Related papers: Geometric-Algebra Quantum-Like Algorithms: Simon's…
One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the…
Simon's problem is one of the most important problems demonstrating the power of quantum computing. Recently, an interesting distributed quantum algorithm for Simon's problem was proposed, where a key sorting operator requiring a large…
Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and…
It is well-known that Shor's factorization algorithm, Simon's period-finding algorithm, and Deutsch's original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the…
The ultimate objective of this paper is to create a stepping stone to the development of new quantum algorithms. The strategy chosen is to begin by focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the class of…
The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…
Daniel Simon's 1994 discovery of an efficient quantum algorithm for solving the hidden subgroup problem (HSP) over Z_2^n provided one of the first algebraic problems for which quantum computers are exponentially faster than their classical…
Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In…
The arguments given in this paper suggest that Grover's and Shor's algorithms are more closely related than one might at first expect. Specifically, we show that Grover's algorithm can be viewed as a quantum algorithm which solves a…
Amongst the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
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,…
We present a quantum algorithm solving the greatest common divisor (GCD) problem. This quantum algorithm possesses similar computational complexity with classical algorithms, such as the well-known Euclidean algorithm for GCD. This…
Quantum algorithm is a key tool for cryptanalysis. At present, people are committed to building powerful quantum algorithms and tapping the potential of quantum algorithms, so as to further analyze the security of cryptographic algorithms…
Simon's hidden subgroup algorithm was the first quantum algorithm to prove the superiority of quantum computing over classical computing in terms of complexity. Measurement-based quantum computing (MBQC) is a formulation of quantum…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…