Related papers: Efficient Variational Quantum Linear Solver for St…
We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational…
Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…
Measurement-based quantum computing uses measurement patterns on predefined quantum resource states to execute quantum logic. Quantum simulation offers an important use case on near-term devices. However, pattern optimization depends on the…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…
The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li,~Saad and Sosonkina [NLAA, 2003] for solving general nonsymmetric linear systems. The parallel…
Variational quantum algorithms are a promising hybrid framework for solving chemistry and physics problems with broad applicability to optimization as well. They are particularly well suited for noisy intermediate scale quantum (NISQ)…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
The variational quantum eigensolver has been proposed as a low-depth quantum circuit that can be employed to examine strongly correlated systems on today's noisy intermediate-scale quantum computers. We examine details associated with the…
We introduce an approach for estimating the expectation values of arbitrary $n$-qubit matrices $M \in \mathbb{C}^{2^n\times 2^n}$ on a quantum computer. In contrast to conventional methods like the Pauli decomposition that utilize $4^n$…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…
The discretized Poisson equation matrix (DPEM) in 1D has been shown to require an exponentially large number of terms when decomposed in the Pauli basis when solving numerical linear algebra problems on a quantum computer. Additionally,…
Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
We investigate ancilla-free linear combination of unitaries (LCU) as a framework for approximating complex quantum circuits. This is particularly effective for quantum optimization algorithms, where candidate solutions can be evaluated…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…