Matchgate circuits deeply thermalize

• URL: http://arxiv.org/abs/2412.01884v1
• Date: Mon, 02 Dec 2024 19:00:00 GMT
• Title: Matchgate circuits deeply thermalize
• Authors: Mircea Bejan, Benjamin Béri, Max McGinley,
• Abstract summary: We study the ensemble of states generated by performing projective measurements on the output of a random matchgate quantum circuit. For large system sizes, it converges towards a universal ensemble that is uniform over the manifold of Gaussian fermionic states. We numerically find that local matchgate circuits deeply thermalize after a timescale $t sim L2$ set by the diffusive spreading of quantum information.
• Score: 0.0
• License:
• Abstract: We study the ensemble of states generated by performing projective measurements on the output of a random matchgate (or free-fermionic) quantum circuit. We rigorously show that this `projected ensemble' exhibits deep thermalization: For large system sizes, it converges towards a universal ensemble that is uniform over the manifold of Gaussian fermionic states. As well as proving moment-wise convergence of these ensembles, we demonstrate that the full distribution of any physical observable in the projected ensemble is close to its universal form in Wasserstein-1 distance, which we argue is an appropriate and efficiently computable measure of convergence when studying deep thermalization. Using this metric, we also numerically find that local matchgate circuits deeply thermalize after a timescale $t \sim L^2$ set by the diffusive spreading of quantum information. Our work opens up new avenues to experimentally accessible protocols to probe the emergence of quantum statistical mechanics and benchmark quantum simulators.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Area laws and thermalization from classical entropies in a Bose-Einstein condensate [0.0]
  Local quantum entropies are nonlinear functionals of the underlying quantum state. We show that suitably chosen classical entropies capture the very same features as their quantum analogs.
  arXiv  Detail & Related papers  (2024-04-18T16:53:03Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Field theory approach to eigenstate thermalization in random quantum circuits [0.0]
  We use field-theoretic methods to explore the statistics of eigenfunctions of the Floquet operator for a large family of quantum circuits. The correlation function of the quasienergy eigenstates is calculated and shown to exhibit random matrix circular unitary ensemble statistics.
  arXiv  Detail & Related papers  (2022-10-12T18:00:00Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Dynamical purification and the emergence of quantum state designs from the projected ensemble [0.0]
  Quantum thermalization in a many-body system is defined by the approach of local subsystems towards a universal form. Projected ensemble can mimic the behavior of a maximally entropic, uniformly random ensemble. We show that absence of dynamical purification in the space-time dual dynamics yields exact state-designs for all moments $k$ at the same time.
  arXiv  Detail & Related papers  (2022-04-28T17:19:32Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits [1.1968749490556412]
  We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement. We find that while R'enyi entropies grow sub-ballistically as $sqrttt$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R'enyi entropies grow ballistically with time.
  arXiv  Detail & Related papers  (2021-07-21T18:00:13Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Recovering quantum correlations in optical lattices from interaction quenches [0.0]
  Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Currently a direct measurement of local coherent currents is out of reach. We show how to achieve that by measuring densities that are altered in response to quenches to non-interacting dynamics.
  arXiv  Detail & Related papers  (2020-05-18T18:03:33Z)

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.