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 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 Implementation of Shor’s Algorithm in QISKIT by Quantum Computing using IBMQ

2021 ◽  
Vol 10 (2) ◽  
pp. 1166-1170
Keyword(s):  
Machine Learning ◽  
Quantum Computing ◽  
Polynomial Time ◽  
Classical Algorithm ◽  
Shor's Algorithm ◽  
Quantum Machine Learning

Quantum machine learning is the combination of quantum computing and classical machine learning. It helps in solving the problems of one field to another field. Shor’s algorithm is used for factoring the integers in polynomial time. Since the bestknown classical algorithm requires super polynomial time to factor the product of two primes, the widely used cryptosystem, RSA, relies on factoring being impossible for large enough integers. In this paper we will focus on the quantum part of Shor’s algorithm, which actually solves the problem of period finding. In polynomial time factoring problem can be turned into a period finding problem so an efficient period finding algorithm can be used to factor integers efficiently.

scholarly journals Quantum computing, postselection, and probabilistic polynomial-time

2005 ◽  
Vol 461 (2063) ◽  
pp. 3473-3482 ◽  
Author(s):  
Scott Aaronson
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Polynomial Time ◽  
Quantum Computer ◽  
Complexity Class ◽  
Complete Problems ◽  
Probabilistic Polynomial Time

I study the class of problems efficiently solvable by a quantum computer, given the ability to ‘postselect’ on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or probabilistic polynomial-time. Using this result, I show that several simple changes to the axioms of quantum mechanics would let us solve PP-complete problems efficiently. The result also implies, as an easy corollary, a celebrated theorem of Beigel, Reingold and Spielman that PP is closed under intersection, as well as a generalization of that theorem due to Fortnow and Reingold. This illustrates that quantum computing can yield new and simpler proofs of major results about classical computation.

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 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

Introduction to Quantum Computing

2020 ◽  
pp. 259-264
Author(s):  
Andreas Bolfing
Keyword(s):  
Quantum Computing ◽  
Quantum Theory ◽  
Large Scale ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Public Key ◽  
Public Key Cryptosystems ◽  
Shor's Algorithm ◽  
Mathematical Problems ◽  
The Impact

This chapter gives a brief introduction to quantum computing, which is the discipline of studying algorithms based on the principles of quantum theory. It outlines the two fundamental quantum algorithms, which are known as Grover’s and Shor’s algorithm, which are able to solve number-theoretical problems that are intractable for present conventional computers. Thus, this chapter also shows the impact of these quantum algorithms on present cryptography under the assumption of the existence of a large-scale quantum computer, concluding that quantum computing poses a serious threat to public-key cryptosystems, because their underlying mathematical problems can be solved efficiently by using Shor’s algorithm.

scholarly journals Optimal teleportation via noisy quantum channels without additional qubit resources

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Dong-Gil Im ◽  
Chung-Hyun Lee ◽  
Yosep Kim ◽  
Hyunchul Nha ◽  
M. S. Kim ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Quantum Teleportation ◽  
Quantum Communication ◽  
Quantum Noise ◽  
Single Copy ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Near Term

AbstractQuantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.

Quantum circuits for simple periodic functions

2014 ◽  
Vol 14 (9&10) ◽  
pp. 763-776
Author(s):  
Omar Gamel ◽  
Daniel F.V. James
Keyword(s):  
Quantum Computing ◽  
Periodic Function ◽  
Quantum Circuits ◽  
Special Importance ◽  
Periodic Functions ◽  
Single Period ◽  
Shor's Algorithm ◽  
Toffoli Gates ◽  
One To One

Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period $p$. We conjecture that to create a simple periodic function of period $p$, where $p$ is an $n$-bit number, one needs at most $n$ Toffoli gates.

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