Related papers: Approximating Fractional Time Quantum Evolution

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

In this work, we present a comprehensive framework for approximating the weakly singular power-law kernel $t^{\alpha-1}$ of fractional integral and differential operators, where $\alpha \in (0,1)$ and $t \in [\delta,T]$ with…

This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…

Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…

Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…

Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most…

Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale…

We defined ordered black boxes in which for a partial $J$ we try to predict just a bound in $J$ to a function restricted to $C_\alpha$. The existence results are closely related to pcf, propagating downward. We can start with trivial cases.

Fourier extension is an approximation scheme in which a function on an arbitary bounded domain is approximated using a classical Fourier series on a bounding box. On the smaller domain the Fourier series exhibits redundancy, and it has the…

Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…

Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…

Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…

The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…

We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution…

There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: <U(t)>=exp(at)+... This expression plays the crucial role in considerations of problems…

Population-based evolutionary algorithms are often considered when approaching computationally expensive black-box optimization problems. They employ a selection mechanism to choose the best solutions from a given population after comparing…

Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…

We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…