A Quantum Computer for Shor's Algorithm

2004 ◽  
Author(s):  
Philip H. Bucksbaum
Keyword(s):  
Quantum Computer ◽  
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 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 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.

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 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

scholarly journals Quantum Simulation Logic, Oracles, and the Quantum Advantage

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 800 ◽  
Author(s):  
Niklas Johansson ◽  
Jan-Åke Larsson
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Success Probability ◽  
Quantum Simulation ◽  
Query Complexity ◽  
Integer Factorization ◽  
Simulation Framework ◽  
Shor's Algorithm ◽  
Quantum Query ◽  
Do So

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor’s algorithm for integer factorization.

scholarly journals Quantum-Resistant Network for Classical Client Compatibility

2021 ◽  
Vol 50 (2) ◽  
pp. 224-235
Author(s):  
Te-Yuan Lin ◽  
Chiou-Shann Fuh
Keyword(s):  
Quantum Computing ◽  
Polynomial Time ◽  
Time Complexity ◽  
Quantum Computer ◽  
Quantum Network ◽  
Network Infrastructure ◽  
Zero Knowledge ◽  
Shor's Algorithm ◽  
Computational Security ◽  
Computational Difficulty

Quantum computing is no longer a thing of the future. Shor’s algorithm proved that a quantum computer couldtraverse key of factoring problems in polynomial time. Because the time-complexity of the exhaustive keysearch for quantum computing has not reliably exceeded the reasonable expiry of crypto key validity, it is believedthat current cryptography systems built on top of computational security are not quantum-safe. Quantumkey distribution fundamentally solves the problem of eavesdropping; nevertheless, it requires quantumpreparatory work and quantum-network infrastructure, and these remain unrealistic with classical computers.In transitioning to a mature quantum world, developing a quantum-resistant mechanism becomes a stringentproblem. In this research, we innovatively tackled this challenge using a non-computational difficulty schemewith zero-knowledge proof in order to achieve repellency against quantum computing cryptanalysis attacks foruniversal classical clients.

scholarly journals How to detect whether Shor’s algorithm succeeds against large integers without a quantum computer

2021 ◽  
Vol 195 ◽  
pp. 145-151
Author(s):  
Daniel Chicayban Bastos ◽  
Luis Antonio Brasil Kowada
Keyword(s):  
Quantum Computer ◽  
Shor's Algorithm
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