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Register a new userMatrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
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Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the development of better quantum algorithms (quantum error correction codes) and for the realization of a quantum theory of gravity. Quantum computing and deep learning offer us potentially useful approaches to study the dynamics of matrix quantum mechanics. In this paper we perform a systematic survey for quantum computing and deep learning approaches to matrix quantum mechanics, comparing them to Lattice Monte Carlo simulations. In particular, we test the performance of each method by calculating the low-energy spectrum.
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The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of the strong interaction, the quantum chromodynamics defined on the hypercubic space-time lattice. After a brief summary of the empirical nucleon-nucleon (NN) potentials which can fit the NN scattering experiments in high precision, we outline the basic formulation to derive the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe-Salpeter amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a $32^4$ lattice with the lattice spacing $a simeq 0.137 $fm (lattice volume (4.4 fm)$^4$) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at KEK. We found that the calculated NN potential at low energy has basic features expected from the empirical NN potentials; attraction at long and medium distances and the repulsive core at short distance. Various future directions along this line of research are also summarized.
We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix
We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab-initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semi-positive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperature.
We consider the problem of including $Lambda$ hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons is typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energy of the light hypernuclei. In this exploratory work we use spin-independent nucleon-nucleon and hyperon-nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon-nucleon interactions, as well as applications to other quantum many-body systems.
Gauge field theories play a central role in modern physics and are at the heart of the Standard Model of elementary particles and interactions. Despite significant progress in applying classical computational techniques to simulate gauge theories, it has remained a challenging task to compute the real-time dynamics of systems described by gauge theories. An exciting possibility that has been explored in recent years is the use of highly-controlled quantum systems to simulate, in an analog fashion, properties of a target system whose dynamics are difficult to compute. Engineered atom-laser interactions in a linear crystal of trapped ions offer a wide range of possibilities for quantum simulations of complex physical systems. Here, we devise practical proposals for analog simulation of simple lattice gauge theories whose dynamics can be mapped onto spin-spin interactions in any dimension. These include 1+1D quantum electrodynamics, 2+1D Abelian Chern-Simons theory coupled to fermions, and 2+1D pure Z2 gauge theory. The scheme proposed, along with the optimization protocol applied, will have applications beyond the examples presented in this work, and will enable scalable analog quantum simulation of Heisenberg spin models in any number of dimensions and with arbitrary interaction strengths.
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