Related papers: A Brief Introduction to Quantum Query Complexity
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…
This is a set of lecture notes for a graduate-level course on quantum algorithms, with an emphasis on quantum optimization algorithms. It is developed for applied mathematicians and engineers, and requires no previous background in quantum…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
We use the benefits and components of classical computers every day. However, there are many types of problems which, as they grow in size, their computational complexity grows larger than classical computers will ever be able to solve.…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). To start off with, we offer a concise exposition of the technique, which easily extends…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…