Classical simulation of free-fermionic dynamics and quantum chemistry with magic input

• URL: http://arxiv.org/abs/2604.26813v1
• Date: Wed, 29 Apr 2026 15:42:59 GMT
• Title: Classical simulation of free-fermionic dynamics and quantum chemistry with magic input
• Abstract summary: We show that for a class of paired non-Gaussian fermionic states, quantum simulation primitives can be efficiently approximated to additive error under free-fermionic dynamics.
• Score: 0.15554979526414522
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Establishing the precise computational boundary between classically tractable fermionic systems and those capable of genuine quantum advantage is a central challenge in quantum simulation. While injecting non-Gaussian ``magic" inputs into free-fermion circuits is widely expected to generate intractable complexity, we identify a physically motivated intermediate regime. Supported by rigorous bounds and numerical evidence, we show that for a class of paired non-Gaussian fermionic states, essential quantum simulation primitives -- transition amplitudes, overlaps, and arbitrary-weight number correlators -- can be efficiently approximated to additive error under free-fermionic dynamics. This tractability stems from an algebraic reduction that compresses exponentially large multiparticle interference into a single coefficient of a multivariate Pfaffian polynomial. Because these classical estimators match the intrinsic $O(1/\sqrt{K})$ statistical uncertainty of quantum hardware utilizing $K$ measurement shots, they constitute a practical benchmark. Building on this foundation, we construct an additive-error estimator for high-weight Wilson observables in the noninteracting quench of recent trapped-ion experiments, providing a rigorous classical benchmark. Extending this to quantum chemistry, we demonstrate that core overlap-based subroutines for antisymmetrized products of strongly orthogonal geminals admit exact Pfaffian reductions. Ultimately, these results sharpen the boundary of quantum advantage, establishing that the paired-electron scaffold is effectively dequantized and clarifying exactly where quantum resources are indispensable.

Related papers

• Certifying coherence in quantum devices under classical control [33.72751145910978]
  We prove that coherence can be fully characterised through a hierarchy of semidefinite programs.<n>For the important special case of qubits, we exploit conceptual connections with the theory of joint measurability.<n>We apply these methods to determine whether quantum channels are able to preserve coherence or are inherently coherence-breaking.
  arXiv  Detail & Related papers  (2026-06-02T14:20:45Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines [7.716642023459826]
  Instantaneous quantum quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models.<n>We show that barren plateaus depend on the generator set and the spectrum of the chosen kernel.<n>We identify regimes in which low-weight-biased kernels avoid exponential suppression in structured topologies.
  arXiv  Detail & Related papers  (2026-02-11T17:12:56Z)
• Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: The case of QSSEP and QSSIP [2.035631599424874]
  We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems.<n>We show that the cumulant generating function of the integrated current, at large scales, obeys a large deviation principle.<n>We identify the leading finite-size corrections to the current statistics.
  arXiv  Detail & Related papers  (2026-01-23T16:45:31Z)
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting [0.0]
  We develop a comprehensive replica Keldysh field theory for general quantum-jump processes in bosonic and fermionic systems.<n>Our formalism provides a unified description of pure-state quantum trajectories under efficient detection and mixed-state dynamics.
  arXiv  Detail & Related papers  (2025-12-18T13:34:00Z)
• The Born Ultimatum: Conditions for Classical Surrogation of Quantum Generative Models with Correlators [1.397434225914932]
  Quantum Circuit Born Machines (QCBMs) are powerful quantum generative models that sample according to the Born rule.<n>Recent train-classical, deploy-quantum approaches propose training classical surrogates of QCBMs and using quantum devices only for inference.<n>We analyze the limitations of these methods arising from deployment discrepancies between classically trained and quantumly deployed parameters.
  arXiv  Detail & Related papers  (2025-11-03T18:51:24Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Quantum dynamics in frustrated Ising fullerenes [37.881496223977706]
  This study experimentally demonstrates quantum fluctuations lifting the degenerate ground-state manifold of classical magnetic configurations.<n>We observe significant performance improvement across generations of superconducting quantum annealers.
  arXiv  Detail & Related papers  (2025-05-13T22:12:11Z)
• 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)
• Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems [0.0]
  We extend the nonequilibrium bosonic Dynamical Mean Field Theory to Markovian open quantum systems. As a first application, we address the steady-state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump.
  arXiv  Detail & Related papers  (2020-08-06T10:35:26Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)
• Hartree-Fock on a superconducting qubit quantum computer [30.152226344347064]
  Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of $rm H_6$, $rm H_8$, $rm H_10$ and $rm H_12$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments.
  arXiv  Detail & Related papers  (2020-04-08T18:00:06Z)

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.