardware-native coalescence metric and a Non-Hermitian Quantum Geometric Tensor readout that distinguishes state-topological and band-topological signatures in interacting many-body systems. An importance-sampling mitigation strategy removes the need for ancilla-based post-selection while retaining polynomial computational scaling. On the non-Hermitian Hubbard chain, non-

What carries the argument

Independent variational circuits for the left and right eigenvectors optimized under a biorthogonal objective function, together with the Exceptional-Point Detector that uses a coalescence metric.

Load-bearing premise

The importance-sampling mitigation strategy removes the need for ancilla-based post-selection while retaining polynomial computational scaling.

What would settle it

A calculation on one of the tested chains showing that the variance of the importance-sampled estimator grows exponentially with system size would falsify the polynomial-scaling claim.

Figures

Figures reproduced from arXiv: 2606.18916 by Akoramurthy B, Surendiran B, Xiaochun Cheng.

Figure 1
Figure 1. Figure 1: Experimental demonstration of parity-time (PT) symmetry dynamics and exceptional-point detection using variational quantum eigensolvers on IBM quantum processors. (a) Hardware-efficient variational ansatz employed for the bi-variational quantum eigensolver (B-VQE), showing parameterized single-qubit rotations, entangling layers, and exceptional-point detection (EPD) measurement strategy. (b) PT-phase trans… view at source ↗
Figure 2
Figure 2. Figure 2: B-VQE circuit architecture and optimisation convergence (Qiskit-Aer simulation). (a) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: B-VQE energy accuracy across the PT transition (Qiskit-Aer noise-model simulation). (a) [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: EP detection via coalescence metric under hardware noise. (a) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Noise mitigation benchmarking (Qiskit-Aer). (a) [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: NH-Hubbard many-body phase diagram. (a) Colour map of the phase index ZW t, γt computed via B-VQE for N = 10 sites with Ne = 5 electrons (half-filling), U t = 4. Four phases are identified: ergodic (blue), NH-MBL (green), PT-broken ergodic (orange), and skin-localised (purple). Phase boundaries are shown as dashed lines: the MBL critical disorder Wcγ (blue dashed) and the EP/PT-breaking boundary γEPW (red … view at source ↗
Figure 7
Figure 7. Figure 7: Exceptional-point detection and biorthogonal Berry curvature. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Biorthogonal entanglement entropy. (a) Sbioℓ vs subsystem size ℓ for a chain of N = 20 sites in four distinct phases: ergodic (blue circles, volume-law), NH-MBL (green squares, logarithmic area-law), EP-critical (gold triangles, ceff3 · lnsin πℓN ), and PT-broken (red diamonds, exponentially suppressed). (b) Critical scaling of Sbio vs ln ξ (correlation length ξ) for three values of ceff: the unitary CFT … view at source ↗
Figure 9
Figure 9. Figure 9: NISQ resource benchmarking. (a) Post-selection success probability Psucc vs system size n for three strategies: standard post-selection (red, exponential decay), importance-sampling mitigation (blue, polynomial), and zero￾noise extrapolation (ZNE, green, roughly constant). The IS scheme (this work) maintains Psucc > 0.4 up to n = 16. (b) Circuit depth (left axis) and state fidelity F (right axis, dashed) v… view at source ↗
Figure 10
Figure 10. Figure 10: NH-XXZ many-body scar dynamics. (a) Loschmidt echo |Lt| 2 vs time for three phases: ergodic (blue, rapid decay), NH scar state (green, persistent revivals), and near-EP scar (gold, strongly enhanced revivals approaching unit height). The near-EP enhancement of coherent revivals is a direct consequence of the exceptional-point amplification of scar coherence. (b) Complex spectrum ImEn vs non-Hermiticity γJ… view at source ↗
Figure 11
Figure 11. Figure 11: NHSE and Fermi skin in the 2D NH t-J model. (a) Many-body density ⟨nx,y⟩ on a 6 × 6 cluster (γt = 0.8, J t = 0.3) showing the hallmark NHSE corner/edge accumulation. The exponential density gradient from the corner is quantified by the NHSE localisation length ξNHSE = 1| ln teff|. (b) Non-Hermitian band structure ReEk (blue solid) and ImEk (red dashed) for the ky = 0 cut. States below the chemical potenti… view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript introduces the Biorthogonal Variational Quantum Eigensolver (B-VQE) for non-Hermitian many-body systems. Independent variational circuits represent left and right eigenstates, optimized with a biorthogonal objective function; an Exceptional-Point Detector identifies coalescence points via a hardware-native metric, and a Non-Hermitian Quantum Geometric Tensor readout distinguishes topological signatures. An importance-sampling strategy is proposed to eliminate ancilla post-selection while preserving polynomial scaling. Validation on a non-Hermitian Hubbard chain, XXZ spin chain, and 2D (t-J) model reports relative energy errors below 5×10^{-3} and accurate exceptional-point and phase-boundary resolution, all on noise-free simulations.

Significance. If the biorthogonal optimization and importance-sampling mitigation prove robust, the method would enable direct access to non-Hermitian phase diagrams (skin-effect topology, entanglement criticality, quantum scars) on NISQ devices without exponential post-selection overhead, filling a gap between existing Hermitian VQE variants and open-system simulation needs.

major comments (1)
  1. [Abstract] Abstract: the positioning of B-VQE as a 'scalable NISQ methodology' rests on noise-free simulation metrics (relative energy errors <5×10^{-3}, EP location accuracy); no analysis or data is supplied on how the importance-sampling estimator behaves under decoherence, readout error, or gate noise, leaving the central hardware-applicability claim unanchored.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the positioning of B-VQE as a 'scalable NISQ methodology' rests on noise-free simulation metrics (relative energy errors <5×10^{-3}, EP location accuracy); no analysis or data is supplied on how the importance-sampling estimator behaves under decoherence, readout error, or gate noise, leaving the central hardware-applicability claim unanchored.

    Authors: We agree that the manuscript reports results exclusively from noise-free simulations and supplies no numerical analysis of the importance-sampling estimator under decoherence, readout error, or gate noise. Consequently the abstract's description of B-VQE as a 'scalable NISQ methodology' is not anchored by hardware-relevant data. We will revise the abstract to state that the method is validated on ideal circuits and that its behavior under realistic NISQ noise remains to be studied. We will also add a short paragraph in the conclusions outlining how the polynomial scaling of the importance sampler may interact with noise and noting this as a direction for future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript introduces B-VQE via independent left/right variational circuits, a biorthogonal objective, EPD coalescence metric, NH-QGT readout, and importance-sampling mitigation, then reports numerical accuracies on three models. No equations appear in the supplied text, so no derivation step can be shown to reduce by construction to a fitted input, self-definition, or self-citation chain. The central claims rest on newly stated algorithmic elements whose outputs are not tautological to the inputs; the absence of any quoted reduction satisfies the hard rule against manufacturing circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; all technical details are absent.

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Reference graph

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