Complexity in multiqubit and many-body systems

• URL: http://arxiv.org/abs/2507.22246v1
• Date: Tue, 29 Jul 2025 21:46:43 GMT
• Title: Complexity in multiqubit and many-body systems
• Authors: Imre Varga,
• Abstract summary: In case of an $n$-qubit system the disturbance due to depolarization and dephasing is identified.<n>Many body systems modelled using deformed random matrix ensembles and deformed two-body random interaction ensembles.<n>States with maximal complexity mark the cross-over or the transition point between integrability and full quantum chaos.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The complexity of $n$-qubit and many body systems is investigated. In case of an $n$-qubit system the disturbance due to depolarization and dephasing is identified based on a certain complexity quantity defined as the difference of the Shannon-entropy and the R\'enyi entropy of order two. In case of the effect of the depolarization the quantum system is replaced by a fully separable, i.e. classical state with probability $p$ while it remains unchanged with probability $1-p$. Whereas dephasing is modelled by destructing the appropriate off-diagonal elements of the density matrix also with probability $p$. For both cases the state with maximal complexity marks the border between the most quantum and most classical limits. Furthermore we also show that many body systems modelled using deformed random matrix ensembles, deformed two-body random interaction ensembles and also the system of one-dimensional Heisenberg-model of spins subject to a random, local magnetic field exhibiting many body localization transition, the states with maximal complexity mark the cross-over or the transition point between integrability and full quantum chaos. Finally we address the question of identifying the cross-over in the thermalization properties within large sets of quantum chaotic states using the survival probability of an excitation of a many body system. All these results show that the complexity parameter defined on a combination of the von Neumann entropy and the R\'enyi entropy of 2nd order is a meaningful and informative parameter to detect whenever a system is in a cross-over state between the otherwise trivial extremal cases of integrability or localization and quantum chaos or ergodic behavior.

Related papers

• Complexity transitions in chaotic quantum systems [11.541252326816975]
  We study the transition from chaotic to integrable phases in several paradigmatic models.<n>We compare three complementary complexity markers -- fractal dimension, von Neumann entanglement entropy, and stabilizer R'enyi entropy.
  arXiv  Detail & Related papers  (2025-05-14T18:07:18Z)
• Generalized quantum asymptotic equipartition [11.59751616011475]
  AEP states that in the limit of a large number of independent and identically distributed (i.i.d.) random experiments, the output sequence is virtually certain to come from the typical set.<n>We prove a generalized quantum AEP beyond the i.i.d. framework where the random samples are drawn from two sets of quantum states.<n>We propose a new framework for quantum resource theory in which state transformations are performed without requiring precise characterization of the states being manipulated.
  arXiv  Detail & Related papers  (2024-11-06T16:33:16Z)
• Complexity of two-level systems [0.0]
  Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed.<n>The complexity is defined as the difference between the Shannon-entropy and the second order R'enyi-entropy.<n>It is shown that the system attains maximal complexity for special choice of control parameters.
  arXiv  Detail & Related papers  (2024-08-10T13:47:18Z)
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces [0.0]
  We derive an analytical expression for the time-averaged quantum Fisher information (QFI) that applies to all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness, multipartite entanglement and quantum chaos.
  arXiv  Detail & Related papers  (2024-07-16T15:11:20Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.<n>We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.<n>We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors [22.983795509221974]
  We experimentally measure the spectral form factor (SFF) to probe the presence or absence of chaos in quantum many-body systems. This work unveils a new way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing the correlations in eigenenergies and eigenstates.
  arXiv  Detail & Related papers  (2024-03-25T16:59:00Z)
• From Spectral Theorem to Statistical Independence with Application to System Identification [11.98319841778396]
  We provide first quantitative handle on decay rate of finite powers of state transition matrix $|Ak|$. It is shown that when a stable dynamical system has only one distinct eigenvalue and discrepancy of $n-1$: $|A|$ has a dependence on $n$, resulting dynamics are inseparable. We show that element-wise error is essentially a variant of well-know Littlewood-Offord problem.
  arXiv  Detail & Related papers  (2023-10-16T15:40:43Z)
• Predictive complexity of quantum subsystems [0.0]
  We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. Predictions are formed by equivalence classes of state vectors in the exterior Hilbert space. It can also serve as a local order parameter that can distinguish long and short range entanglement.
  arXiv  Detail & Related papers  (2023-09-26T18:58:56Z)
• Cosmological complexity of the modified dispersion relation [3.0346001106791323]
  The curvature perturbation of the scalar field is identified with the two-mode squeezed state. Our numeric indicates that the complexity of the modified dispersion relation will have a non-linear pattern after the horizon exits. Since the modified dispersion relation can be dubbed as the consequences of various frameworks of quantum gravity, it could be applicable to these frameworks.
  arXiv  Detail & Related papers  (2023-09-04T13:26:20Z)
• Multipartite entanglement of the topologically ordered state in a perturbed toric code [18.589873789289562]
  We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$frac12$ toric code model. Our results provide insights to topological phases, which are robust against external disturbances, and are candidates for topologically protected quantum computation.
  arXiv  Detail & Related papers  (2021-09-07T20:20:21Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)

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.