Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively-shallow quantum circuits, and it is also robust against the effect of quantum noises.
Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively-shallow quantum circuits, and it is also robust against the effect of quantum noises.
Nonequilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying nonequilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of nonequilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively shallow quantum circuits, and it is also robust against the effect of quantum noises.
Abstract Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum (NISQ) computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum eigensolver (VQE) is one of the aforementioned algorithms designed to determine the ground-state of many-body Hamiltonians. Here, we apply the VQE to study the ground-state properties of N -component fermions. With such knowledge, we study the persistent current of interacting SU( N ) fermions, which is employed to reliably map out the different quantum phases of the system. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on NISQ computers.
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.
Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ansatze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. In this paper, we introduce the ``excited iterative qubit-excitation-based variational quantum eigensolver'' (e-IQEB-VQE) protocol to calculate molecular excited state energies. The e-IQEB-VQE constructs efficient problem-tailored ansatze by iteratively appending evolutions of qubit excitation operators. The e-IQEB-VQE is an adaptation of the IQEB-VQE protocol, designed to be less dependent on the choice of an initial reference state. We perform classical numerical simulations for LiH and BeH2 to benchmark the performance of the IQEB-VQE. We demonstrate that the e-IQEB-VQE can construct highly accurate ansatze that require at least an order of magnitude fewer CNOTs than standard fixed UCC ansatze, such as the UCCSD and the GUCCSD.
Quantum computers have the potential to deliver speed-ups for solving certain important problems that are intractable for classical counterparts, making them a promising avenue for advancing modern computation. However, many quantum algorithms require deep quantum circuits, which are challenging to implement on current noisy devices. To address this limitation, variational quantum algorithms (VQAs) have been actively developed, enabling practical quantum computing in the noisy intermediate-scale quantum (NISQ) era. Among them, the variational quantum eigensolver (VQE) stands out as a leading approach for solving problems in quantum chemistry, many-body physics, and even integer factorization. The VQE algorithm can be implemented on various quantum hardware platforms, including photonic systems, quantum dots, trapped ions, neutral atoms, and superconducting circuits. In particular, photonic platforms offer several advantages: they operate at room temperature, exhibit low decoherence, and support multiple degrees of freedom, making them suitable for scalable, high-dimensional quantum computation. Here we present methodologies for realizing VQE on photonic systems, highlighting their potential for practical quantum computing. We first provide a theoretical overview of the VQE framework, focusing on the procedure for variationally estimating ground state energies. We then explore how photonic systems can implement these processes, showing that a wide variety of problems can be addressed using either multiple qubit states or a single qudit state.
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) hardware to estimate eigenvalues of many-body Hamiltonians. Unlike fully quantum approaches such as quantum phase estimation (QPE), VQE trades deep coherent circuits for repeated state preparation, measurement, and classical optimization, making it more compatible with limited qubit counts and finite coherence times. Recent developments have focused on reducing quantum resource requirements while retaining chemically meaningful wavefunction structure. In this paper, we examine recent progress in VQE methods for molecular electronic structure with an emphasis on three themes: (i) strategies for circuit and ansatz complexity reduction, including adaptive and selectively screened approaches, (ii) chemically motivated workflows that combine VQE with orbital optimization, fragmentation, and localized active-space ideas to better address strong correlation, and (iii) extensions of VQE to excited-state calculations. Throughout, we emphasize the tradeoffs among parameter count, gate depth, symmetry preservation, measurement overhead, and classical preprocessing, and discuss where these approaches may become most useful for chemically challenging active spaces. We also highlight benchmarking considerations for assessing both accuracy and resource requirements, and conclude with a perspective on regimes in which VQE may offer the greatest long-term value, particularly multireference active spaces and low-lying excited-state manifolds.