Minimal effective Gibbs ansatz: A simple protocol for extracting an accurate thermal representation for quantum simulation

Cohn, Jeffrey; Yang, Fan; Najafi, Khadijeh; Jones, Barbara; Freericks, J. K.

doi:10.1103/physreva.102.022622

Cited by 22 publications

(12 citation statements)

References 31 publications

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“…While jψ β i is straightforward to compute on a classical machine, a scheme to implement the unnatural nonunitary evolution on a quantum computer has been recently proposed [87]. Thus, random circuits might also provide a means to prepare thermal states on NISQ devices, complementary to other approaches for this task [87][88][89][90].…”

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confidence: 99%

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Richter

Pal

2021

Phys. Rev. Lett.

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In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one-and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

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mentioning

confidence: 99%

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Richter

Pal

2021

Phys. Rev. Lett.

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“…While |ψ β is straight-forward to compute on a classical machine, a scheme to implement the unnatural nonunitary evolution on a quantum computer has been recently proposed [75]. Thus, random circuits might also provide a means to prepare thermal states on NISQ devices, complementary to other approaches for this task [75][76][77][78].…”

Section: Discussionmentioning

confidence: 99%

Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

Richter,

Pal

2020

Preprint

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In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one-and twodimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

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“…The method uses a variation of the QPE on a quantum computer to find the Green's function of the system. An approach that uses a small set of pure states to obtain properties of a thermal state was numerically applied to a ten-site Hubbard model [284].…”

Section: Thermal Statesmentioning

confidence: 99%

Simulating Quantum Materials with Digital Quantum Computers

Bassman,

Urbanek,

Metcalf

et al. 2021

Preprint

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Quantum materials exhibit a wide array of exotic phenomena and practically useful properties. A better understanding of these materials can provide deeper insights into fundamental physics in the quantum realm as well as advance technology for entertainment, healthcare, and sustainability. The emergence of digital quantum computers (DQCs), which can efficiently perform quantum simulations that are otherwise intractable on classical computers, provides a promising path forward for testing and analyzing the remarkable, and often counter-intuitive, behavior of quantum materials. Equipped with these new tools, scientists from diverse domains are racing towards achieving physical quantum advantage (i.e., using a quantum computer to learn new physics with a computation that cannot feasibly be run on any classical computer). The aim of this review, therefore, is to provide a summary of progress made towards this goal that is accessible to scientists across the physical sciences. We will first review the available technology and algorithms, and detail the myriad ways to represent materials on quantum computers. Next, we will showcase the simulations that have been successfully performed on currently available DQCs, emphasizing the variety of properties, both static and dynamic, that can be studied with this nascent technology. Finally, we work through two examples of how to map a materials problem onto a DQC, with full code included in the Supplementary Material. It is our hope that this review can serve as an organized overview of progress in the field for domain experts and an accessible introduction to scientists in related fields interested in beginning to perform their own simulations of quantum materials on DQCs.

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Minimal effective Gibbs ansatz: A simple protocol for extracting an accurate thermal representation for quantum simulation

Cited by 22 publications

References 31 publications

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

Simulating Quantum Materials with Digital Quantum Computers

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