Related papers: Monte Carlo simulation of stoquastic Hamiltonians
We study classical polynomial-time approximation algorithms for the transverse-field Ising model (TFIM) Hamiltonian, allowing a mixture of ferromagnetic and anti-ferromagnetic interactions between pairs of qbits, alongside transverse field…
Recently, Huggins et. al. [Nature, 603, 416-420 (2022)] devised a general projective Quantum Monte Carlo method suitable for implementation on quantum computers. This hybrid approach, however, relies on a subroutine -the computation of the…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
In a typical finite temperature quantum Monte Carlo (QMC) simulation, estimators for simple static observables such as specific heat and magnetization are known. With a great deal of system-specific manual labor, one can sometimes also…
Direct Monte Carlo simulations of the Enskog-Boltzmann equation for a spatially uniform system of smooth inelastic spheres are performed. In order to reach a steady state, the particles are assumed to be under the action of an external…
We present a classical Monte Carlo (MC) scheme which efficiently estimates an imaginary-time, decaying signal for stoquastic (i.e. sign-problem-free) local Hamiltonians. The decay rates in this signal correspond to Hamiltonian eigenvalues…
In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In…
We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show the dominance of the pairwise terms in the autoregressive…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this…
We study a Hamiltonian lattice version of the two-dimensional Wess-Zumino model. Preliminary results obtained by Quantum Monte Carlo with a many-parameter guiding wave function are presented. We analyze the pattern of supersymmetry breaking…
Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
We propose a quantum algorithm for simulating spin models based on periodic modulation of transmon qubits. Using Floquet theory we derive an effective time-averaged Hamiltonian, which is of the general XYZ class, different from the…
We use a quantum Monte Carlo method to study the ground state and thermodynamic phase transitions of the spin supersolid phase in the S=1 Heisenberg model with uniaxial anisotropy. The thermal melting of the supersolid phase shows unqiue…
Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the…
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this…
We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields…
By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by…
In order to extend the recently proposed Monte Carlo Hamiltonian to many-body systems, we suggest to concept of a stochastic basis. We apply it to the chain of $N_s=9$ coupled anharmonic oscillators. We compute the spectrum of excited…