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The design of quantum control methods has been shown to greatly improve the performance of many evolving quantum technologies. To this end, the usage of adiabatic dynamics to drive quantum systems is seriously limited by the action of…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…
Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Open quantum systems are a rich area of research in the intersection of quantum mechanics and stochastic analysis. By considering a variety of master equations, we unify multiple views of autonomous and controlled open quantum systems and,…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…
The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations…
Statistical multispecies models of multiarea marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance…
We give a quantum logspace algorithm for powering contraction matrices, that is, matrices with spectral norm at most~1. The algorithm gets as an input an arbitrary $n\times n$ contraction matrix $A$, and a parameter $T \leq…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…