Phase Transitions in the Classical Simulability of Open Quantum Systems

Azad, Fatemeh; Hallam, Andrew; Morley, James G.; Green, A. G.

doi:10.48550/arxiv.2111.06408

Cited by 3 publications

(3 citation statements)

References 50 publications

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“…This model has a groundstate quantum phase transition at g/J = 1 and a dynamical quantum phase transition when a groundstate prepared on one side of the critical point (say g/J > 1) is evolved with a Hamiltonian on the opposite side (say g/J < 1). Though an exact solution can be obtained using a Jordan-Wigner transformation, much remains to be understood and its dynamical and thermalisation properties are the subject of current research interest [28][29][30].…”

Section: A Quantum Phase Transitionsmentioning

confidence: 99%

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin,

Wimalaweera,

Barratt

et al. 2022

Preprint

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We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states. CONTENTS I. Introduction 1 II. Results 2 A. Quantum Phase Transitions 3 B. Groundstate Optimisation 3 C. Calculating and Optimising Overlaps 5 D. Quantum Dynamics 6 III. Discussion 7 IV. Methods 8 A. Fixed-point equations 8 B. Error Mitigation Strategies 8 References 9

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Section: A Quantum Phase Transitionsmentioning

confidence: 99%

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin,

Wimalaweera,

Barratt

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…is evolved with a Hamiltonian on the opposite side (say g/J < 1). Though an exact solution can be obtained using a Jordan-Wigner transformation, much remains to be understood and its dynamical and thermalisation properties are the subject of current research interest [28][29][30].…”

Section: A Quantum Phase Transitionsmentioning

confidence: 99%

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Dborin

Wimalaweera

Barratt

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The quantum simulation of complex quantum phenomena exploring the exponentially large Hilbert space have been enriched by using entanglement as a probe. Entanglement provides a non-trivial parametrization of the many-body states which has ramifications for their simulability [17][18][19]. For non-equilibrium phenomena the dynamics of entanglement can exhibit universal features characterizing the phase of matter and its coarse grained properties, which can be a useful tool for visualizing macroscopic quantum coherence.…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation using noisy unitary circuits and measurements

Lunt¹,

Richter²,

Pal³

2021

Preprint

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Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steadystate entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.

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Phase Transitions in the Classical Simulability of Open Quantum Systems

Cited by 3 publications

References 50 publications

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

Quantum simulation using noisy unitary circuits and measurements

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