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Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator…
We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems that are coupled with harmonic baths. The algorithms are based on evolving the integro-differential equations where the…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
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…
Quantum Monte Carlo integration, a quantum algorithm for calculating expectations that provides a quadratic speed-up compared to its classical counterpart, is now attracting increasing interest in the context of its industrial and…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
We introduce a variational quantum solver for combinatorial optimizations over $m=\mathcal{O}(n^k)$ binary variables using only $n$ qubits, with tunable $k>1$. The number of parameters and circuit depth display mild linear and sublinear…
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\bf 79}, 195117 (2009); Reboredo, {\it ibid.} {\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
Quantum Monte Carlo coupled with neural network wavefunctions has shown success in computing ground states of quantum many-body systems. Existing optimization approaches compute the energy by sampling local energy from an explicit…
In high-energy particle physics, complex Monte Carlo (MC) simulations are needed to compare theory predictions to measurable quantities. Many and large MC samples are needed to be generated to take into account all the systematics.…
The atomic cluster expansion (ACE) (Drautz, 2019) yields a highly efficient and intepretable parameterisation of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
Quantum Monte Carlo methods provide in principle an accurate treatment of the many-body problem of the ground and excited states of condensed systems. In practice, however, uncontrolled errors such as those arising from the fixed-node and…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
We present a simple, robust and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance…
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…
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 present and apply a general-purpose, multi-start algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to…
A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized…