Abstract
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.22 MoreReceived 23 August 2021Accepted 20 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010324Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLattice gauge theoryMachine learningQuantum algorithmsSupersymmetric field theoriesTechniquesHybrid Monte Carlo algorithmPath-integral Monte CarloQuantum InformationParticles & Fields
Highlights
Gauge-gravity duality [1,2] translates difficult problems in quantum gravity to well-defined problems in nongravitational quantum theories
We briefly introduce the pros and cons of these numerical approaches to matrix models: Monte Carlo simulations—Monte Carlo simulations can be used to study problems that can be accessed by the Euclidean path integral, such as canonical thermodynamics and Euclidean correlation functions
Let us start with the bosonic matrix model, i.e., a matrix model consisting of only bosonic degrees of freedom
Summary
Gauge-gravity duality [1,2] translates difficult (or intractable) problems in quantum gravity to well-defined problems in nongravitational quantum theories. Focus of this paper—By listing the differences between the available numerical methods, it is clear that quantum computing and deep learning can, in principle, be very useful tools in solving matrix models These allow a direct representation of quantum states (encoded in qubits or neural networks), which is needed to access the quantum information stored in the wave function. As for the VQE, the specific architecture that we use does not show a satisfactory performance at strong coupling, perhaps due to the variational forms parametrized by the quantum circuits not adequately probing the full gauge-invariant Hilbert space This result shows that going beyond the VQE and using more complicated or fully quantum algorithms is not the correct way to approach matrix quantum mechanics for because they would require even deeper quantum circuits that are more prone to noise on actual quantum hardware. The codes used to generate the data and make the figures are open source and we provide a web site with additional figures and tables in Ref. [33]
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