Taming Trotter Errors with Quantum Resources

• URL: http://arxiv.org/abs/2604.13486v1
• Date: Wed, 15 Apr 2026 05:19:11 GMT
• Title: Taming Trotter Errors with Quantum Resources
• Abstract summary: We study the statistical behavior of algorithmic errors arising in Hamiltonian simulation based on the Trotter- Suzuki formula.<n>We find that the variance of the Trotter error decreases with increasing entanglement entropy, indicating a stronger concentration of error for entangled states.<n>We also find that the kurtosis of the error exhibits a negative linear dependence on magic, implying that states with high magic possess lighter-tailed error distributions.
• Score: 12.91232523472933
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Quantum simulation is a cornerstone application of quantum computing, yet how fundamental quantum resources--entanglement and non-stabilizerness (``magic")--shape simulation fidelity remains an open question. In this work, we establish a rigorous connection between these resources and the statistical behavior of algorithmic errors arising in Hamiltonian simulation based on the Trotter-Suzuki formula. By analyzing ensembles of states with fixed entanglement entropy or magic, we make two key discoveries: First, the variance of the Trotter error decreases with increasing entanglement entropy, indicating a stronger concentration of error for entangled states. Moreover, we find that the kurtosis of the error exhibits a negative linear dependence on magic, implying that states with high magic possess lighter-tailed error distributions and thus a reduced probability of large deviations. These findings reveal a subtle phenomenon: quantum resources that obstruct classical emulation may, paradoxically, enhance the intrinsic robustness of quantum simulation, highlighting a constructive interplay between complexity and stability in quantum computation.

Related papers

• Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory [37.724232080494424]
  Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description.<n>We calculate entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory.<n>We find a crossover denoted by $g_star$ where the ground state passes from a more magic-rich regime into a regime with less magic.
  arXiv  Detail & Related papers  (2026-06-08T18:00:00Z)
• Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons [16.71116343065157]
  arrow of time in quantum many-body systems stems from Hamiltonian evolution to scramble quantum information and increase entanglement.<n>We study the structure of quantum information scrambling and chaotic dynamics.<n>Our results push the fundamental limits of dynamical revers of complex quantum systems.
  arXiv  Detail & Related papers  (2025-06-24T18:00:05Z)
• Quantum extreme learning machines for photonic entanglement witnessing [30.432877421232842]
  Quantum extreme learning machines (QELMs) embody a powerful alternative for witnessing quantum entanglement.<n>We implement a photonic QELM that leverages the orbital angular momentum of photon pairs as an ancillary degree of freedom.<n>Unlike conventional methods, our approach does not require fine-tuning, precise calibration, or refined knowledge of the apparatus.
  arXiv  Detail & Related papers  (2025-02-25T16:55:35Z)
• Simulating quantum chaos without chaos [1.7942265700058988]
  We introduce a novel class of quantum Hamiltonians that fundamentally challenges the conventional understanding of quantum chaos. Our ensemble is computationally indistinguishable from the Gaussian unitary ensemble (GUE) of strongly-interacting Hamiltonians. This stark contrast between efficient computational indistinguishability and traditional chaos indicators calls into question fundamental assumptions about the nature of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-23T18:01:50Z)
• Beyond-classical computation in quantum simulation [21.45294717016955]
  We show that superconducting quantum annealing processors can generate samples in close agreement with solutions of the Schr"odinger equation.<n>We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses.<n>We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer.
  arXiv  Detail & Related papers  (2024-03-01T19:00:04Z)
• Quantum correlations in the steady state of light-emitter ensembles from perturbation theory [0.0]
  In systems of light emitters subject to single-emitter or two-emitter driving, the steady state perturbed away from the U(1) limit exhibits spin squeezing. Our main result is that in systems of light emitters subject to single-emitter or two-emitter driving, the steady state perturbed away from the U(1) limit generically exhibits spin squeezing.
  arXiv  Detail & Related papers  (2024-02-26T18:50:30Z)
• Extracting randomness from magic quantum states [3.9000096678531606]
  We show that when a subsystem of a quantum state is measured, the resultant unmeasured part of the system can exhibit a high degree of randomness.<n>Our findings suggest an approach to quantifying correlations within magic quantum states beyond the conventional paradigm of entanglement.
  arXiv  Detail & Related papers  (2024-02-15T18:33:21Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum signatures of chaos in noisy tomography [0.0]
  We use continuous measurement quantum tomography as a paradigm to study quantum chaos.<n>We define a quantity to capture the scrambling of errors, an out-of-time-ordered correlator (OTOC) between two operators under perturbed and unperturbed system dynamics.<n>Our results demonstrate not only a fundamental link between Loschmidt echo and scrambling of errors, as captured by "error OTOCs", but that such a link can have operational consequences in quantum information processing.
  arXiv  Detail & Related papers  (2022-11-21T07:32:53Z)
• Quantum simulation of dissipative collective effects on noisy quantum computers [0.0]
  We put forward the first fully quantum simulation of dissipative collective phenomena on a real quantum computer. The quantum simulation is based on the recently introduced multipartite collision model. We implement the algorithm on some IBM quantum computers to simulate superradiance and subradiance between a pair of qubits.
  arXiv  Detail & Related papers  (2022-01-27T15:50:58Z)
• Long-Time Error-Mitigating Simulation of Open Quantum Systems on Near Term Quantum Computers [38.860468003121404]
  We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field -- the Hubbard atom. Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware.
  arXiv  Detail & Related papers  (2021-08-02T21:36:37Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Quantum Entropic Causal Inference [30.939150842529052]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links.
  arXiv  Detail & Related papers  (2021-02-23T15:51:34Z)

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.