Related papers: Quantum divide and conquer
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly…
Control and learning are key to technological advancement, both in the classical and quantum domains, yet their interrelationship is insufficiently clear in the literature, especially between classical and quantum definitions of control and…
The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
Despite years of effort, the quantum machine learning community has only been able to show quantum learning advantages for certain contrived cryptography-inspired datasets in the case of classical data. In this note, we discuss the…
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…
Quantum Machine Learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources…
The formula-evaluation problem is defined recursively. A formula's evaluation is the evaluation of a gate, the inputs of which are themselves independent formulas. Despite this pure recursive structure, the problem is combinatorially…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover's algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at…
This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
This paper considers the triangle finding problem in the CONGEST model of distributed computing. Recent works by Izumi and Le Gall (PODC'17), Chang, Pettie and Zhang (SODA'19) and Chang and Saranurak (PODC'19) have successively reduced the…
A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of…
A locking protocol between two parties is as follows: Alice gives an encrypted classical message to Bob which she does not want Bob to be able to read until she gives him the key. If Alice is using classical resources, and she wants to…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…