Solvable Quantum Circuits with non-Markovian Influence Matrices

• URL: http://arxiv.org/abs/2607.25969v1
• Date: Tue, 28 Jul 2026 16:51:26 GMT
• Title: Solvable Quantum Circuits with non-Markovian Influence Matrices
• Abstract summary: We propose a new systematic approach to generating quantum circuits with complex dynamics.<n>The resulting influence matrices are non-Markovian, exhibiting nontrivial temporal correlations.<n>We show that, contrary to previous solvable instances, these circuits produce patterns of correlations that closely resemble that of typical many-body systems.
• Score: 0.13999481573773073
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Influence matrices encode the action exerted on local subsystems by the rest of an extended quantum many-body system during their evolution. Thus, knowledge of the influence matrix facilitates computationally efficient simulations of local dynamics. Here we propose a new systematic approach to generating quantum circuits with complex dynamics for which the influence matrices can be written down exactly. In contrast to previous frameworks of this kind, such as dual-unitary circuits, the resulting influence matrices are non-Markovian, exhibiting nontrivial temporal correlations. We explicitly construct a broad family of circuits of this kind, based on dressing free-fermion (matchgate) circuits with appropriately chosen interaction terms. We show that, contrary to previous solvable instances, these circuits produce patterns of correlations that closely resemble that of typical many-body systems. Our approach can be directly interpreted in terms of an error correction scheme where the terms breaking the solvability of the influence matrices play the role of errors.

Related papers

• Exact subsystem dynamics in the deterministic Floquet-PXP model [0.0]
  Rule 201 is a deterministic version of the Floquet-PXP model.<n>We provide the solution, and multi-time autocorrelation functions.
  arXiv  Detail & Related papers  (2026-06-25T17:46:33Z)
• Low Rank Structure of the Reduced Transition Matrix [0.13999481573773073]
  influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics.<n>Recent work has shown that influence matrices carry strong temporal correlations even in maximally chaotic systems.<n>We show that the reduced transition matrix, a suitable combination of influence matrices that directly determines local expectation values, can nevertheless be efficiently approximated.
  arXiv  Detail & Related papers  (2026-05-12T19:13:34Z)
• Disordered Dynamics in High Dimensions: Connections to Random Matrices and Machine Learning [52.26396748560348]
  We provide an overview of high dimensional dynamical systems driven by random matrices.<n>We focus on applications to simple models of learning and generalization in machine learning theory.
  arXiv  Detail & Related papers  (2026-01-03T00:12:32Z)
• Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling [0.0]
  We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable.<n>We obtain exact expressions for (higher-order) correlations between matrix elements and show these to be stable away from the solvable point.<n>These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly-solvable many-body models.
  arXiv  Detail & Related papers  (2025-09-09T18:01:45Z)
• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers [62.997667081978825]
  Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. We show that the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
  arXiv  Detail & Related papers  (2023-02-23T09:43:49Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Measuring decoherence by commutation relations decay for quasilinear quantum stochastic systems [2.0508733018954843]
  We study a class of open quantum systems with an algebraic structure of dynamic variables. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. We quantify the decoherence in terms of the perturbation rate of the commutation relations decay.
  arXiv  Detail & Related papers  (2022-10-13T05:53:08Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Influence matrix approach to many-body Floquet dynamics [0.0]
  We introduce an approach to study quantum many-body dynamics inspired by the Feynman-Vernon influence functional. The central object in our approach is the influence matrix (IM), which describes the effect of the system on the dynamics of a local subsystem.
  arXiv  Detail & Related papers  (2020-09-21T18:04:58Z)

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.