Shor’s Algorithm with a Linear-Optics Quantum Computer

2007 ◽  
Author(s):  
Daniel F. James
Keyword(s):  
Quantum Computer ◽  
Linear Optics ◽  
Shor's Algorithm

Implementation of Shor's algorithm on a linear nearest neighbour qubit array

2004 ◽  
Vol 4 (4) ◽  
pp. 237-251
Author(s):  
A.G. Fowler ◽  
S.J. Devitt ◽  
L.C.L. Hollenberg
Keyword(s):  
Quantum Computer ◽  
Computer Architectures ◽  
Quantum Circuits ◽  
Single Line ◽  
Nearest Neighbour ◽  
Leading Order ◽  
Shor's Algorithm

Shor's algorithm, which given appropriate hardware can factorise an integer N in a time polynomial in its binary length L, has arguably spurred the race to build a practical quantum computer. Several different quantum circuits implementing Shor's algorithm have been designed, but each tacitly assumes that arbitrary pairs of qubits within the computer can be interacted. While some quantum computer architectures possess this property, many promising proposals are best suited to realising a single line of qubits with nearest neighbour interactions only. In light of this, we present a circuit implementing Shor's factorisation algorithm designed for such a linear nearest neighbour architecture. Despite the interaction restrictions, the circuit requires just 2L+4 qubits and to leading order requires 8L^4 2-qubit gates arranged in a circuit of depth 32L^3 --- identical to leading order to that possible using an architecture that can interact arbitrary pairs of qubits.

scholarly journals Circuit for Shor's algorithm using 2n+3 qubits

2003 ◽  
Vol 3 (2) ◽  
pp. 175-185
Author(s):  
S. Beauregard
Keyword(s):  
Polynomial Time ◽  
Quantum Computer ◽  
Quantum Gates ◽  
Factorization Algorithm ◽  
Shor's Algorithm ◽  
Classical Computer

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 implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored.

scholarly journals Implementation of Shor’s Quantum Factoring Algorithm using ProjectQ Framework

2019 ◽  
Vol 8 (6S3) ◽  
pp. 52-56
Keyword(s):  
Quantum Computing ◽  
Computer Science ◽  
Polynomial Time ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Prime Factorization ◽  
Shor's Algorithm ◽  
Computer Simulators ◽  
Testing And Evaluation ◽  
Factoring Algorithm

Prime number factorization is a problem in computer science where the solution to that problem takes super-polynomial time classically. Shor’s quantum factoring algorithm is able to solve the problem in polynomial time by harnessing the power of quantum computing. The implementation of the quantum algorithm itself is not detailed by Shor in his paper. In this paper, an approach and experiment to implement Shor’s quantum factoring algorithm are proposed. The implementation is done using Python and a quantum computer simulator from ProjectQ. The testing and evaluation are completed in two computers with different hardware specifications. User time of the implementation is measured in comparison with other quantum computer simulators: ProjectQ and Quantum Computing Playground. This comparison was done to show the performance of Shor’s algorithm when simulated using different hardware. There is a 33% improvement in the execution time (user time) between the two computers with the accuracy of prime factorization in this implementation is inversely proportional to the number of qubits used. Further improvements upon the program that has been developed for this paper is its accuracy in terms of finding the factors of a number and the number of qubits used, as previously mentioned.

scholarly journals Analysis of circuit imperfections in BosonSampling

2015 ◽  
pp. 489-512
Author(s):  
Anthony Leverrier ◽  
Raul Garcia-Patron
Keyword(s):  
Fault Tolerance ◽  
Quantum Computer ◽  
State Of The Art ◽  
Optical Element ◽  
Single Photons ◽  
Linear Optics ◽  
Tolerance Mechanism ◽  
Optical Elements ◽  
Full Quantum

BosonSampling is a problem where a quantum computer offers a provable speedup over classical computers. Its main feature is that it can be solved with current linear optics technology, without the need for a full quantum computer. In this work, we investigate whether an experimentally realistic BosonSampler can really solve BosonSampling without any fault-tolerance mechanism. More precisely, we study how the unavoidable errors linked to an imperfect calibration of the optical elements affect the final result of the computation. We show that the fidelity of each optical element must be at least 1 − O(1/n^2 ), where n refers to the number of single photons in the scheme. Such a requirement seems to be achievable with state-of-the-art equipment.

MINIMAL EXECUTION TIME OF SHOR'S ALGORITHM AT LOW TEMPERATURES

2009 ◽  
Vol 07 (01) ◽  
pp. 287-296
Author(s):  
M. A. AVILA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Execution Time ◽  
Low Temperatures ◽  
Quantum Computer ◽  
Common Belief ◽  
Zero Temperature ◽  
Decoherence Time ◽  
Shor's Algorithm ◽  
The Common

The minimal time, T Shor , in which a one-way quantum computer can execute Shor's algorithm is derived. In the absence of an external magnetic field, this quantity diverges at very small temperatures. This result coincides with that of Anders et al. obtained simultaneously to ours but using thermodynamical arguments. Such divergence contradicts the common belief that it is possible to do quantum computation at low temperatures. It is shown that in the presence of a weak external magnetic field, T Shor becomes a quantized quantity which vanishes at zero temperature. Decoherence is not a problem because T Shor /τ dec < 10-9, where τdec is decoherence time.

scholarly journals Universal quantum computation with shutter logic

2006 ◽  
Vol 6 (6) ◽  
pp. 495-515
Author(s):  
J.C. Garcia-Escartin ◽  
P. Chamorro-Posada
Keyword(s):  
Quantum Computation ◽  
Quantum Logic ◽  
Quantum Computer ◽  
Quantum Memory ◽  
Linear Optics ◽  
Cnot Gate ◽  
Free Model ◽  
Universal Quantum

We show that universal quantum logic can be achieved using only linear optics and a quantum shutter device. With these elements, we design a quantum memory for any number of qubits and a CNOT gate which are the basis of a universal quantum computer. An interaction-free model for a quantum shutter is given.

scholarly journals A Review on the Impact of Quantum Computing on Blockchain Technology

2021 ◽  
Vol 9 (10) ◽  
pp. 972-975
Author(s):  
Roman B. Shrestha
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Grover’S Algorithm ◽  
Blockchain Technology ◽  
Technological Advances ◽  
Shor's Algorithm ◽  
Grover's Algorithm ◽  
The Impact

Abstract: Blockchain is a promising revolutionary technology and is scalable for countless applications. The use of mathematically complex algorithms and hashes secure a blockchain from the risk of potential attacks and forgery. Advanced quantum computing algorithms like Shor’s and Grover’s are at the heart of breaking many known asymmetric cyphers and pose a severe threat to blockchain systems. Although a fully functional quantum computer capable of performing these attacks might not be developed until the next decade or century, we need to rethink designing the blockchain resistant to these threats. This paper discusses the potential impacts of quantum computing on blockchain technology and suggests remedies for making blockchain technology more secure and resistant to such technological advances. Keywords: Quantum Computing, Blockchain, Shor’s Algorithm, Grover’s Algorithm, Cryptography

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