Related papers: Quantum Approximate Counting, Simplified
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the…
In this paper, we introduce an efficient algorithm for the quantum amplitude estimation task which works in noisy intermediate-scale quantum(NISQ) devices. The quantum amplitude estimation is an important problem which has various…
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…
In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. \emph{Basic Quantum Algorithms} revisits the earliest quantum algorithms. The journey began in 1985 with Deutsch…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
We study the quantum summation QS algorithm of Brassard, Hoyer, Mosca and Tapp, which approximates the arithmetic mean of a Boolean function defined on $N$ elements. We present sharp error bounds of the QS algorithm in the worst-average…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are…
The Jones polynomial, discovered in 1984, is an important knot invariant in topology. Among its many connections to various mathematical and physical areas, it is known (due to Witten) to be intimately connected to Topological Quantum Field…
A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…
Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are…
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
By introducing the "comparison and replacement" (CNR) operation, we propose a general-purpose pure quantum approximate optimization algorithm and derive its core optimization mechanism quantitatively. The algorithm is constructed to a…
Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit…
We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis…