Related papers: An efficient quantum algorithm for the one-dimensi…
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamical properties can be computed from its grand canonical potential according to standard procedures. In general, there is no closed…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary…
We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions, mesoscopic variables, of the lattice…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
We attempt the use of a unitary operator to approximate the lattice Boltzmann collision operator. We use a modified amplitude encoding to bypass the renormalization that would have required classical processing at every step (thus eroding…
Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in…
We derive a lattice approximation for a class of equilibrium quantum statistics describing the behaviour of any combination and number of bosonic and fermionic particles with any sufficiently binding potential. We then develop an intuitive…
Quantum simulation of Lattice Gauge Theories has been proposed and used as a method to overcome theoretical difficulties in dealing with the non-perturbative nature of such models. In this work we focus on two important bottlenecks that…
We propose a single-step simplified lattice Boltzmann algorithm capable of performing magnetohydrodynamic (MHD) flow simulations in pipes for very small values of magnetic Reynolds numbers $R_m$. In some previous works, most lattice…
Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of…
Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators…