Unraveling the emergence of quantum state designs in systems with symmetry
- URL: http://arxiv.org/abs/2402.08949v3
- Date: Wed, 21 Aug 2024 17:17:22 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 during the early time evolution in comparison to the cases when the symmetry is broken.
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://creativecommons.org/licenses/by/4.0/
- 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 translation symmetry. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. 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
- Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems [0.0]
The quantum Mpemba effect is the counter-intuitive non-equilibrium phenomenon wherein the dynamic restoration of a broken symmetry occurs more rapidly when the initial state exhibits a higher degree of symmetry breaking.
Here we focus on a two-dimensional free-fermion lattice employing the entanglement asymmetry as a measure of symmetry breaking.
We find that the quantum Mpemba effect is strongly affected by the size of the system in the transverse dimension, with the potential to either enhance or spoil the phenomenon depending on the initial states.
arXiv Detail & Related papers (2024-03-07T13:38:40Z) - Action formalism for geometric phases from self-closing quantum
trajectories [55.2480439325792]
We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system.
We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
arXiv Detail & Related papers (2023-12-22T15:20:02Z) - 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) - Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits [0.0]
We consider quantum circuits in one and two dimensions comprising randomly applied unitary gates and local measurements.
In the absence of randomness, the protocol generates a symmetry-protected long-range entangled state in a finite-depth circuit.
We find two important time scales that we associate with the emergence of certain symmetry generators.
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) - 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) - 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) - Symmetry-adapted variational quantum eigensolver [0.7734726150561086]
We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm.
The symmetry-adapted VQE scheme simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry.
arXiv Detail & Related papers (2019-12-31T02:13:11Z)
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.