Related papers: Monte Carlo Hamiltonian - From Statistical Physics…
Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we…
Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo…
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.…
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…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method, in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. We consider two quantum…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately,…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and…
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem,…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
Monte Carlo methods are now an essential part of the statistician's toolbox, to the point of being more familiar to graduate students than the measure theoretic notions upon which they are based! We recall in this note some of the advances…
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…
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…