Basis-Adaptive Sparse-State Simulation of Quantum Circuits

• URL: http://arxiv.org/abs/2605.27285v1
• Date: Tue, 26 May 2026 17:02:39 GMT
• Title: Basis-Adaptive Sparse-State Simulation of Quantum Circuits
• Abstract summary: We introduce an algorithm called Basis-Adaptive Sparse-State Simulation (BASS)<n>BASS updates each qubit's local representation basis during execution rather than locking the computational basis for the entire circuit.<n>On structured brickwork circuits, BASS achieves substantially higher fidelity than the fixed-basis approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical simulation of many-body quantum systems remains economical only when wavefunction amplitudes stay localized in the working basis. Fixed-basis sparse-state simulators scale memory as $\mathcal{O}(k)$ by keeping the largest computational-basis amplitudes; however, fidelity drops once entanglement or basis rotations spread weight across the Hilbert space. In this work, we introduce an algorithm called Basis-Adaptive Sparse-State Simulation (BASS), which updates each qubit's local representation basis during execution rather than locking the computational basis for the entire circuit. Before truncation, each qubit is rotated into the eigenbasis of its single-qubit reduced density matrix, following the natural-orbital idea from quantum chemistry, so the retained amplitudes stay clustered. We prove that top-$k$ selection is uniquely optimal for one-step truncation in any fixed basis and that the one-body reduced-density-matrix eigenbasis is a stationary product basis for the inverse participation ratio (PR), with a residual bounded by local entanglement coherence. We perform a systematic benchmarking over a variety of quantum circuits and demonstrate that the ratio \(k/\text{PR}_Z\) (sparse budget over computational participation ratio) serves as an indicator for regimes in which adaptive measurement bases provide a performance advantage. On structured brickwork circuits, BASS achieves substantially higher fidelity than the fixed-basis approach, while incurring only a moderate increase in wall-clock time in the memory-limited regime. Moreover, for disordered Ising circuits, BASS systematically provides an improvement of approximately one order of magnitude in state overlap at a fixed computational budget.

Related papers

• A Recursive Module-Coupling Algorithm for Computing Low-Energy Eigenstates [10.630729434802996]
  Finding the eigenstates of a many-body Hamiltonian is a fundamental challenge in physics and computational science.<n>We propose a quantum-circuit implementation that provides a quantum multistate eigensolver.<n> experiments on IBM quantum processors show that eigenstate preparation with reasonable fidelities is achievable even in the current NISQ era.
  arXiv  Detail & Related papers  (2026-09-02T10:04:23Z)
• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• EQE-QAOA: An Equivalence-Preserving Qubit Efficient Framework for Combinatorial Optimization [54.05451096499336]
  Existing techniques rely on qubit reduction at the cost of information loss, leading to degraded computational performance.<n>We propose the Equivalence-preserving Qubit Efficient QAOA, which significantly reduces the required number of qubits without degrading performance.<n>We show that it is broadly applicable to large-scale optimization problems, excluding only unconstrained problems with completely independent variables.
  arXiv  Detail & Related papers  (2026-04-20T13:57:49Z)
• Verifying random matrix product states with autoregressive local measurements [7.085044605508094]
  Matrix product states (MPS) are a central language for one-dimensional quantum matter.<n>We introduce an emphautoregressive importance sampler that draws Pauli strings sequentially from efficiently computable conditional distributions.<n>We also develop a grouped extension that constructs qubit-wise commuting measurement settings via a emphsorting string.
  arXiv  Detail & Related papers  (2026-04-17T13:12:27Z)
• Resource-Scalable Fully Quantum Metropolis-Hastings for Integer Linear Programming [0.0]
  We introduce a fully quantum Metropolis-Hastings algorithm for Metropolis linear programming.<n>Each walk step is a unitary update that prepares coherent candidate moves.<n>We show that the method provides a coherent, resource-characterized baseline for fully quantum constraint programming.
  arXiv  Detail & Related papers  (2026-02-11T19:01:45Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Tradeoffs between quantum and classical resources in linear combination of unitaries [0.07388859384645262]
  The linear combination of unitaries (LCU) algorithm is a building block of many quantum algorithms.<n>We propose a quantum algorithm that manages the tradeoff between sampling cost and the circuit size.
  arXiv  Detail & Related papers  (2025-12-06T03:10:22Z)
• Hybrid Reward-Driven Reinforcement Learning for Efficient Quantum Circuit Synthesis [0.0]
  A reinforcement learning framework is introduced for the efficient synthesis of quantum circuits.<n>The framework combines a static, domain-informed reward that guides the agent toward the target state with customizable dynamic penalties.<n> Benchmarking on graph-state preparation tasks for up to seven qubits, we demonstrate that the algorithm consistently discovers minimal-depth circuits.
  arXiv  Detail & Related papers  (2025-07-22T14:39:20Z)
• Branch-and-bound digitized counterdiabatic quantum optimization [39.58317527488534]
  Branch-and-bound algorithms effectively solve convex optimization problems, relying on the relaxation the objective function to obtain tight lower bounds.<n>We propose a branch-and-bound digitized counterdiabatic quantum optimization (BB-DCQO) algorithm that addresses the relaxation difficulties.
  arXiv  Detail & Related papers  (2025-04-21T18:19:19Z)
• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations [44.99833362998488]
  This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM)<n>We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall.<n>Our results confirm the validity of the approach, achieving median error fidelities on the order of $10-3$ and success probabilities sufficient for practical quantum state sampling.
  arXiv  Detail & Related papers  (2025-04-17T15:41:48Z)
• Adaptive Bayesian Optimization for Robust Identification of Stochastic Dynamical Systems [4.0148499400442095]
  This paper deals with the identification of linear derivation systems, where the unknowns include system coefficients and noise variances.<n>A sample-efficient global optimization method based on Bayesian optimization is proposed.<n>Experiments show that the EGP-based BO consistently outperforms MLE via steady-state filtering and expectation-maximization.
  arXiv  Detail & Related papers  (2025-03-09T01:38:21Z)
• Estimating Non-Stabilizerness Dynamics Without Simulating It [43.80709028066351]
  Iterative Clifford Circuit Renormalization (I CCR) is designed to efficiently handle the dynamics of non-stabilizerness in quantum circuits.<n>I CCR embeds the complex dynamics of non-stabilizerness in the flow of an effective initial state.<n>We implement the I CCR algorithm to evaluate the non-stabilizerness dynamics for systems of size up to N = 1000.
  arXiv  Detail & Related papers  (2024-05-09T18:57:55Z)
• Efficient quantum algorithm to simulate open systems through a single environmental qubit [0.0]
  We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers.<n>Under fixed accuracy conditions, our algorithm enables a reduction in the number of trotter steps compared to other approaches.
  arXiv  Detail & Related papers  (2023-11-16T16:45:30Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)

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.