相关论文: Simulation of Shor algorithm for discrete logarith…

We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both…

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show…

Shor's shockingly fast quantum algorithm for solving the period-finding problem is a threat for the most common public-key primitives, as it can be efficiently applied to solve both the Integer Factorisation Problem and the Discrete…

Quantum computing has the potential to revolutionize cryptography by breaking classical public-key cryptography schemes, such as RSA and Diffie-Hellman. However, breaking the widely used 2048-bit RSA using Shor's quantum factoring algorithm…

We propose a semiclassical version of Shor's quantum algorithm to factorize integer numbers, based on spin-1/2 SU(2) generalized coherent states. Surprisingly, we find evidences that the algorithm's success probability is not too severely…

Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and…

Shor's quantum factoring algorithm and a few other efficient quantum algorithms break many classical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for…

Post Quantum and Quantum Cryptography schemes are feasible quantum computer applications for 7G networks. These schemes could possibly replace existing schemes. These algorithms have been compromised by advances in quantum search algorithms…

Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…

We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equation for…

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…

The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…

The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…

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…

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…

We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory qubits and the number of operations required to perform factorization, using the algorithm…

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…

Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…

In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…

We present a novel use case for quantum computation: the sensitivity analysis for a risk model used at Deutsche B\"orse Group. Such an analysis is computationally too expensive to perform on classical computers. We show in detail how the…