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Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product…
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
A distributed algorithm is described for solving a linear algebraic equation of the form $Ax=b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
In this paper two algorithms solving circuit satisfiability problem over supernilpotent algebras are presented. The first one is deterministic and is faster than fastest previous algorithm presented by Aichinger. The second one is…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the…
We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…