Related papers: Two Classical Queries versus One Quantum Query
Even if Google AI's Sycamore processor is efficient for the particular task it has been designed for it fails to deliver universal computational capacity. Furthermore, even classical devices implementing transverse homoclinic orbits realize…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit…
A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results…
We present an oracle problem, which we call the Repeated Randomness problem, that a quantum algorithm can solve in one query, while any classical algorithm requires $\Omega(\log n)$ queries, where the oracle function has $2^n$ inputs. This…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…
The well-known Deutsch Algorithm (DA) and Deutsch-Jozsha Algorithm (DJA) both are used as an evidence to the power of quantum computers over classical computation mediums. In these theoretical experiments, it has been shown that a quantum…
Although classical computing has excelled in a wide range of applications, there remain problems that push the limits of its capabilities, especially in fields like cryptography, optimization, and materials science. Quantum computing…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the…
A quantum computer (QC) can solve many computational problems more efficiently than a classic one. The field of QCs is growing: companies (such as DWave, IBM, Google, and Microsoft) are building QC offerings. We position that software…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only…
We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form…
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…
The capacity of a classical-quantum channel (or in other words the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's Problem - a black box period-finding problem which has an exponential gap between the classical and quantum runtime. Using an…
It is well known, and appreciated, that quantum computers have the potential to be the most powerful computational devices ever created. This newfound power comes from a quantum parallelism effect that allows the computer to be in multiple…