Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Rinaldi, Enrico; Han, Xizhi; Hassan, Mohammad; Feng, Yuan; Nori, Franco; McGuigan, Michael; Hanada, Masanori

doi:10.1103/prxquantum.3.010324

Cited by 40 publications

(51 citation statements)

References 49 publications

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“…Both models can be defined with local Hamiltonians described in details by Ref. [9] and the sought-after physical states are those invariant under SU(2) gauge transformations.…”

Section: Resultsmentioning

confidence: 99%

“…Our benchmark focuses on the expectation value of relevant operators (energy, gauge Casimir) for various strengths of the gauge coupling λ = g 2 N = 2g 2 . For these SU(2) gauge models, where the number of degrees of freedom is limited, we can compare directly with results from exact diagonalization of a truncated Hamiltonian (using the Fock basis) in the limit where the truncation effects are negligible [9]. Moreover, for the supersymmetric model we know that the energy of the ground state is exactly zero at each coupling due to supersymmetry.…”

Section: Resultsmentioning

confidence: 99%

“…Deep artificial neural network architectures, routinely used in the context of density estimation, can be used to efficiently approximate quantum states, without imposing constraining structures on the wave function or limiting their representation power by focusing on simple distributions. Recently, different numerical approaches to matrix model wave functions have been compared in [9].…”

Section: Introductionmentioning

confidence: 99%

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Neural quantum states for supersymmetric quantum gauge theories

Han¹,

Rinaldi²

2021

Preprint

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Supersymmetric quantum gauge theories are important mathematical tools in high energy physics. As an example, supersymmetric matrix models can be used as a holographic description of quantum black holes. The wave function of such supersymmetric gauge theories is not known and it is challenging to obtain with traditional techniques. We employ a neural quantum state ansatz for the wave function of a supersymmetric matrix model and use a variational quantum Monte Carlo approach to discover the ground state of the system. We discuss the difficulty of including bosonic particles and fermionic particles, as well as gauge degrees of freedom.Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

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“…Both models can be defined with local Hamiltonians described in details by Ref. [9] and the sought-after physical states are those invariant under SU(2) gauge transformations.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Neural quantum states for supersymmetric quantum gauge theories

Han¹,

Rinaldi²

2021

Preprint

Self Cite

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“…One can can take an approach of thermodynamics using Hamiltonian quantum cosmology [56] [57] [58] [59] [60] or the thermodynamics of Matrix models [61]. In either case quantum computing should be a useful tool to examine the states and thermodynamic observables [62] [63] [64] [65].…”

Section: Discussionmentioning

confidence: 99%

Quantum Computing of Schwarzschild-de Sitter Black Holes and Kantowski-Sachs Cosmology

Joseph¹,

White²,

Chandra³

et al. 2022

Preprint

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The quantum mechanics of Schwarzschild-de Sitter black holes is of great recent interest because of their peculiar thermodynamic properties as well as their realization in modern dark energy cosmology which indicates the presence of a small positive cosmological constant. We study Schwarzschild-de Sitter black holes and also the Kantowki-Sachs Cosmology using quantum computing. In these cases in addition to the Hamiltonian there is a Mass operator which plays an important role in describing the quantum states of the black hole and Kantowski-Sachs cosmology. We compute the spectrum of these operators using classical and quantum computing. For quantum computing we use the Variational Quantum Eigensolver which is hybrid classical-quantum algorithm that runs on near term quantum hardware. We perform our calculations using 4, 6 and 8 qubits in a harmonic oscillator basis, realizing the quantum operators of the Schwarzschild-de Sitter black hole and Kantowski-Sachs cosmology in terms of 16 × 16, 64 × 64 and 256 × 256 matrices respectively. For the 4 qubit case we find highly accurate results but for the other cases we find a more refined variational ansatz will be necessary to accurately represent the quantum states of a Schwarzschild-de Sitter black hole or Kantowki-Sachs cosmology accurately on a quantum computer.

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“…By dimensionally reducing supersymmetric theories all the way down to (0+1)-dimensional quantum mechanics, we end up with significantly simpler systems to analyze. In addition to reducing the number of degrees of freedom, which makes these theories promising targets for near-term quantum simulation [2][3][4][5], the dimensionally reduced systems also tend to be super-renormalizable. In many cases a one-loop counterterm calculation suffices to restore supersymmetry in the continuum limit [6], with no need for the numerical fine-tuning typically required in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Thermal phase structure of dimensionally reduced super-Yang--Mills

Schaich¹,

Jha²,

Joseph³

2022

Preprint

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We present our current results from ongoing lattice investigations of the Berenstein-Maldacena-Nastase deformation of maximally supersymmetric Yang-Mills quantum mechanics. We focus on the thermal phase structure of this theory, which depends on both the temperature 𝑇 and the deformation parameter 𝜇, through the dimensionless ratios 𝑇/𝜇 and 𝑔 = 𝜆/𝜇 3 with 𝜆 the 't Hooft coupling. We determine the critical 𝑇/𝜇 of the confinement transition for couplings 𝑔 that span three orders of magnitude, to connect weak-coupling perturbative calculations and large-𝑁 dual supergravity predictions in the strong-coupling limit. Analyzing multiple lattice sizes up to 𝑁 𝜏 = 24 and numbers of colors up to 𝑁 = 16 allows initial checks of the large-𝑁 continuum limit.

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Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Cited by 40 publications

References 49 publications

Neural quantum states for supersymmetric quantum gauge theories

Neural quantum states for supersymmetric quantum gauge theories

Quantum Computing of Schwarzschild-de Sitter Black Holes and Kantowski-Sachs Cosmology

Thermal phase structure of dimensionally reduced super-Yang--Mills

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