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.

Single Qubit Quantum Gates Implemented with Silicon Micro Ring Resonators

1969 ◽  
Author(s):  
Matteo Pennacchietti
Keyword(s):  
Ring Resonator ◽  
Quantum Computer ◽  
Ring Resonators ◽  
Quantum Gates ◽  
Advantages And Disadvantages ◽  
Single Qubit ◽  
Current State ◽  
On Chip ◽  
Classical Computer ◽  
Future Work

Quantum computers offer a new way of doing information processing by harnessing the unique properties of quantum mechanics, opening new possibilities for solving computationally difficult but useful problems more efficiently than a traditional classical computer (such as simulating molecular interactions). There are several ways of physically implementing a quantum computer, each with its own advantages and disadvantages. An approach which uses photons (i.e., particles of light), known as Linear Optical Quantum Computing (LOQC), has gained traction in the last decade. This approach uses integrated photonic technologies to design chips that can manipulate bits of quantum information – known as qubits – which are encoded in light. My undergraduate thesis research has focused on the investigation of new implementations of single qubit quantum gates – the physical structures which manipulate single qubits to do computation. Using a nano-scale silicon photonic device known as a micro-ring resonator, I have developed a novel configuration which in theory, should be able to implement any single qubit operation. Realizing single qubit gates using micro ring resonators could prove to provide a large improvement in the scalability of an integrated photonic quantum computer. My research has shown an almost 200 times increase in the on-chip density of single qubit gates over the current state of the art in the literature can be achieved by using a ring resonator architecture. This research may lay the foundation for future work on a new scalable implementation of quantum computer that uses light to solve the world’s most difficult problems.

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.

QUANTUM-STATISTICAL SIMULATIONS FOR QUANTUM CIRCUITS

2002 ◽  
Vol 13 (07) ◽  
pp. 931-945 ◽  
Author(s):  
KURT FISCHER ◽  
HANS-GEORG MATUTTIS ◽  
NOBUYASU ITO ◽  
MASAMICHI ISHIKAWA
Keyword(s):  
Prime Numbers ◽  
Quantum Circuits ◽  
Decomposition Technique ◽  
Shor's Algorithm ◽  
Quantum Statistical ◽  
Classical Computer

Using a Hubbard–Stratonovich like decomposition technique, we implemented simulations for the quantum circuits of Simon's algorithm for the detection of the periodicity of a function and Shor's algorithm for the factoring of prime numbers on a classical computer. Our approach has the advantage that the dimension of the problem does not grow exponentially with the number of qubits.

The Realization of New Computing Model and System Research Related to Quantum Computer

2014 ◽  
Vol 1078 ◽  
pp. 413-416
Author(s):  
Hai Yan Liu
Keyword(s):  
Quantum Computing ◽  
High Performance ◽  
Quantum Physics ◽  
Quantum Computer ◽  
Quantum Computers ◽  
Information Coding ◽  
Computing Model ◽  
Mechanics Model ◽  
Electronic Spin ◽  
Classical Computer

The ultimate goal of quantum calculation is to build high performance practical quantum computers. With quantum mechanics model of computer information coding and computational principle, it is proved in theory to be able to simulate the classical computer is currently completely, and with more classical computer, quantum computation is one of the most popular fields in physics research in recent ten years, has formed a set of quantum physics, mathematics. This paper to electronic spin doped fullerene quantum aided calculation scheme, we through the comprehensive use of logic based network and based on the overall control of the two kinds of quantum computing model, solve the addressing problem of nuclear spin, avoids the technical difficulties of pre-existing. We expect the final realization of the quantum computer will depend on the integrated use of in a variety of quantum computing model and physical realization system, and our primary work shows this feature..

scholarly journals Quantum Guarded-Command Language (qGCL) for Maximum Value

d'CARTESIAN ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 8
Author(s):  
Aisya Putri ◽  
Jullia Titaley ◽  
Benny Pinontoan
Keyword(s):  
Quantum Computer ◽  
Command Language ◽  
Quantum Bit ◽  
Maximum Value ◽  
Computer Calculations ◽  
Classical Computer

On a classical computer or a binary computer, calculations are done simultaneously so as to produce the equations and algorithms. The result of this research shows that to determined maximum value specified in the algorithm using quantum Guarded-Command Language (qGCl) in quantum computer. Initially determine of maximum value was construct in Djikstra’s Guarded-Command Language (GCL) which is then implemented on Zuliani’s probability Guarded-Command Language (pGCL) furthermore applying to quantum Guarded-Command Language (qGCL) for last result. Of concern here is the speed in resolving a problem or calculate problem. Due to the Quantum Computer has a Quantum Bit (qubit) and a phenomenon commonly called superposition. Keywords: GCL, pGCL, qGCL, quantum computer.

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 Elucidating reaction mechanisms on quantum computers

2017 ◽  
Vol 114 (29) ◽  
pp. 7555-7560 ◽  
Author(s):  
Markus Reiher ◽  
Nathan Wiebe ◽  
Krysta M. Svore ◽  
Dave Wecker ◽  
Matthias Troyer
Keyword(s):  
Reaction Mechanisms ◽  
Quantum Computer ◽  
Quantum Error Correction ◽  
Quantum Computers ◽  
Chemical Systems ◽  
Small Quantum ◽  
Quantum Technology ◽  
Classical Computer ◽  
Quantum Error ◽  
Biological Nitrogen

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

TOWARD A PRACTICAL ENVIRONMENT FOR QUANTUM PROGRAMMING

2005 ◽  
Vol 03 (supp01) ◽  
pp. 133-141
Author(s):  
S. YAMASHITA ◽  
M. NAKANISHI ◽  
K. WATANABE
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
The Other ◽  
Quantum Programming ◽  
Grover Search ◽  
Classical Computer

This paper proposes a practical framework for quantum programming. In our framework, the parts of a program to be performed on a quantum computer are almost automatically determined, and the other parts are performed on a classical computer. We only consider Grover Search to be performed on a quantum computer in the framework because the other quantum algorithms known so far cannot be applied to general cases. By considering only Grover Search, we have several advantages that show our framework is really practical.

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