Query: shor algorithm quantum circuit

Candidate papers:

abstract: We report a proof of principle demonstration of Shor's algorithm with photons generated by an on demand semiconductor quantum dot single photon source for the first time. A fully compiled version of Shor's algorithm for factoring 15 has been accomplished with a significantly reduced resource requirement that employs the four photon cluster state. Genuine multiparticle entanglement properties are confirmed to reveal the quantum character of the algorithm and circuit. The implementation realizes the Shor's algorithm with deterministic photonic qubits, which opens new applications for cluster state beyond one way quantum computing.
author_names: Zhao-Chen Duan

Jin-Peng Li

Jian Qin

Ying Yu

Yongheng Huo

Sven Hofling

Chao-Yang Lu

Nai-Le Liu

Kai Chen

Jian-Wei Pan
title: Proof of principle demonstration of compiled Shor's algorithm using a quantum dot single photon source.
venue: Optics express
year: 2020

abstract: This paper discusses and demonstrates the construction of a quantum modular exponentiation circuit in the Qiskit simulator for use in Shor's Algorithm for integer factorization problem (IFP) which is deemed to be able to crack RSA cryptosystems when a large qubit quantum computer exists. We base our implementation on Vedral, Barenco, and Ekert (VBE) proposal of quantum modular exponentiation, one of the firsts to explicitly provide the aforementioned circuit. Furthermore, we present an example simulation of how to construct a 7xmod 15 circuit in a step by step manner, giving clear and detailed information and consideration that currently not provided in the existing literature, and present the whole circuit for use in Shor's Algorithm. Our present simulation shows that the 4 bit VBE quantum modular exponentiation circuit can be constructed, simulated, and measured in Qiskit, while the Shor's Algorithm incorporating this VBE approach itself can be constructed but not yet simulated due to an overly large number of QASM instructions.
author_names: Harashta Tatimma Larasati

Howon Kim
title: Simulation of Modular Exponentiation Circuit for Shor's Algorithm in Qiskit
venue: 2020 14th International Conference on Telecommunication Systems, Services, and Applications (TSSA
year: 2020

abstract: Abstract The presented work provides a new prospective of quantum computer hardware development through ballistic nanowires with Rashba effect. We address Rashba effect as a possible mechanism to realize novel qubit gates in nanowires. We apply our results to the design of a new quantum circuit for Fourier algorithm, which shows an improved quantum cost in terms of the number of gates. The current system can be successfully implemented to increase the production of quantum computer experimentally thanks to the absence of impurities. The introduced circuit will enhance the scope of experimental and theoretical research for the realization of other quantum algorithms, such as phase estimation and Shor's algorithms.
author_names: Ali H Homid

Mohammed R Sakr

Abdel-Baset A Mohamed

Mahmoud Abdel-Aty

A -S F Obada
title: Rashba control to minimize circuit cost of quantum Fourier algorithm in ballistic nanowires
venue: Physics Letters A
year: 2019

abstract: 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 classical bits and controls, is employed to demonstrate Kitaev's approach to Shor's factorization algorithm. For the first time, Shor's factorization of a 24 bit integer is simulated with Quantum Kit in a mere 26 minutes on a modest desktop with Intel Core i5 7400T, 2.4GHz and 12GB RAM, while the largest number factorized so far has been a 20 bit integer run on a supercomputer. For the conventional Shor's algorithm, Quantum Kit is about 35 times faster than previously reported simulation times, whereas, with Kitaev's approach, Quantum Kit is 6 orders of magnitude faster in Shor's factorization of exactly the same number.
author_names: Archana Tankasala

Hesameddin Ilatikhameneh
title: Quantum Kit: Simulating Shor's Factorization of 24 Bit Number on Desktop
year: 2019

abstract: Very recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion trap quantum computer. In this note, we remark that the report is somewhat misleading because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles behind the demonstration have not been explained properly, including its correctness and complexity.
author_names: Zhengjun Cao

Lihua Liu
title: A Note On One Realization of a Scalable Shor Algorithm
venue: ArXiv
year: 2016

abstract: Our implementation of the quantum circuit in Shor's algorithm directly follows the circuit described in [1] The circuit is composed of the following modules: Quantum Fourier Transform (QFT) QFT addition, modular QFT addition, modular multiplication, and the controlledUa gate. For each of these modules, our implementation has functions which construct the corresponding circuits, given the input qubits as parameters. Upon completion of the circuit, we follow the process given by [2] to get the period r of y mod N from the output c. From this period, we can find a solution to x 1 mod N Finally, we compute GCD(x 1, N) and GCD(x 1, N) if x is nontrivial, then one of these values will be a factor of X.
author_names: Alec Brickner-abrickne
title: Shor s Algorithm in Pyquil
year: 2019

abstract: We present a novel and efficient, in terms of circuit depth, design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the Quantum Fourier transform (QFT) Draper's adders to build more complex arithmetic blocks: quantum multiplier/accumulators by constants and quantum dividers by constants. These arithmetic blocks are effectively architected into a quantum modular multiplier which is the fundamental block for the modular exponentiation circuit, the most computational intensive part of Shor's algorithm. The proposed modular exponentiation circuit has a depth of about 2000n2 and requires 9n 2 qubits, where n is the number of bits of the classic number to be factored. The total quantum cost of the proposed design is 1600n3. The circuit depth can be further decreased by more than three times if the approximate QFT implementation of each adder unit is exploited.
author_names: Archimedes Pavlidis

Dimitris Gizopoulos
title: Fast quantum modular exponentiation architecture for Shor's factoring algorithm
venue: Quantum Inf. Comput.
year: 2014

abstract: Recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion trap quantum computer. We remark that the report is flawed because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles behind the demonstration have not been explained properly, including its correctness and complexity.
author_names: Zhengjun Cao

Lihua Liu
title: Comment on "Realization of a scalable Shor algorithm"
venue: IACR Cryptol. ePrint Arch.
year: 2015

abstract: We present a novel and efficient, in terms of circuit depth, design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the Quantum Fourier.
title: Fast quantum modular exponentiation architecture for Shor's factoring algorithm
year: 2014

abstract: We construct a quantum circuit for Shor's factoring algorithm that uses 2n 2 qubits,where n is the length of the number to be factored. The depth and size of the circuitare O(n3) and O(n3 log n) respectivel) The number of qubits used in the circuit is lessthan that in any other quantum circuit ever constructed for Shor's factoring algorithm.Moreover, the size of the circuit is about half the size of Beauregard's quantum circuitfor Shor's factoring algorithm, which uses 2n 3 qubits.
author_names: Yasuhiro Takahashi

Noboru Kunihiro
title: A quantum circuit for shor's factoring algorithm using 2n 2 qubits
venue: Quantum Inf. Comput.
year: 2006