Hybrid Quantum-Classical Eigensolver with Real-Space Sampling and Symmetric Subspace Measurements

• URL: http://arxiv.org/abs/2510.19219v1
• Date: Wed, 22 Oct 2025 04:03:40 GMT
• Title: Hybrid Quantum-Classical Eigensolver with Real-Space Sampling and Symmetric Subspace Measurements
• Authors: Lei Xu, Ling Wang,
• Abstract summary: We propose a hybrid quantum-classical eigensolver to address the computational challenges of strongly correlated quantum many-body systems.<n>Our approach combines real-space sampling of tensor-network-bridged quantum circuits with symmetric subspace measurements.
• Score: 7.924603170890832
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a hybrid quantum-classical eigensolver to address the computational challenges of simulating strongly correlated quantum many-body systems, where the exponential growth of the Hilbert space and extensive entanglement render classical methods intractable. Our approach combines real-space sampling of tensor-network-bridged quantum circuits with symmetric subspace measurements, effectively constraining the wavefunction within a substaintially reduced Hilbert space for efficient and scalable simulations of versatile target states. The system is partitioned into equal-sized subsystems, where quantum circuits capture local entanglement and tensor networks reconnect them to recover global correlations, thereby overcoming partition-induced limitations. Symmetric subspace measurements exploit point-group symmetries through a many-to-one mapping that aggregates equivalent real-space configurations into a single symmetric state, effectively enhancing real-space bipartition entanglement while elimilating redundant degrees of freedom. The tensor network further extends this connectivity across circuits, restoring global entanglement and correlation, while simultaneously enabling generative sampling for efficient optimization. As a proof of concept, we apply the method to the periodic $J_1\!-\!J_2$ antiferromagnetic Heisenberg model in one and two dimensions, incorporating translation, reflection, and inversion symmetries. With a small matrix product state bond dimension of up to 6, the method achieves an absolute energy error of $10^{-5}$ for a 64-site periodic chain and a $6\times6$ torus after bond-dimension extrapolation. These results validate the accuracy and efficiency of the hybrid eigensolver and demonstrate its strong potential for scalable quantum simulations of strongly correlated systems.

Related papers

• Engineering quantum criticality and dynamics on an analog-digital simulator [26.76525389323686]
  We use coherent mapping between the Rydberg and hyperfine qubits in a neutral atom array simulator to engineer and probe complex quantum dynamics.<n>We first demonstrate dynamical engineering of ring-exchange and particle hopping dynamics via Floquet driving.<n>We employ closed-loop optimization to target an out-of-equilibrium critical quantum spin liquid of the Rokhsar-Kivelson type.
  arXiv  Detail & Related papers  (2026-02-20T19:00:00Z)
• Quantum channel for modeling spin-motion dephasing in Rydberg chains [44.99833362998488]
  We introduce a quantum channel to model the dissipative dynamics resulting from the coupling between spin and motional degrees of freedom in chains of neutral atoms with Rydberg interactions.<n>We benchmark the accuracy of our approach against exact diagonalization for small systems, identifying its regime of validity and the onset of perturbative breakdown.<n>We then apply the quantum channel to compute fidelity loss during transport of single-spin excitations across extended Rydberg chains in intractable regimes via exact diagonalization.
  arXiv  Detail & Related papers  (2025-06-30T17:37:38Z)
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions [36.94429692322632]
  We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment.<n>We find sufficient conditions under which dynamical decoupling works for such systems.<n>Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method [0.0]
  Nonequilibrium dynamics of highly-controlled quantum systems is a challenging issue in statistical physics.<n>We develop a discrete phase-space approach for general SU($N$) spin systems.<n>We numerically demonstrate that the cluster discrete truncated Wigner approximation can reproduce key results in a recent experiment.
  arXiv  Detail & Related papers  (2024-04-29T11:08:44Z)
• A quantum eigenvalue solver based on tensor networks [0.0]
  Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases. This study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.
  arXiv  Detail & Related papers  (2024-04-16T02:04:47Z)
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas [41.94295877935867]
  We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions.
  arXiv  Detail & Related papers  (2023-05-12T04:12:04Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• A characteristic-spectral-mixed scheme for six-dimensional Wigner-Coulomb dynamics [3.4595872018157308]
  Numerical resolution for 6-D Wigner dynamics under the Coulomb potential faces with the combined challenges of high dimensionality, nonlocality, oscillation and singularity. We propose a massively parallel solver, termed the CHAracteristic-Spectral-Mixed (CHASM) scheme.
  arXiv  Detail & Related papers  (2022-05-05T00:59:25Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Efficient and Flexible Approach to Simulate Low-Dimensional Quantum Lattice Models with Large Local Hilbert Spaces [0.08594140167290096]
  We introduce a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms.
  arXiv  Detail & Related papers  (2020-08-19T14:13:56Z)

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.