Related papers: A simple and efficient algorithm for computing the…
This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function. As such, it may be taken as an…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a refined algorithm, which reduces the size of the register and simplifies the function evaluation, is proposed. The refined version allows a simpler analysis of…
A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…
Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
Algorithms for computing the classical Gaussian quadrature rules (Gauss--Jacobi, Gauss--Laguerre, and Gauss--Hermite) are presented, based on globally convergent fourth-order iterative methods combined with asymptotic approximations, which…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…