Quantum Computing and Quantum Information Processing

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Quantum Science and Technology".

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 9423

Special Issue Editor

Special Issue Information

Dear Colleagues,

The foundations of quantum theory were formulated over a hundred years ago, but it was not until the last quarter century that quantum theory left the tranquillity of physical laboratories. Theoretical and technological developments have allowed for serious treatment of the new research discipline commonly known as quantum information processing. It seems that we will sooner or later enter the era of technological use of quantum technology.

Therefore, we hope that this Special Issue will provide an overall picture of the discussed problems and up-to-date findings to both researchers and  students and that the readers will ultimately benefit from reading the contributions.

Scope: Potential topics (theories and experiments) dealing with, but not limited to, the following subheadings are deemed suitable for publication:

  • Quantum algorithms;
  • Quantum computing;
  • Quantum communication;
  • Quantum complexity theory;
  • Quantum cryptography;
  • Quantum games;
  • Quantum information processing;
  • Quantum networks;
  • Quantum programing.

Prof. Jan Sladkowski
Guest Editor

Manuscript Submission Information

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Keywords

  • quantum information
  • quantum computing
  • quantum algorithms
  • quantum communication
  • quantum programing
  • quantum games and quantum networks

Published Papers (4 papers)

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Research

13 pages, 11617 KiB  
Article
Nash Equilibria of Quantum Games in the Special Two-Parameter Strategy Space
Appl. Sci. 2022, 12(22), 11530; https://doi.org/10.3390/app122211530 - 13 Nov 2022
Cited by 2 | Viewed by 1073
Abstract
The aim of the paper is to examine pure Nash equilibria in a quantum game that extends the classical bimatrix game of dimension 2. The strategies of quantum players are specific types of two-parameter unitary operations such that the resulting quantum game is [...] Read more.
The aim of the paper is to examine pure Nash equilibria in a quantum game that extends the classical bimatrix game of dimension 2. The strategies of quantum players are specific types of two-parameter unitary operations such that the resulting quantum game is invariant under isomorphic transformations of the input classical game. We formulate general statements for the existence and form of Nash equilibria and discuss their Pareto efficiency. We prove that, depending on the payoffs of a classical game, the corresponding quantum game may or may not have Nash equilibria in the set of unitary strategies under study. Some of the equilibria cease to be equilibria if the players’ strategy set is the three-parameter special unitary group. Full article
(This article belongs to the Special Issue Quantum Computing and Quantum Information Processing)
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17 pages, 485 KiB  
Article
Quantum Circuit Design of Toom 3-Way Multiplication
Appl. Sci. 2021, 11(9), 3752; https://doi.org/10.3390/app11093752 - 21 Apr 2021
Cited by 7 | Viewed by 2755
Abstract
In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba multiplication. For the use in quantum computation, prior work considered the Toom-2.5 variant rather than the [...] Read more.
In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba multiplication. For the use in quantum computation, prior work considered the Toom-2.5 variant rather than the classically faster and more prominent Toom-3, primarily to avoid the nontrivial division operations inherent in the latter circuit. In this paper, we investigate the quantum circuit for Toom-3 multiplication, which is expected to give an asymptotically lower depth than the Toom-2.5 circuit. In particular, we designed the corresponding quantum circuit and adopted the sequence proposed by Bodrato to yield a lower number of operations, especially in terms of nontrivial division, which is reduced to only one exact division by 3 circuit per iteration. Moreover, to further minimize the cost of the remaining division, we utilize the unique property of the particular division circuit, replacing it with a constant multiplication by reciprocal circuit and the corresponding swap operations. Our numerical analysis shows that the resulting circuit indeed gives a lower asymptotic complexity in terms of Toffoli depth and qubit count compared to Toom-2.5 but with a large number of Toffoli gates that mainly come from realizing the division operation. Full article
(This article belongs to the Special Issue Quantum Computing and Quantum Information Processing)
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11 pages, 592 KiB  
Article
Quantum Modular Adder over GF(2n − 1) without Saving the Final Carry
Appl. Sci. 2021, 11(7), 2949; https://doi.org/10.3390/app11072949 - 25 Mar 2021
Cited by 4 | Viewed by 2546
Abstract
Addition is the most basic operation of computing based on a bit system. There are various addition algorithms considering multiple number systems and hardware, and studies for a more efficient addition are still ongoing. Quantum computing based on qubits as the information unit [...] Read more.
Addition is the most basic operation of computing based on a bit system. There are various addition algorithms considering multiple number systems and hardware, and studies for a more efficient addition are still ongoing. Quantum computing based on qubits as the information unit asks for the design of a new addition because it is, physically, wholly different from the existing frequency-based computing in which the minimum information unit is a bit. In this paper, we propose an efficient quantum circuit of modular addition, which reduces the number of gates and the depth. The proposed modular addition is for the Galois Field GF(2n1), which is important as a finite field basis in various domains, such as cryptography. Its design principle was from the ripple carry addition (RCA) algorithm, which is the most widely used in existing computers. However, unlike conventional RCA, the storage of the final carry is not needed due to modifying existing diminished-1 modulo 2n1 adders. Our proposed adder can produce modulo sum within the range 0,2n2 by fewer qubits and less depth. For comparison, we analyzed the proposed quantum addition circuit over GF(2n1) and the previous quantum modular addition circuit for the performance of the number of qubits, the number of gates, and the depth, and simulated it with IBM’s simulator ProjectQ. Full article
(This article belongs to the Special Issue Quantum Computing and Quantum Information Processing)
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15 pages, 296 KiB  
Article
On Correlated Equilibria in Marinatto–Weber Type Quantum Games
Appl. Sci. 2020, 10(24), 9003; https://doi.org/10.3390/app10249003 - 16 Dec 2020
Viewed by 1114
Abstract
Players’ choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players’ choices can be correlated due to [...] Read more.
Players’ choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players’ choices can be correlated due to a classical probability distribution, and if no player benefits by a unilateral deviation from the vector of recommended strategies, the probability distribution is a correlated equilibrium. The aim of this paper is to investigate relation between correlated equilibria and Nash equilibria in the MW-type schemes for quantum games. Full article
(This article belongs to the Special Issue Quantum Computing and Quantum Information Processing)
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