Optimization of Trial Wave Functions for Hamiltonian Lattice Models

The energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo is formally identical to a problem of fitting data: we reexamine it from a statistical maximum-likelihood point of view. We detect the origin of the problem of convergence that is often encountered in practice and propose an alternative procedure for optimization of trial wave functions in quantum Monte Carlo. We successfully test this proposal by optimizing a trial w...

With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions. The previous work has shown the success of this method in (1+1)-dimensional quantum mechanical systems. In this work we apply it to higher dimensional systems.

We present a modification of the Hybrid Monte Carlo algorithm for tackling the critical slowing down of generating Markov chains of lattice gauge configurations towards the continuum limit. We propose a new method to exchange information within an ensemble of Markov chains, and use it to construct an approximate inverse Hessian matrix of the action inspired from quasi-Newton algorithms for optimization. The kinetic term of the molecular dynamics evolution includes the approxi...

As a prerequisite to dynamical fermion simulations a detailed study of optimal parameters and scaling behavior is conducted for the quenched Schr\"odinger functional at fixed renormalized coupling. We compare standard hybrid overrelaxation techniques with local and global hybrid Monte Carlo. Our efficiency measure is designed to be directly relevant for the strong coupling constant as used by the ALPHA collaboration.

The COntractor REnormalization group (CORE) approximation, a new method for solving Hamiltonian lattice systems, is introduced. The approach combines variational and contraction techniques with the real-space renormalization group approach and is systematically improvable. Since it applies to lattice systems of infinite extent, the method is suitable for studying critical phenomena and phase structure; systems with dynamical fermions can also be treated. The method is tested ...

We describe a numerical algorithm for computing spin glass ground states with a high level of reliability. The method uses a population based search and applies optimization on multiple scales. Benchmarks are given leading to estimates of the performance on large lattices.

We explore the application of quantum optimal control (QOC) techniques to state preparation of lattice field theories on quantum computers. As a first example, we focus on the Schwinger model, quantum electrodynamics in 1+1 dimensions. We demonstrate that QOC can significantly speed up the ground state preparation compared to gate-based methods, even for models with long-range interactions. Using classical simulations, we explore the dependence on the inter-qubit coupling str...

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimension...

We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques. We demonstrate the effectiveness of this approach by u...