Variational Thermal Quantum Simulation via Thermofield Double States

Wu, Jingxiang; Hsieh, Timothy H.

doi:10.1103/physrevlett.123.220502

Cited by 163 publications

(196 citation statements)

References 48 publications

(49 reference statements)

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“…2a). We also note interesting recent works on how to prepare a TFD state using quantum circuits [30][31][32]; however, these approaches are limited to the moderate system sizes accessible on present-day quantum simulators, similar to the experiments of Refs. [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Diagnosing quantum chaos in many-body systems using entanglement as a resource

Lantagne-Hurtubise

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Can

et al. 2020

Phys. Rev. Research

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Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various models, but their experimental study requires the ability to evolve quantum states backward in time, similar to the canonical Loschmidt echo measurement. In some simple systems, backward time evolution can be achieved by reversing the sign of the Hamiltonian; however in most interacting many-body systems, this is not a viable option. Here we propose a new family of protocols for OTOC measurement that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of the system. We show that, remarkably, in this situation the Lyapunov chaos exponent λL can be extracted from the measurement of an ordinary two-point correlation function. As an unexpected bonus, we find that our proposed method yields the so-called "regularized" OTOC -a quantity that is believed to most directly indicate quantum chaos. According to recent theoretical work, the TFD state can be prepared as the ground state of two weakly coupled identical systems and is therefore amenable to experimental study. We illustrate the utility of these protocols on the example of the maximally chaotic Sachdev-Ye-Kitaev model and support our findings by extensive numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Diagnosing quantum chaos in many-body systems using entanglement as a resource

Lantagne-Hurtubise

Plugge

Can

et al. 2020

Phys. Rev. Research

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“…Unless we find a way to modify the Hamiltonian which encodes information on temperature and changes its eigenvalues, the VQE algorithm won't be applicable here. In the future, we also plan to use techniques from [11], [12], [14] and [15] to perform a variational quantum computation of the thermo double state. Since the operator we use is similar to a time-evolution operator, we can use the techniques of quantum walks to analyze the effect of the operator on quantum states.…”

Section: Discussionmentioning

confidence: 99%

“…The theory was developed by Takahashi and Umezawa in [10] and by Das in [1]. It is also covered by Cottrell in [11] and by Wu in [12].…”

Section: Introduction -Discrete Quantum Mechanicsmentioning

confidence: 99%

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Thermo Field Dynamics on a Quantum Computer

Miceli

McGuigan

2019

2019 New York Scientific Data Summit (NYSDS)

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In this project we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we implemented a real-time therom field dynamics formalism, which has the added benefit of being able to compute quantities that are both time-and temperature-dependent. To implement thermo field dynamics we apply a unitary transformation [1] to discrete quantum mechanical operators to make new Hamiltonians with encoded temperature dependence. The method works normally for fermions, which have a finite representation, but needs some modification to work with bosons. These Hamiltonians are then processed into a Pauli matrix representation in order to be used as input for IBM's Qiskit package [2]. We then use IBM's quantum simulator to calculate an approximation to the Hamiltonaian's ground state energy via the variational quantum eigensolver (VQE) algorithm [3]. This approximation is then compared to a classically calculated value for the exact energy. The thermo field dynamics quantum algorithm has general applications to material science, high-energy physics and nuclear physics, particularly in those situations involving realtime evolution at high temperature.

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“…In this work, we use protocols (18) inspired by the alternation of unitary operators that forms the basis of the quantum approximate optimization algorithm (QAOA) (22). This scheme allows us to use unitary operations to control the effective temperature of a subsystem, thus foregoing the need of an external heat bath.…”

mentioning

confidence: 99%

Generation of thermofield double states and critical ground states with a quantum computer

Zhu

Johri

Linke

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

106

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Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum–classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.

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Variational Thermal Quantum Simulation via Thermofield Double States

Cited by 163 publications

References 48 publications

Diagnosing quantum chaos in many-body systems using entanglement as a resource

Diagnosing quantum chaos in many-body systems using entanglement as a resource

Thermo Field Dynamics on a Quantum Computer

Generation of thermofield double states and critical ground states with a quantum computer

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