Unraveling the emergence of quantum state designs in systems with symmetry
- URL: http://arxiv.org/abs/2402.08949v2
- Date: Sun, 17 Mar 2024 16:22:16 GMT
- Title: Unraveling the emergence of quantum state designs in systems with symmetry
- Authors: Naga Dileep Varikuti, Soumik Bandyopadhyay,
- Abstract summary: We study the emergence of state designs from the random generator states exhibiting symmetries.
We find faster convergence of the trace distance in the initial time, however, it saturates to a finite value deviating from random matrix prediction at a late time.
We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.
- Score: 15.699822139827916
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics. Symmetries, on the other hand, are expected to reduce the randomness of a state. Despite being ubiquitous, the effects of symmetry on quantum state designs remain an outstanding question. The recently introduced projected ensemble framework generates efficient approximate state t-designs by hinging on projective measurements and many-body quantum chaos. In this work, we examine the emergence of state designs from the random generator states exhibiting symmetries. Leveraging on translation symmetry, we analytically establish a sufficient condition for the measurement basis leading to the state t-designs. Then, by making use of the trace distance measure, we numerically investigate the convergence to the designs. Subsequently, we inspect the violation of the sufficient condition to identify bases that fail to converge. We further demonstrate the emergence of state designs in a physical system by studying the dynamics of a chaotic tilted field Ising chain with periodic boundary conditions. We find faster convergence of the trace distance in the initial time, however, it saturates to a finite value deviating from random matrix prediction at a late time, in contrast to the case with open boundary condition. To delineate the general applicability of our results, we extend our analysis to other symmetries. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.
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) - Asymptotic behavior of continuous weak measurement and its application
to real-time parameter estimation [4.329298109272387]
The quantum trajectory of weak continuous measurement for the magnetometer is investigated.
We find that the behavior is insensitive to the initial state in the following sense: given one realization, the quantum trajectories starting from arbitrary initial statesally converge to the em same realization-specific em pure state.
arXiv Detail & Related papers (2023-11-03T17:50:45Z) - Edge modes and symmetry-protected topological states in open quantum
systems [0.0]
Topological order offers possibilities for processing quantum information which can be immune to imperfections.
We show robustness of certain aspects of $ZZtimes Z$ symmetry-protected trajectory (SPT) order against a wide class of dissipation channels.
Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases.
arXiv Detail & Related papers (2023-10-13T21:09:52Z) - Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.
This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
arXiv Detail & Related papers (2023-10-04T09:51:00Z) - Ground or Excited State: a State-Specific Variational Quantum
Eigensolver for Them All [0.0]
Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in quantum devices.
We propose a unified VQE framework that treats the ground and excited states in the same footings.
We introduce the notion of totally symmetric, spin-scalar unitary which maintains the purity of the reference at each step of the optimization.
arXiv Detail & Related papers (2023-08-21T13:39:58Z) - Stabilization of symmetry-protected long-range entanglement in
stochastic quantum circuits [0.0]
We consider quantum circuits in one and two dimensions consisting of randomly applied unitary gates and local measurements.
We find two important time scales which we associate with the emergence of certain symmetry generators.
We devise error-mitigation protocols that provide significant improvement on both time scales.
arXiv Detail & Related papers (2023-06-22T16:09:12Z) - Geometric phases along quantum trajectories [58.720142291102135]
We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
arXiv Detail & Related papers (2023-01-10T22:05:18Z) - 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) - Bose-Einstein condensate soliton qubit states for metrological
applications [58.720142291102135]
We propose novel quantum metrology applications with two soliton qubit states.
Phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes.
arXiv Detail & Related papers (2020-11-26T09:05:06Z) - State preparation and measurement in a quantum simulation of the O(3)
sigma model [65.01359242860215]
We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site.
We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes.
We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
arXiv Detail & Related papers (2020-06-28T23:44:12Z) - Measurement-induced quantum criticality under continuous monitoring [0.0]
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement.
We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength.
We propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations.
arXiv Detail & Related papers (2020-04-24T19:35:28Z)
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.