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Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
Variational quantum eigensolver (VQE), which attracts attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that…
The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…
In this work we propose an efficient black-box solver for two-dimensional stationary diffusion equations, which is based on a new robust discretization scheme. The idea is to formulate an equation in a certain form without derivatives with…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
We propose and analyse a class of analytically solvable models of quantum reinforcement learning (QRL), formulated as finite-horizon Markov decision processes in finite-dimensional Hilbert spaces. The models are built around a…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
Given a set of $n$ points on a plane, in the Minimum Weight Triangulation problem, we wish to find a triangulation that minimizes the sum of Euclidean length of its edges. This incredibly challenging problem has been studied for more than…
In this thesis we deal with two different topics. In the first half we investigate how the Bayesian formalism can be introduced into the problem of quantum thermometry -- a field which exploits the high level of control in coherent devices…
We demonstrate a method for exact determination of the quadratic curve of minimal energy and minimal curvature variation through three non-colinear points in the plane, including methods to determine the tangent vector and curvature at any…
Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. We consider the (small)…