Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models

• URL: http://arxiv.org/abs/2310.01699v2
• Date: Sat, 11 Nov 2023 20:20:47 GMT
• Title: Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Authors: Hanchen Liu, Vikram Ravindranath, and Xiao Chen
• Abstract summary: We construct 2-dimensional bipartite cluster states and perform single-qubit measurements on the bulk qubits. We bridge this boundary state entanglement transition and the measurement-induced phase transition in the non-unitary 1+1-dimensional circuit. Specifically, we establish a relation between the boundary state entanglement transition and the sampling complexity of the bipartite $2$d cluster state.
• Score: 2.7354851983299784
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we construct 2-dimensional bipartite cluster states and perform single-qubit measurements on the bulk qubits. We explore the entanglement scaling of the unmeasured 1-dimensional boundary state and show that under certain conditions, the boundary state can undergo a volume-law to an area-law entanglement transition driven by variations in the measurement angle. We bridge this boundary state entanglement transition and the measurement-induced phase transition in the non-unitary 1+1-dimensional circuit via the transfer matrix method. We also explore the application of this entanglement transition on the computational complexity problems. Specifically, we establish a relation between the boundary state entanglement transition and the sampling complexity of the bipartite $2$d cluster state, which is directly related to the computational complexity of the corresponding Ising partition function with complex parameters. By examining the boundary state entanglement scaling, we numerically identify the parameter regime for which the $2$d quantum state can be efficiently sampled, which indicates that the Ising partition function can be evaluated efficiently in such a region.

Related papers

• Concomitant Entanglement and Control Criticality Driven by Collective Measurements [0.0]
  We study Adaptive quantum circuits where a quantum many-body state is controlled using measurements and conditional unitary operations. We find two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state. We attribute this feature and the apparent coincidence of the control and entanglement transitions to the global nature of the control.
  arXiv  Detail & Related papers  (2024-09-10T18:00:03Z)
• Probing critical phenomena in open quantum systems using atom arrays [3.365378662696971]
  At quantum critical points, correlations decay as a power law, with exponents determined by a set of universal scaling dimensions. Here, we employ a Rydberg quantum simulator to adiabatically prepare critical ground states of both a one-dimensional ring and a two-dimensional square lattice. By accounting for and tuning the openness of our quantum system, we are able to directly observe power-law correlations and extract the corresponding scaling dimensions.
  arXiv  Detail & Related papers  (2024-02-23T15:21:38Z)
• Complex dynamics approach to dynamical quantum phase transitions: the Potts model [0.0]
  This paper introduces complex dynamics methods to study dynamical quantum phase transitions in the one- and two-dimensional quantum 3-state Potts model. We show that special boundary conditions can alter the nature of the transitions, and verify the claim for the one-dimensional system by transfer matrix calculations. Our approach can be extended to multi-variable problems, higher dimensions, and approximate RG transformations expressed as rational functions.
  arXiv  Detail & Related papers  (2023-08-28T18:26:41Z)
• Multipartite entanglement theory with entanglement-nonincreasing operations [91.3755431537592]
  We extend the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states.
  arXiv  Detail & Related papers  (2023-05-30T12:53:56Z)
• Triviality of quantum trajectories close to a directed percolation transition [0.0]
  We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state.
  arXiv  Detail & Related papers  (2022-12-28T18:52:56Z)
• Embed to Control Partially Observed Systems: Representation Learning with Provable Sample Efficiency [105.17746223041954]
  Reinforcement learning in partially observed Markov decision processes (POMDPs) faces two challenges. It often takes the full history to predict the future, which induces a sample complexity that scales exponentially with the horizon. We propose a reinforcement learning algorithm named Embed to Control (ETC), which learns the representation at two levels while optimizing the policy.
  arXiv  Detail & Related papers  (2022-05-26T16:34:46Z)
• Determining ground-state phase diagrams on quantum computers via a generalized application of adiabatic state preparation [61.49303789929307]
  We use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. We are able to calculate an accurate phase diagram on both two and three site systems using IBM quantum machines.
  arXiv  Detail & Related papers  (2021-12-08T23:59:33Z)
• Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization [58.720142291102135]
  We propose a method for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. We observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.
  arXiv  Detail & Related papers  (2021-04-21T10:36:57Z)
• Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases [55.41644538483948]
  Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. Our results open new horizons for measurement-enabled quantum control of many-body topological states.
  arXiv  Detail & Related papers  (2021-02-10T19:00:00Z)
• Measurement-Driven Phase Transition within a Volume-Law Entangled Phase [0.0]
  We study a transition between two kinds of volume-law entangled phases in non-local but few-body unitary dynamics. In one phase, a finite fraction belongs to a fully-entangled state, while in the second phase, the steady-state is a product state over extensively many, finite subsystems.
  arXiv  Detail & Related papers  (2020-05-06T18:01:32Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.