相关论文: More On Grover's Algorithm

Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the…

This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the…

Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This…

We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…

Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…

We show a possible way to implement the Grover algorithm in large nuclear spins 1/2<I<9/2 in semiconductors. The Grover sequence is performed by means of multiphoton transitions that distribute the spin amplitude between the nuclear spin…

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…

The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…

These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…

A new approach to the classical limit of Grover's algorithm is discussed by assuming a very rapid dephasing of a system between consecutive Grover's unitary operations, which drives pure quantum states to decohered mixed states. One can…

Tomography has reached its practical limits in characterization of new quantum devices, and there is a need for a new means of characterizing and validating new technological advances in this field. We propose a different verification…

Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific…

We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover…

This is continuation of the approach to performing quantum algorithms using geometric structures which was presented by Aerts and Czachor. We solve the Simon's problem which, next to the Shor's alghorithm, is a representative of a quantum…

This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…

In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.

Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method a task that lies at the heart of modern information security, particularly on the internet. This algorithm…

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in…