Exceptional-Point-Anchored Variational Quantum Eigensolver for Non-Hermitian Many-Body Phase Diagrams: Bridging Skin-Effect Topology and Entanglement Criticality on NISQ Hardware
异常点锚定的非厄米多体相图变分量子本征求解器:在NISQ硬件上桥接趋肤效应拓扑与纠缠临界性
Akoramurthy B, Surendiran B, Xiaochun Cheng
AI总结 提出双正交变分量子本征求解器(B-VQE),通过独立变分电路表示左右本征态并优化双正交目标函数,结合异常点检测器和非厄米量子几何张量,实现NISQ硬件上非厄米多体系统的相图构建。
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我们引入了双正交变分量子本征求解器(B-VQE),一种用于在噪声中等规模量子(NISQ)硬件上模拟非厄米多体系统的量子算法。非厄米量子物质表现出异常点、宇称-时间对称性破缺和非厄米趋肤效应,然而现有的量子算法通常依赖于昂贵的后选择过程,并且不是为捕获双正交本征态而设计的。B-VQE采用独立的变分电路来表示非厄米哈密顿量的左、右本征态,并优化一个直接跟踪非厄米相变的双正交目标函数。该框架包含一个异常点检测器(EPD),通过硬件原生的并合度量识别异常点,以及一个非厄米量子几何张量(NH-QGT)读出,用于区分相互作用多体系统中的态拓扑和带拓扑特征。为了克服传统非厄米模拟相关的指数开销,我们开发了一种重要性采样缓解策略,消除了基于辅助位的后选择需求,同时保持多项式计算规模。我们在三个代表性模型上验证了该方法:非厄米Hubbard链、非厄米XXZ自旋链和二维非厄米(t)-(J)模型。B-VQE在无噪声模拟中实现了低于(5\ imes10^{-3})的相对能量误差,并高精度定位了异常点,同时解析了与局域化、量子疤痕和趋肤效应物理相关的相边界。这些结果确立了B-VQE作为一种可扩展的NISQ方法论,用于构建非厄米多体相图并探索开放量子系统中的拓扑和临界现象。
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.