Related papers: Lower Bounds for Parallel Quantum Counting
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…
We present a practical application of parallel symbolic computation in General Relativity: the calculation of curvature invariants for large dimension. We discuss the structure of the calculations, an implementation of the technique and…
Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidences that quantum computers could…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the success probabilities for the two…
In the literature of stochastic orders, one rarely finds results that can be considered as criteria for the non-comparability of random variables. In this paper, we provide results that enable researchers to use simple tools to conclude…
We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed…
We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap.…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
The quantum machine learning model is emerging as a new model that merges quantum computing and machine learning. Simulating very deep quantum machine learning models requires a lot of resources, increasing exponentially based on the number…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
A new method for computing sums on a quantum computer is introduced. This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits. This approach also…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
We developed a practical quantum advantage benchmarking framework that connects the accumulation of entropy in a quantum processing unit and the degradation of the solution to a target optimization problem. The benchmark is based on…
In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum Advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) multivariate quadratic…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…