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By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
Gutzwiller functions are popular variational wavefunctions for correlated electrons in Hubbard models. Following the variational principle, we are interested in the Gutzwiller parameters that minimize e.g. the expectation value of the…
This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…
We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interaction. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
Variational Quantum Algorithms have emerged as promising tools for solving optimization problems on quantum computers. These algorithms leverage a parametric quantum circuit called ansatz, where its parameters are adjusted by a classical…
Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more…
We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the…
An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The…
A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying…
We present a variational wavefunction which explains the behaviour of the supersolid state formed by hard-core bosons on the triangular lattice. The wavefunction is a linear superposition of {\em only and all} configurations minimising the…
We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations,…
Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator…
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave…
The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic…
The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such…
We present a new approach-the ALVar estimator-to estimation of asymptotic variance in sequential Monte Carlo methods, or, particle filters. The method, which adjusts adaptively the lag of the estimator proposed in [Olsson, J. and Douc, R.…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
We present a simple and efficient method to optimize within energy minimization the determinantal component of the many-body wave functions commonly used in quantum Monte Carlo calculations. The approach obtains the optimal wave function as…