Quantum Computing II

2020 ◽  
pp. 245-262
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Entanglement ◽  
Arbitrary Number ◽  
Quantum Fourier Transform ◽  
Grover’S Algorithm ◽  
Computing Algorithm ◽  
Shor's Algorithm ◽  
Grover's Algorithm

This chapter deals with some of the most prominent successes of quantum computing. The most well-known quantum computing algorithm, Shor’s algorithm for factoring a number in its prime factors, is discussed in details. The key to Shor’s algorithm is the quantum Fourier transform that is explained with the help of simple examples. The role of quantum entanglement is also discussed. The next important quantum computing algorithm is Grover’s algorithm that helps in searching an item in an unsorted database. This algorithm is motivated by first discussing a quantum shell game in which a pea hidden under one of the four shells is found in one measurement with certainty each time. This amazing result is then generalized to an arbitrary number of objects and Grover’s algorithm.

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 Mermin polynomials for non-locality and entanglement detection in Grover’s algorithm and Quantum Fourier Transform

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Henri de Boutray ◽  
Hamza Jaffali ◽  
Frédéric Holweck ◽  
Alain Giorgetti ◽  
Pierre-Alain Masson
Keyword(s):  
Fourier Transform ◽  
Quantum Fourier Transform ◽  
Grover’S Algorithm ◽  
Grover's Algorithm ◽  
Entanglement Detection ◽  
Non Locality

scholarly journals Human-Competitive Evolution of Quantum Computing Artefacts by Genetic Programming

2006 ◽  
Vol 14 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Paul Massey ◽  
John A. Clark ◽  
Susan Stepney
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Genetic Programming ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Quantum Fourier Transform ◽  
Competitive Evolution ◽  
Specific Quantum

We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

scholarly journals QUANTUM PHASE ESTIMATION WITH AN ARBITRARY NUMBER OF QUBITS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350008
Author(s):  
CHEN-FU CHIANG
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Diophantine Approximation ◽  
Great Difficulty ◽  
Quantum Computers ◽  
Phase Estimation ◽  
Quantum Fourier Transform ◽  
Factorization Algorithm ◽  
Simultaneous Diophantine Approximation ◽  
Parallel Circuits

Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose we have additional k qubits available. Given such a constraint k, we propose an approach for the phase estimation for an eigenphase of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum Fourier transform (QFT) in [R. Cleve and J. Watrous, Fast parallel circuits for quantum fourier transform, Proc. 41st Annual Symp. on Foundations of Computer Science (2000), pp. 526–536.] and adopts classical bits to implement such a task. Our algorithm has the complexity of O(n log k), instead of O(n2) in the conventional QFT, in terms of the total invocation of rotation gates. We also design a scheme to implement the factorization algorithm by using k available qubits via either the continued fractions approach or the simultaneous Diophantine approximation.

scholarly journals Quantum Fourier transform to estimate drive cycles

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Vinayak Dixit ◽  
Sisi Jian
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Computer ◽  
Quantum Fourier Transform ◽  
Real World Data ◽  
Drive Cycle ◽  
Cycle Frequency ◽  
Data Set ◽  
Simple Method ◽  
The Impact

AbstractDrive cycles in vehicle systems are important determinants for energy consumption, emissions, and safety. Estimating the frequency of the drive cycle quickly is important for control applications related to fuel efficiency, emission reduction and improving safety. Quantum computing has established the computational efficiency that can be gained. A drive cycle frequency estimation algorithm based on the quantum Fourier transform is exponentially faster than the classical Fourier transform. The algorithm is applied on real world data set. We evaluate the method using a quantum computing simulator, demonstrating remarkable consistency with the results from the classical Fourier transform. Current quantum computers are noisy, a simple method is proposed to mitigate the impact of the noise. The method is evaluated on a 15 qubit IBM-q quantum computer. The proposed method for a noisy quantum computer is still faster than the classical Fourier transform.

scholarly journals Quantum Fourier Transform Is the Building Block for Creating Entanglement

2021 ◽  
Author(s):  
Mario Mastriani
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Quantum Computing ◽  
Building Block ◽  
Quantum Communication ◽  
Fault Tolerant ◽  
Quantum Fourier Transform ◽  
The Future ◽  
Quantum Internet

Abstract This study demonstrates entanglement can be exclusively constituted by quantum Fourier transform (QFT) blocks. A bridge between entanglement and QFT will allow incorporating a spectral analysis to the already traditional temporal approach of entanglement, which will result in the development of new more performant, and fault-tolerant protocols to be used in quantum computing as well as quantum communication, with particular emphasis in the future quantum Internet.

scholarly journals Halving the cost of quantum addition

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 74 ◽  
Author(s):  
Craig Gidney
Keyword(s):  
Fourier Transform ◽  
Quantum Computation ◽  
Modular Arithmetic ◽  
Quantum Fourier Transform ◽  
Integer Arithmetic ◽  
Shor's Algorithm ◽  
Surface Code ◽  
The Cost ◽  
Do So

We improve the number of T gates needed to perform an n-bit adder from 8n+O(1) to 4n+O(1). We do so via a "temporary logical-AND" construction which uses four T gates to store the logical-AND of two qubits into an ancilla and zero T gates to later erase the ancilla. This construction is equivalent to one by Jones, except that our framing makes it clear that the technique is far more widely applicable than previously realized. Temporary logical-ANDs can be applied to integer arithmetic, modular arithmetic, rotation synthesis, the quantum Fourier transform, Shor's algorithm, Grover oracles, and many other circuits. Because T gates dominate the cost of quantum computation based on the surface code, and temporary logical-ANDs are widely applicable, this represents a significant reduction in projected costs of quantum computation. In addition to our n-bit adder, we present an n-bit controlled adder circuit with T-count of 8n+O(1), a temporary adder that can be computed for the same cost as the normal adder but whose result can be kept until it is later uncomputed without using T gates, and discuss some other constructions whose T-count is improved by the temporary logical-AND.

Sign in / Sign up

Export Citation Format

Share Document