Quantum simulation of many-body dynamics with noise-robust Trotter decomposition based on symmetric structures

• URL: http://arxiv.org/abs/2505.04552v2
• Date: Thu, 23 Oct 2025 12:26:41 GMT
• Title: Quantum simulation of many-body dynamics with noise-robust Trotter decomposition based on symmetric structures
• Authors: Bo Yang, Naoki Negishi,
• Abstract summary: Suzuki-Trotter decomposition provides framework for simulating quantum dynamics on quantum hardware.<n>We propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices.<n>Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.
• Score: 3.7159810638207813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Suzuki-Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise, and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding $0.98$ when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.

Related papers

• Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits [1.9573380763700712]
  We propose an exact sampling algorithm that integrates tensor network contraction techniques with a Markov process.<n>As a demonstration, we target the challenge of generating samples from ideal and noisy QAOA circuits with up to 476 qubits.
  arXiv  Detail & Related papers  (2025-10-28T09:33:11Z)
• Resource-Efficient Hadamard Test Circuits for Nonlinear Dynamics on a Trapped-Ion Quantum Computer [1.2063443893298391]
  We propose a low-depth implementation of a class of Hadamard test circuits.<n>We develop a parameterized quantum ansatz specifically tailored for variational algorithms.<n>Our findings demonstrate a significant reduction in single- and two-qubit gate counts.
  arXiv  Detail & Related papers  (2025-07-25T13:16:54Z)
• Error mitigation of shot-to-shot fluctuations in analog quantum simulators [46.54051337735883]
  We introduce an error mitigation technique that addresses shot-to-shot fluctuations in the parameters for the Hamiltonian governing the system dynamics.<n>We rigorously prove that amplifying this shot-to-shot noise and extrapolating to the zero-noise limit recovers noiseless results for realistic noise distributions.<n> Numerically, we predict a significant enhancement in the effective many-body coherence time for Rydberg atom arrays under realistic conditions.
  arXiv  Detail & Related papers  (2025-06-19T18:00:00Z)
• Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise [49.97673761305336]
  Noise remains a major obstacle to achieving reliable quantum algorithms.<n>We present a provably noise-resilient training theory and algorithm to enhance the robustness of parameterized quantum circuit classifiers.
  arXiv  Detail & Related papers  (2025-05-24T02:51:34Z)
• Circuit structure-preserving error mitigation for High-Fidelity Quantum Simulations [12.76515927552115]
  We present a circuit structure-preserving error mitigation framework for parameterized quantum circuits.<n>A key advantage of our approach lies in its ability to retain the original circuit architecture while effectively characterizing and mitigating gate errors.<n>Our strategy offers a practical solution for addressing gate-induced errors and significantly broadens the scope of feasible quantum simulations on current quantum hardware.
  arXiv  Detail & Related papers  (2025-05-22T18:00:03Z)
• Trapped-ion quantum simulation of the Fermi-Hubbard model as a lattice gauge theory using hardware-aware native gates [0.43914426871918816]
  Trotterization-based quantum simulations have shown promise, but implementations on current hardware are limited by noise.<n>A mapping of the Fermi-Hubbard model to a Z2 LGT was recently proposed that restricts the dynamics to a subspace protected by additional symmetries, and its ability for post-selection error mitigation was verified through noisy classical simulations.<n>In particular, a novel combination of iteratively preconditioned gradient descent (IPG) and subsystem von Neumann Entropy compression reduces the 2-qubit gate count of FHM quantum simulation by 35%.
  arXiv  Detail & Related papers  (2024-11-12T13:21:12Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma.<n>This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles.<n>We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Sachdev-Ye-Kitaev model on a noisy quantum computer [1.0377683220196874]
  We study the SYK model -- an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. We compute return probability after time $t$ and out-of-time order correlators (OTOC) which is a standard observable of quantifying the chaotic nature of quantum systems.
  arXiv  Detail & Related papers  (2023-11-29T19:00:00Z)
• Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws [0.0]
  Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. We present an adaptive Trotterization algorithm to cope with time-dependent Hamiltonians. We validate the algorithm for a time-dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.
  arXiv  Detail & Related papers  (2023-07-19T09:20:02Z)
• 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)
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations [55.41644538483948]
  We study strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. We find that the gate complexity using second order Trotter- Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2022-07-07T09:39:40Z)
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression [0.0]
  We demonstrate a post-quench dynamics simulation of a Heisenberg model on present-day IBM quantum hardware. We show how to measure the required cost function, the overlap between the time-evolved and variational states, on present-day hardware. In addition to carrying out simulations on real hardware, we investigate the performance and scaling behavior of the algorithm with noiseless and noisy classical simulations.
  arXiv  Detail & Related papers  (2021-12-23T15:44:47Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• 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)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware [6.445605125467574]
  We develop quantum algorithms for Hamiltonian simulation "one level below" the circuit model. We analyse the impact of these techniques under the standard error model. We derive analytic circuit identities for efficiently synthesising multi-qubit evolutions from two-qubit interactions.
  arXiv  Detail & Related papers  (2020-03-15T18:22:02Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Term Grouping and Travelling Salesperson for Digital Quantum Simulation [6.945601123742983]
  Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian makes such an approach unsuitable for near-term devices. We propose a new term ordering strategy, max-commute-tsp, that simultaneously mitigates both algorithmic and physical errors.
  arXiv  Detail & Related papers  (2020-01-16T18:33:24Z)

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.