Related papers: Sign Embedding Quantum Algorithms for Matrix Equat…

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups.…

A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which ``unravels'' the quantum Master equation can be used for the…

We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…

The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…

In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra…

We study the sign problem in the Hubbard model on the hexagonal lattice away from half-filling using the Lefschetz thimbles method. We identify the saddle points, reduce their amount, and perform quantum Monte Carlo (QMC) simulations using…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties. Under generic assumptions, these are symplectic manifolds with natural global action-angle coordinates. This paper is concerned…

Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time $\beta$ and system size. The sign problem…

Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine…

Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently,…

We derive an asymptotic expansion for off-diagonal coherent-state matrix elements of non-polynomial operators in gauge theories admitting holomorphic coherent-state representations. The derivation combines stationary-phase analysis with an…

Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…

The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…

Solving linear and nonlinear differential equations with large degrees of freedom is an important task for scientific and industrial applications. In order to solve such differential equations on a quantum computer, it is necessary to embed…

Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

Quantum state preparation, also known as encoding or embedding, is a crucial initial step in many quantum algorithms and often constrains theoretical quantum speedup in fields such as quantum machine learning and linear equation solvers.…