Related papers: Approximating Fractional Time Quantum Evolution
We consider an algorithm to approximate complex-valued periodic functions $f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm.…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
Due to the significant progress made in the implementation of quantum hardware, efficient methods and tools to design corresponding algorithms become increasingly important. Many of these tools rely on functional representations of certain…
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a…
Compilation of unitaries into a sequence of physical quantum gates is a critical prerequisite for execution of quantum algorithms. This work introduces STOQ, a stochastic search protocol for approximate unitary compilation into a sequence…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We introduce the problem of unitarization. Unitarization is the problem of taking $k$ input quantum circuits that produce orthogonal states from the all $0$ state, and create an output circuit implementing a unitary with its first $k$…
Quantum algorithms for simulation of Hamiltonian evolution are often based on product formulae. The fractal methods give a systematic way to find arbitrarily high-order product formulae, but result in a large number of exponentials. On the…