Related papers: A Continuous Variable Shor Algorithm

We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to…

Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which a subgroup H of a group G must be determined from a quantum state y uniformly supported…

Following the example of Shor's algorithm for period-finding in the integers, we explore the hidden subgroup problem (HSP) for discrete infinite groups. On the hardness side, we show that HSP is NP-hard for the additive group of rational…

Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…

An alternative quantum algorithm for the discrete logarithm problem is presented. The algorithm uses two quantum registers and two Fourier transforms whereas Shor's algorithm requires three registers and four Fourier transforms. A crucial…

Shor's algorithm is one of the most prominent quantum algorithms, yet finding efficient implementations remains an active research challenge. While many approaches focus on low-level modular arithmetic optimizations, a broader perspective…

Given a propositional formula F(x,y), a Skolem function for x is a function \Psi(y), such that substituting \Psi(y) for x in F gives a formula semantically equivalent to \exists F. Automatically generating Skolem functions is of significant…

We give an overview of the Hidden Subgroup Problem (HSP) as of July 2010, including new results discovered since the survey of arXiv:quant-ph/0411037v1. We recall how the problem provides a framework for efficient quantum algorithms and…

The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…

There is a folkloric belief that a depth-$\Theta(m)$ quantum circuit is needed to estimate the trace of the product of $m$ density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum…

We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to…

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers[1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems[2] and photonic systems[3-5],…

This paper aims to determine the exact success probability at each step of Shor's algorithm. Although the literature usually provides a lower bound on this probability, we present an improved bound. The derived formulas enable the…

The execution cost of quantum algorithms is typically quantified through asymptotic gate counts and qubit register sizes, yet these metrics do not directly capture which genuinely quantum resources, and in what amount, must be created and…

Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…

In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…

The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…

In this note we describe a simple and intriguing observation: the quantum Fourier transform (QFT) over $Z_q$, which is considered the most ``quantum'' part of Shor's algorithm, can in fact be simulated efficiently by classical computers.…

We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…

We report a proof-of-concept demonstration of a quantum order-finding algorithm for factoring the integer 21. Our demonstration involves the use of a compiled version of the quantum phase estimation routine, and builds upon a previous…