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In order to assess potential advantages of quantum algorithms that require quantum oracles as subroutines, the careful evaluation of the overall complexity of the oracles themselves is crucial. This study examines the quantum routines…

Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the…

The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically…

Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…

With small-scale quantum processors transitioning from experimental physics labs to industrial products, these processors allow us to efficiently compute important algorithms in various fields. In this paper, we propose a quantum algorithm…

Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant…

Grover's quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a…

Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…

This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean…

We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…

By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database…

Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…

This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a…

Perceptron model is a fundamental linear classifier in machine learning and also the building block of artificial neural networks. Recently, Wiebe et al. (arXiv:1602.04799) proposed that the training of a perceptron can be quadratically…

Quantum cryptanalysis is essential for evaluating the security of cryptographic systems against the threat of quantum computing. Recently, Shi {\it et al.} introduced a dedicated quantum attack on block cipher constructions based on…

The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there are no standard ways to…

This paper considers the quantum query complexity of {\it $\eps$-biased oracles} that return the correct value with probability only $1/2 + \eps$. In particular, we show a quantum algorithm to compute $N$-bit OR functions with…

We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of…

The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…