Basis Adaptive Algorithm for Quantum Many-Body Systems on Quantum Computers

• URL: http://arxiv.org/abs/2512.12753v1
• Date: Sun, 14 Dec 2025 16:34:19 GMT
• Title: Basis Adaptive Algorithm for Quantum Many-Body Systems on Quantum Computers
• Authors: Anutosh Biswas, Sayan Ghosh, Ritajit Majumdar, Mostafizur Rahaman, Manoranjan Kumar,
• Abstract summary: A new basis adaptive algorithm is introduced to efficiently find the ground-state properties of quantum many-body systems.<n>We benchmark this approach on the spin-1/2 XXZ chain up to 24 qubits using the IBM Heron processor.
• Score: 2.4713653282916126
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A new basis adaptive algorithm for hybrid quantum-classical platforms is introduced to efficiently find the ground-state (gs) properties of quantum many-body systems. The method addresses limitations of many algorithms, such as Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) etc by using shallow Trotterized circuits for short real-time evolution on a quantum processor. The sampled basis is then symmetry-filtered by using various symmetries of the Hamiltonian which is then classically diagonalized in the reduced Hilbert space. We benchmark this approach on the spin-1/2 XXZ chain up to 24 qubits using the IBM Heron processor. The algorithm achieves sub-percent accuracy in ground-state energies across various anisotropy regimes. Crucially, it outperforms the Sampling Krylov Quantum Diagonalization (SKQD) method, demonstrating a substantially lower energy error for comparable reduced-space dimensions. This work validates symmetry-filtered, real-time sampling as a robust and efficient path for studying correlated quantum systems on current near-term hardware.

Related papers

• Quantum Jacobi-Davidson Method [2.6739754727815708]
  We develop and implement the Quantum Jacobi-Davidson (QJD) method and its quantum diagonalization variant, the Sample-Based Quantum Jacobi-Davidson (SBQJD) method.<n>Our results show that both QJD and SBQJD achieve significantly faster convergence and fewer Pauli measurements compared to the recently reported Quantum Davidson method.<n>These findings establish the QJD framework as an efficient general-purpose subspace-based technique for solving quantum eigenvalue problems.
  arXiv  Detail & Related papers  (2026-02-02T05:39:09Z)
• 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)
• Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search [0.7639610349097473]
  This article proposes a gradient-free Monte Carlo Tree Search (MCTS) technique to automate the process of quantum circuit design.<n>Compared to previous MCTS research, our technique reduces the number of quantum circuit evaluations by a factor of 10 up to 100.<n>The resulting quantum circuits exhibit up to three times fewer CNOT gates, which is important for implementation on noisy quantum hardware.
  arXiv  Detail & Related papers  (2025-02-06T10:52:11Z)
• 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)
• Benchmarking Variational Quantum Eigensolvers for Entanglement Detection in Many-Body Hamiltonian Ground States [37.69303106863453]
  Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. We use a specific class of VQA named variational quantum eigensolvers (VQEs) to benchmark them at entanglement witnessing and entangled ground state detection. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
  arXiv  Detail & Related papers  (2024-07-05T12:06:40Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Fast-Forwarding with NISQ Processors without Feedback Loop [0.0]
  We present the Classical Quantum Fast Forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. Our work provides a $104$ improvement over the previous record.
  arXiv  Detail & Related papers  (2021-04-05T14:29:33Z)

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.