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.

Bounds on the quantity of entanglement in parallel quantum computing of a single ensemble quantum computer

2014 ◽  
Vol 92 (2) ◽  
pp. 159-162
Author(s):  
M. Ávila Aoki ◽  
Guo Hua Sun ◽  
Shi Hai Dong
Keyword(s):  
Quantum Computing ◽  
Upper Bound ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Point Of View ◽  
The Other ◽  
Quantum Computers ◽  
Other Hand ◽  
Speed Up ◽  
Parallel Mode

Speeding up of the processing of quantum algorithms has been focused on from the point of view of an ensemble quantum computer (EQC) working in a parallel mode. As a consequence of such efforts, additional speed up has been achieved for processing both Shor’s and Grover’s algorithms. On the other hand, in the literature there is scarce concern about the quantity of entanglement contained in EQC approaches, for this reason in the present work we study such a quantity. As a first result, an upper bound on the quantity of entanglement contained in EQC is imposed. As a main result we prove that equally weighted states are not appropriate for EQC working in parallel mode. In order that our results are not exclusively purely theoretical, we exemplify the situation by discussing the entanglement on an ensemble of n1 = 3 diamond quantum computers.

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 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 Characterizing large-scale quantum computers via cycle benchmarking

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Alexander Erhard ◽  
Joel J. Wallman ◽  
Lukas Postler ◽  
Michael Meth ◽  
Roman Stricker ◽  
...  
Keyword(s):  
Large Scale ◽  
Ion Trap ◽  
Quantum Computer ◽  
System Size ◽  
Quantum Computers ◽  
Large Set ◽  
Correlated Noise ◽  
Noise Sources ◽  
Total Process ◽  
Qubit Gate

AbstractQuantum computers promise to solve certain problems more efficiently than their digital counterparts. A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an algorithm running on large-scale processors. Current characterization techniques are unable to adequately account for the exponentially large set of potential errors, including cross-talk and other correlated noise sources. Here we develop cycle benchmarking, a rigorous and practically scalable protocol for characterizing local and global errors across multi-qubit quantum processors. We experimentally demonstrate its practicality by quantifying such errors in non-entangling and entangling operations on an ion-trap quantum computer with up to 10 qubits, and total process fidelities for multi-qubit entangling gates ranging from $$99.6(1)\%$$99.6(1)% for 2 qubits to $$86(2)\%$$86(2)% for 10 qubits. Furthermore, cycle benchmarking data validates that the error rate per single-qubit gate and per two-qubit coupling does not increase with increasing system size.

Hidden symmetry detection on a quantum computer

2007 ◽  
Vol 7 (1&2) ◽  
pp. 83-92
Author(s):  
R. Schutzhold ◽  
W.G. Unruh
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Self Similarity ◽  
Hidden Subgroup Problem ◽  
Hidden Symmetry ◽  
Speed Up ◽  
Subgroup Problem ◽  
Discrete Scale

The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved efficiently by quantum computers, it will be demonstrated by means of a simple example, that the detection of more general hidden (two-point) symmetries {$V\{f(x),f(U[x])\}=0$} by a quantum algorithm can also admit an exponential speed-up. E.g., one member of this class of symmetries {$V\{f(x),f(U[x])\}=0$} is discrete self-similarity (or discrete scale invariance).

scholarly journals Quantum Differential and Linear Cryptanalysis

2016 ◽  
pp. 71-94 ◽  
Author(s):  
Marc Kaplan ◽  
Gaëtan Leurent ◽  
Anthony Leverrier ◽  
María Naya-Plasencia
Keyword(s):  
Quantum Computing ◽  
The Other ◽  
Quantum Computers ◽  
Linear Cryptanalysis ◽  
Quantum Cryptanalysis ◽  
Classical World ◽  
Speed Up ◽  
Symmetric Ciphers ◽  
Quantum Computations ◽  
Scientific Fields

Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already anticipating this threat by proposing and studying a number of potentially quantum-safe alternatives for those primitives. On the other hand, symmetric primitives seem less vulnerable against quantum computing: the main known applicable result is Grover’s algorithm that gives a quadratic speed-up for exhaustive search. In this work, we examine more closely the security of symmetric ciphers against quantum attacks. Since our trust in symmetric ciphers relies mostly on their ability to resist cryptanalysis techniques, we investigate quantum cryptanalysis techniques. More specifically, we consider quantum versions of differential and linear cryptanalysis. We show that it is usually possible to use quantum computations to obtain a quadratic speed-up for these attack techniques, but the situation must be nuanced: we don’t get a quadratic speed-up for all variants of the attacks. This allows us to demonstrate the following non-intuitive result: the best attack in the classical world does not necessarily lead to the best quantum one. We give some examples of application on ciphers LAC and KLEIN. We also discuss the important difference between an adversary that can only perform quantum computations, and an adversary that can also make quantum queries to a keyed primitive.

Can Quantum Computers Solve Linear Algebra Problems to Advance Engineering Applications?

2018 ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Quantum Computing ◽  
Linear Algebra ◽  
Quantum Algorithms ◽  
Finite Difference Methods ◽  
Engineering Application ◽  
Quantum Circuit ◽  
Quantum Computers ◽  
Measurement Methodology ◽  
Classical Computing ◽  
Richard Feynman

Since its inception by Richard Feynman in 1982, quantum computing has provided an intriguing opportunity to advance computational capabilities over classical computing. Classical computers use bits to process information in terms of zeros and ones. Quantum computers use the complex world of quantum mechanics to carry out calculations using qubits (the quantum analog of a classical bit). The qubit can be in a superposition of the zero and one state simultaneously unlike a classical bit. The true power of quantum computing comes from the complexity of entanglement between many qubits. When entanglement is realized, quantum algorithms for problems such as factoring numbers and solving linear algebra problems show exponential speed-up relative to any known classical algorithm. Linear algebra problems are of particular interest in engineering application for solving problems that use finite element and finite difference methods. Here, we explore quantum linear algebra problems where we design and implement a quantum circuit that can be tested on IBM’s quantum computing hardware. A set of quantum gates are assimilated into a circuit and implemented on the IBM Q system to demonstrate its algorithm capabilities and its measurement methodology.

scholarly journals Quantum Computing Concepts with Deutsch Jozsa Algorithm

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Poornima Aradyamath ◽  
Naghabhushana N M ◽  
Rohitha Ujjinimatad
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Computation ◽  
Mathematical Description ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Basic Concepts ◽  
Classical Computer

In this paper, we briefly review the basic concepts of quantum computation,  entanglement,  quantum cryptography and quantum fourier  transform.   Quantum algorithms like Deutsch Jozsa, Shor’s   factorization and Grover’s data search are developed using fourier  transform  and quantum computation concepts to build quantum computers.  Researchers are finding a way to build quantum computer that works more efficiently than classical computer.  Among the  standard well known  algorithms  in the field of quantum computation  and communication we  describe  mathematically Deutsch Jozsa algorithm  in detail for  2  and 3 qubits.  Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.

scholarly journals Quantum Computing in the Biomedical Sciences; A Brief Introduction into Concepts and Applications

2019 ◽  
Vol 12 (3) ◽  
pp. 104
Author(s):  
Casper van der Kerk ◽  
Attila Csala ◽  
Aeilko H. Zwinderman
Keyword(s):  
Image Processing ◽  
Quantum Computing ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Biomedical Sciences ◽  
Quantum Bits ◽  
Early Stages ◽  
Made In

Quantum computing is a field that aims to exploit the principles of superposition and entanglement to perform computations. By using quantum bits (qubits) a quantum computer is able to perform certain tasks more efficiently when compared to classical computers. While applied quantum computing is still in its early stages, quantum algorithms on simulated quantum computers have already been applied to certain problems in epidemics modeling and image processing. Furthermore, companies like Google and IBM continue to develop new quantum computers with an increasing number of qubits. While much progress has been made in the recent years, the so called ”quantum supremacy”has not yet been achieved, and quantum computing appears to be still unsuitable for most applications in biomedical sciences.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Computation ◽  
Quantum Algorithms ◽  
Underlying Mechanism ◽  
Quantum States ◽  
Quantum Computers ◽  
Efficient Computation

In Part I we laid the foundation on which quantum algorithms are built. In part II we harnessed such exotic aspects of quantum mechanics as superposition, entanglement and collapse of quantum states to show how powerful quantum algorithms can be constructed for efficient computation. In Part III (the concluding part) we discuss two aspects of quantum computation: (1) the problem of correcting errors that inevitably plague physical quantum computers during computations, by algorithmic means; and (2) a possible underlying mechanism for the collapse of the wave function during measurement.

Sign in / Sign up

Export Citation Format

Share Document