Quantum-to-Classical Computability Transition via Negative Markov Chains

• URL: http://arxiv.org/abs/2604.19889v1
• Date: Tue, 21 Apr 2026 18:11:19 GMT
• Title: Quantum-to-Classical Computability Transition via Negative Markov Chains
• Abstract summary: We show that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system.<n>We show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined over an exponentially large configuration space. Within this framework, quantum complexity arises from the proliferation of stochastic particles, which ultimately renders classical simulation and sampling intractable beyond a certain timescale. In the presence of noise, we demonstrate that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system by suppressing particle growth and making Monte Carlo sampling efficient. As a corollary, we show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability once the noise strength exceeds a critical threshold which can be efficiently determined for any model.

Related papers

• Topology from Decoherence [39.407739937584104]
  We show that decoherence can induce topological phenomena.<n>We demonstrate this in a lattice system subject to environment-induced dephasing.<n>Our results establish correlated quantum noise as a route to topology in open many-body systems.
  arXiv  Detail & Related papers  (2026-07-08T18:00:04Z)
• Exact metastability in a class of driven-dissipative quantum many-body systems [0.0]
  We focus on a class of driven-dissipative many-body open quantum systems having hidden time-reversal symmetry.<n>We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay.<n>Our results allow quantitative insights into metastability and slow dynamics for a range of systems.
  arXiv  Detail & Related papers  (2026-06-05T18:00:01Z)
• Hybrid quantum-classical simulations of semiclassical gravity [39.146761527401424]
  We propose a hybrid quantum-classical algorithm for the simulation of real-time dynamics in interacting quantum field theories coupled to classical fields.<n>By discretizing space and time, we construct an iterative protocol that simulates the Trotterized dynamics of the quantum fields subject to the classical fields.<n>Our work paves the way for future experiments exploring other non-tractable regimes, including non-perturbative interactions of the quantum fields.
  arXiv  Detail & Related papers  (2026-03-06T17:48:21Z)
• 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)
• Effective Kinetic Monte Carlo for a Quantum Epidemic Process [41.99844472131922]
  We show how some weak symmetries of the Lindblad equation allow us to map the dynamics onto a Kinetic Monte Carlo.<n>This simplified, effective dynamics can be described via local jumps coupled with a local deterministic component.
  arXiv  Detail & Related papers  (2025-12-28T14:44:30Z)
• Classically Prepared, Quantumly Evolved: Hybrid Algorithm for Molecular Spectra [41.99844472131922]
  We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems.<n>The method combines classical preparation of a perturbed ground state with short-time quantum evolution of product states sampled from it.
  arXiv  Detail & Related papers  (2025-10-28T19:27:12Z)
• Realization of Trapped Ion Dynamics in the Strong-Field Regime and Non-Markovianity [33.781064984238775]
  We experimentally investigate the dynamics of a trapped ion where the Rabi frequency (Omega) approaches the vibrational mode frequency (nu)<n>Using quantum state tomography, we reconstruct the density matrix and track its evolution to assess non-Markovianity.<n>Our findings establish a pathway for using trapped-ion platforms to investigate non-Markovianity, coherent control, and the fundamental behavior of open quantum systems in extreme regimes.
  arXiv  Detail & Related papers  (2025-10-23T11:25:09Z)
• Towards Quantum Enhanced Adversarial Robustness with Rydberg Reservoir Learning [45.92935470813908]
  Quantum computing reservoir (QRC) leverages the high-dimensional, nonlinear dynamics inherent in quantum many-body systems.<n>Recent studies indicate that perturbation quantums based on variational circuits remain susceptible to adversarials.<n>We investigate the first systematic evaluation of adversarial robustness in a QR based learning model.
  arXiv  Detail & Related papers  (2025-10-15T12:17:23Z)
• Classical representation of the dynamics of quantum spin chains [0.0]
  A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of non-commutative observables.<n>We propose a resolution to this dilemma by introducing an exact representation of their dynamics in terms of classical continuous-time Markov chains.
  arXiv  Detail & Related papers  (2025-02-14T19:00:11Z)
• Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application [0.0]
  We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models.
  arXiv  Detail & Related papers  (2023-02-08T15:58:39Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Importance Sampling Scheme for the Stochastic Simulation of Quantum Spin Dynamics [0.0]
  We develop an importance sampling scheme for the simulation of quantum spin dynamics. An exact transformation is then carried out to preferentially sample trajectories that are close to the dominant one. We demonstrate that this approach is capable of reducing the temporal growth of fluctuations in the quantities.
  arXiv  Detail & Related papers  (2021-03-30T16:18:28Z)

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.