Related papers: Almost-Everywhere Superiority for Quantum Computin…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
In automata theory, the quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to the QFAs augmented with counters or stacks. Moreover, to our…
We design machines that learn how to rotate a quantum bit about an initially unknown direction, encoded in the state of a spin-j particle. We show that a machine equipped with a quantum memory of O(log j) qubits can outperform all machines…
Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Quantum advantage is well-established in centralized computing, where quantum algorithms can solve certain problems exponentially faster than classical ones. In the distributed setting, significant progress has been made in…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space…
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,…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers,…
Simon's problem is an essential example demonstrating the faster speed of quantum computers than classical computers for solving some problems. The optimal separation between exact quantum and classical query complexities for Simon's…
A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…
Quantum computing has garnered significant attention in recent years from both academia and industry due to its potential to achieve a "quantum advantage" over classical computers. The advent of quantum computing introduces new challenges…