Abstract
We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization, are fragile and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs those that depend on local trajectories.
Highlights
Quantum simulators promise solutions to a wide variety of problems in many-body system physics that cannot be solved efficiently by analytic approximation or classical numerical simulation [1,2,3,4,5]
We have studied the effects of chaos arising from a perturbation on the quantum simulation of quantum phase transitions (QPTs) in the LMG Hamiltonian
One expects chaos to play an important role in the reliability of such simulations given the connection between QPTs, bifurcations, unstable fixed points, and instabilities that arise in the semiclassical behavior of an order parameter in the thermodynamic limit
Summary
Quantum simulators promise solutions to a wide variety of problems in many-body system physics that cannot be solved efficiently by analytic approximation or classical numerical simulation [1,2,3,4,5]. In a series of papers, Heyl et al [23] and Sieberer et al [24] studied the simulation of Ising-type Hamiltonians through Trotterization in a gate model In this approximation, the unitary map consists of a series of Floquet maps describing the dynamics of a delta-kicked system, which is quantum chaotic in a particular parameter regime. For models describable in the thermodynamic limit by mean-field theories [25], QPTs are often associated with bifurcations in the phase-space dynamics that governs the order parameters. These bifurcations lead to unstable fixed points and separatrix lines, and we expect chaos to develop in their vicinity in the presence of small perturbations.
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