Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits

• URL: http://arxiv.org/abs/2606.13470v1
• Date: Thu, 11 Jun 2026 15:21:26 GMT
• Title: Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
• Abstract summary: We study a class of monitored quantum circuits driven by random Clifford.<n>We prove the existence and uniqueness of the stationary law, which gives an ergodic description of the long-time dynamics.<n>We then resolve the leadings of steady magic in the weak-magic-magic limit.
• Score: 6.433597709151262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Monitored quantum circuits provide a natural setting in which scrambling, measurements, and measurement-conditioned updates compete within a stochastic many-body dynamics. From the viewpoint of nonstabilizer resource theory, this competition is especially relevant because Clifford-compatible operations preserve the stabilizer structure, while weak non-Clifford perturbations inject magic resource. Most of the existing understanding of monitored quantum circuits has been shaped by numerical simulations and phenomenological descriptions, while a rigorous dynamics theory remains less developed. In this paper, we address this gap by developing an analytical framework which lays a rigorous mathematical foundation for the study of random monitored quantum dynamics. Specifically, we study a class of monitored quantum circuits driven by random Clifford. We prove the existence and uniqueness of the stationary law, which gives an ergodic description of the long-time dynamics. We then resolve the leading asymptotics of steady magic in the weak-magic-injection limit. This tangent description makes the contrast between resource measures transparent: in odd-prime local dimension, the steady Gross--Wigner mana has a linear leading asymptotic, whereas in qubit systems the steady 2-stabilizer Rényi entropy has a quadratic leading asymptotic. These different powers reflect the distinct local geometries of the two resource measures near the stabilizer layer. In this way, this work develops an analytical framework that first establishes the stationary ergodic dynamics of random monitored quantum circuits.

Related papers

• Symmetry Constrained Quantum Error Mitigation for the Schwinger Model [39.146761527401424]
  We exploit the parity and fermion-number symmetries of a gauge theory under depolarising noise.<n>We investigate symmetry verification under digital quantum simulation.
  arXiv  Detail & Related papers  (2026-08-21T13:49:11Z)
• Dynamical redistribution of quantum resources in tree-level Bhabha scattering [2.728572386373239]
  We investigate the tree-level Bhabha scattering process within the framework of quantum resource theory.<n>We show how QED kinematics and Feynman amplitudes strictly dictate resource redistribution.
  arXiv  Detail & Related papers  (2026-07-22T15:18:56Z)
• Dynamical self-dual criticality in Fibonacci-monitored quantum Ising chains [0.0]
  We study the role of Kramers-Wannier duality in monitored dynamics of one-dimensional Ising/Majorana chains.<n>We find that the dynamical extension of this non-invertible symmetry to an out-of-equilibrium setting allows one to organize the dynamical phase diagram of entangled phases.<n>We identify two distinct critical lines, both related to the golden ratio, for Born-rule weak measurements and for random Clifford projective measurements.
  arXiv  Detail & Related papers  (2026-05-22T18:00:02Z)
• Entanglement-facilitated macroscopic cluster formation in quantum many-body dynamics [42.89492957665636]
  We find that initial-state entanglement suppresses the proliferation of true-vacuum bubbles and stabilises macroscopic connected clusters.<n>Our results establish a connection between initial-state preparation and the preservation of global structures.
  arXiv  Detail & Related papers  (2026-05-21T18:21:14Z)
• 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)
• Unravelling the emergence of quantum jumps in a monitored qubit [29.627676149627302]
  Quantum jumps are among the most striking consequences of observation in quantum mechanics.<n>We map measurement-induced transitions in a monitored superconducting qubit.<n>Results reveal that the interplay between coherent driving, measurement, and decoherence gives rise to a hierarchy of distinct dynamical phases.
  arXiv  Detail & Related papers  (2026-02-02T19:00:10Z)
• Generalised fractional Rabi problem [35.18016233072556]
  Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems.<n>In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's function formulation based on the Caputo fractional derivative.<n>We find that even in the absence of external driving, the static Hamiltonian term induces non-trivial spin dynamics with damping features directly linked to the fractional temporal nonlocality.
  arXiv  Detail & Related papers  (2025-10-09T12:51:57Z)
• Anticoncentration and nonstabilizerness spreading under ergodic quantum dynamics [0.0]
  Anticoncentration and equilibration of magic resources under dynamics of random quantum circuits occur at times scaling logarithmically with system size.<n>This work challenges this idea by examining the anticoncentration and magic spreading in one-dimensional ergodic Floquet models and Hamiltonian systems.
  arXiv  Detail & Related papers  (2024-12-13T16:00:34Z)
• Magic spreading in random quantum circuits [0.0]
  We show how rapidly do generic many-body dynamics generate magic resources under the constraints of locality and unitarity.<n>We demonstrate that magic resources equilibrate on timescales logarithmic in the system size, akin to anti-concentration and Hilbert space delocalization phenomena.<n>As random circuits are minimal models for chaotic dynamics, we conjecture that our findings describe the phenomenology of magic resources growth in a broad class of chaotic many-body systems.
  arXiv  Detail & Related papers  (2024-07-04T13:43:46Z)
• Hysteresis and Self-Oscillations in an Artificial Memristive Quantum Neuron [79.16635054977068]
  We study an artificial neuron circuit containing a quantum memristor in the presence of relaxation and dephasing. We demonstrate that this physical principle enables hysteretic behavior of the current-voltage characteristics of the quantum device.
  arXiv  Detail & Related papers  (2024-05-01T16:47:23Z)
• Observation of multiple steady states with engineered dissipation [19.94001756170236]
  We introduce engineered noise into a one-dimensional ten-qubit superconducting quantum processor to emulate a generic many-body open quantum system. We find that the information saved in the initial state maintains in the steady state driven by the continuous dissipation on a five-qubit chain.
  arXiv  Detail & Related papers  (2023-08-25T08:06:44Z)
• 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)
• Localization properties in disordered quantum many-body dynamics under continuous measurement [0.0]
  We study localization properties of continuously monitored dynamics in quantum many-body systems. By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other.
  arXiv  Detail & Related papers  (2023-01-18T03:39:39Z)
• Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically-constrained open many-body system with two absorbing states [0.0]
  We introduce and investigate an open many-body quantum system in which kinetically coherent and dissipative processes compete. Our work shows how the interplay between coherent and dissipative processes as well as constraints may lead to a highly intricate non-equilibrium evolution.
  arXiv  Detail & Related papers  (2022-04-22T07:51:38Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)

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.