scholarly journals Logical Structures Underlying Quantum Computing

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 77 ◽  
Author(s):  
Federico Holik ◽  
Giuseppe Sergioli ◽  
Hector Freytes ◽  
Angel Plastino
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Computational Logics ◽  
Logical Structures

In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Classical Physics ◽  
Core Set ◽  
The World ◽  
Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

scholarly journals Practical Security of RSA Against NTC-Architecture Quantum Computing Attacks

2021 ◽  
Author(s):  
Kai Li ◽  
Qing-yu Cai
Keyword(s):  
Quantum Computing ◽  
Ion Trap ◽  
Quantum Algorithms ◽  
Coherence Time ◽  
Quantum Computers ◽  
Quantum Time ◽  
Speed Up ◽  
Key Length ◽  
Concurrent Architecture ◽  
Qubit Gate

AbstractQuantum algorithms can greatly speed up computation in solving some classical problems, while the computational power of quantum computers should also be restricted by laws of physics. Due to quantum time-energy uncertainty relation, there is a lower limit of the evolution time for a given quantum operation, and therefore the time complexity must be considered when the number of serial quantum operations is particularly large. When the key length is about at the level of KB (encryption and decryption can be completed in a few minutes by using standard programs), it will take at least 50-100 years for NTC (Neighbor-only, Two-qubit gate, Concurrent) architecture ion-trap quantum computers to execute Shor’s algorithm. For NTC architecture superconducting quantum computers with a code distance 27 for error-correcting, when the key length increased to 16 KB, the cracking time will also increase to 100 years that far exceeds the coherence time. This shows the robustness of the updated RSA against practical quantum computing attacks.

scholarly journals Using quantum computing to create efficient algorithms

2021 ◽  
Vol 2056 (1) ◽  
pp. 012059
Author(s):  
I N Balaba ◽  
G S Deryabina ◽  
I A Pinchuk ◽  
I V Sergeev ◽  
S B Zabelina
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Computational Model ◽  
Exponential Growth ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Efficient Algorithms ◽  
Historical Overview ◽  
Computing Model ◽  
Computational Strategy

Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.

Quantum Algorithms

2021 ◽  
pp. 82-101
Author(s):  
Renata Wong ◽  
Amandeep Singh Bhatia
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Computer Hardware ◽  
Quantum Mechanical ◽  
Computational Power ◽  
Quantum Devices ◽  
The Core

In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.

scholarly journals Application of Quantum Computing to Biochemical Systems: A Look to the Future

2020 ◽  
Vol 8 ◽  
Author(s):  
Hai-Ping Cheng ◽  
Erik Deumens ◽  
James K. Freericks ◽  
Chenglong Li ◽  
Beverly A. Sanders
Keyword(s):  
Quantum Computing ◽  
Physical System ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Active Regions ◽  
Quantum Computers ◽  
The Future ◽  
Biochemical Systems ◽  
Near Term ◽  
Different Levels

Chemistry is considered as one of the more promising applications to science of near-term quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Because of the limitations of near-term quantum computers, the most effective strategies split the work over classical and quantum computers. There is a proven set of methods in computational chemistry and materials physics that has used this same idea of splitting a complex physical system into parts that are treated at different levels of theory to obtain solutions for the complete physical system for which a brute force solution with a single method is not feasible. These methods are variously known as embedding, multi-scale, and fragment techniques and methods. We review these methods and then propose the embedding approach as a method for describing complex biochemical systems, with the parts not only treated with different levels of theory, but computed with hybrid classical and quantum algorithms. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with traditional algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future.

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 Modular quantum computing and quantum-like devices

2021 ◽  
pp. 2150020
Author(s):  
R. Vilela Mendes
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Quantum Algorithms ◽  
The Other ◽  
Classical Systems ◽  
Evolution Parameter ◽  
Space Coordinate ◽  
The One ◽  
Classical Computer

The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and on the other hand, that such modules may be constructed out of classical systems obeying quantum-like equations where a space coordinate is the evolution parameter (thus playing the role of time in the quantum algorithms).

scholarly journals Roots of quantum computing supremacy: superposition, entanglement, or complementarity?

2021 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Probability Distributions ◽  
Statistical Tests ◽  
Joint Probability ◽  
Quantum Probability ◽  
Quantum Nonlocality ◽  
Total Probability ◽  
Probabilistic Algorithms ◽  
Quantum Phenomena

AbstractThe recent claim of Google to have brought forth a breakthrough in quantum computing represents a major impetus to further analyze the foundations for any claims of superiority regarding quantum algorithms. This note attempts to present a conceptual step in this direction. I start with a critical analysis of what is commonly referred to as entanglement and quantum nonlocality and whether or not these concepts may be the basis of quantum superiority. Bell-type experiments are then interpreted as statistical tests of Bohr’s principle of complementarity (PCOM), which is, thus, given a foothold within the area of quantum informatics and computation. PCOM implies (by its connection to probability) that probabilistic algorithms may proceed without the knowledge of joint probability distributions (jpds). The computation of jpds is exponentially time consuming. Consequently, classical probabilistic algorithms, involving the computation of jpds for n random variables, can be outperformed by quantum algorithms (for large values of n). Quantum probability theory (QPT) modifies the classical formula for the total probability (FTP). Inference based on the quantum version of FTP leads to a constructive interference that increases the probability of some events and reduces that of others. The physical realization of this probabilistic advantage is based on the discreteness of quantum phenomena (as opposed to the continuity of classical phenomena).

scholarly journals ProjectQ: an open source software framework for quantum computing

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 49 ◽  
Author(s):  
Damian S. Steiger ◽  
Thomas Häner ◽  
Matthias Troyer
Keyword(s):  
Quantum Computing ◽  
Open Source ◽  
Open Source Software ◽  
High Performance ◽  
Quantum Algorithms ◽  
Cloud Service ◽  
Domain Specific Language ◽  
Resource Estimation ◽  
Domain Specific ◽  
Compiler Framework

We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through simulation and enables running them on actual quantum hardware using a back-end connecting to the IBM Quantum Experience cloud service. Through extension mechanisms, users can provide back-ends to further quantum hardware, and scientists working on quantum compilation can provide plug-ins for additional compilation, optimization, gate synthesis, and layout strategies.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Quantum Computing ◽  
Fourier Series ◽  
Linear Algebra ◽  
Quantum Algorithms ◽  
Quantum States ◽  
Efficient Computation

In Part I we laid the foundation on which quantum algorithms are built. In this part we harness such exotic aspects as superposition, entanglement and collapse of quantum states of that foundation to show how powerful quantum algorithms can be constructed for efficient computation. Appendixes A and B are provided to jog the memory of those who are recently out of touch with linear algebra and Fourier series.

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