Research

17 pages, 959 KiB

Open AccessArticle

Quantum-Solving Algorithm for d’Alembert Solutions of the Wave Equation

by Yuanye Zhu

Entropy 2023, 25(1), 62; https://doi.org/10.3390/e25010062 - 29 Dec 2022

Viewed by 1148

When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the [...] Read more.

When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the two approaches. By using the duality quantum algorithm, we construct a quantum-solving algorithm for solving the first-order wave equation, which represents a typical class of partial differential equations. Numerical results of the quantum circuit have high precision consistency with the theoretical d’Alembert solution. Then the routine is applied to the wave equation with either a dissipation or dispersion term. As shown by complexity analysis for all these cases of the wave equation, our algorithm has a quadratic acceleration for each iteration compared to the classical algorithm. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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8 pages, 631 KiB

Open AccessArticle

Tuning the Quantum Properties of ZnO Devices by Modulating Bulk Length and Doping

by Zheng Fan, Gui-Qin Li and Gui-Lu Long

Entropy 2022, 24(12), 1750; https://doi.org/10.3390/e24121750 - 29 Nov 2022

Viewed by 1086

Abstract

The quantum transport properties of ZnO devices with five different bulk configurations are investigated with numerical methods. The calculation results reveal that the transport property at a higher energy range can be tuned by changing the length of central scattering. By substituting some [...] Read more.

The quantum transport properties of ZnO devices with five different bulk configurations are investigated with numerical methods. The calculation results reveal that the transport property at a higher energy range can be tuned by changing the length of central scattering. By substituting some Zn atoms with Cu atoms, it is found that the doped Cu atoms have an obvious effect on the quantum properties at the entire energy range investigated, and could result in different transmission. The properties of ZnO devices are also influenced by the doping positions of Cu atoms. The tuning mechanism relies on the shifting of carrier distributions in the scattering center of the device. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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19 pages, 3607 KiB

Open AccessArticle

Variational Quantum Algorithm Applied to Collision Avoidance of Unmanned Aerial Vehicles

by Zhaolong Huang, Qiting Li, Junling Zhao and Meimei Song

Entropy 2022, 24(11), 1685; https://doi.org/10.3390/e24111685 - 18 Nov 2022

Cited by 3 | Viewed by 1946

Abstract

Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the [...] Read more.

Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs’ collision avoidance model. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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12 pages, 2261 KiB

Open AccessArticle

Demonstration of the Holonomically Controlled Non-Abelian Geometric Phase in a Three-Qubit System of a Nitrogen Vacancy Center

by Shaman Bhattacharyya and Somnath Bhattacharyya

Entropy 2022, 24(11), 1593; https://doi.org/10.3390/e24111593 - 02 Nov 2022

Cited by 1 | Viewed by 1147

Abstract

The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers [...] Read more.

The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. Considering this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (~85%) of three-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate’s dark state with the qubit’s initial state hence decoherence of the multi-qubit system is well-controlled through a π/3 rotation. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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9 pages, 654 KiB

Open AccessFeature PaperArticle

Implementation of Quantum Algorithms via Fast Three-Rydberg-Atom CCZ Gates

by Shiqing Tang, Chong Yang, Dongxiao Li and Xiaoqiang Shao

Entropy 2022, 24(10), 1371; https://doi.org/10.3390/e24101371 - 27 Sep 2022

Cited by 1 | Viewed by 1536

Abstract

Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of [...] Read more.

Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch–Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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23 pages, 1185 KiB

Open AccessArticle

Complex Dynamics of a Cournot Quantum Duopoly Game with Memory and Heterogeneous Players

by Luis Garcia-Perez, Juan Grau-Climent, Ramon Alonso-Sanz and Juan C. Losada

Entropy 2022, 24(10), 1333; https://doi.org/10.3390/e24101333 - 22 Sep 2022

Cited by 4 | Viewed by 1240

Abstract

Previous authors tend to consider a certain range of values of the parameters involved in a game, not taking into account other possible values. In this article, a quantum dynamical Cournot duopoly game with memory and heterogeneous players (one of them is boundedly [...] Read more.

Previous authors tend to consider a certain range of values of the parameters involved in a game, not taking into account other possible values. In this article, a quantum dynamical Cournot duopoly game with memory and heterogeneous players (one of them is boundedly rational and the other one, a naive player) is studied, where the quantum entanglement can be greater than one and the speed of adjustment can be negative. In this context, we analyzed the behavior of the local stability and the profit in those values. Considering the local stability, it is observed that the stability region increases in the model with memory regardless of whether the quantum entanglement is greater than one or whether the speed of adjustment is negative. However, it is also shown that the stability is greater in the negative than in the positive zone of the speed of adjustment and, therefore, it improves the results obtained in previous experiments. This increase of stability enables higher values of speed of adjustment and, as a result of that, the system reaches the stability faster, resulting in a remarkable economic advantage. Regarding the behavior of the profit with these parameters, the principal effect shown is that the application of memory causes a certain delay in the dynamics. Through this article, all these statements are analytically proved and widely supported with several numerical simulations, using different values of the memory factor, the quantum entanglement, and the speed of adjustment of the boundedly rational player. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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12 pages, 753 KiB

Open AccessArticle

Quantum Teleportation and Dense Coding in Multiple Bosonic Reservoirs

by Yu Wang and Ming-Liang Hu

Entropy 2022, 24(8), 1114; https://doi.org/10.3390/e24081114 - 12 Aug 2022

Cited by 4 | Viewed by 1263

Abstract

The effect of a reservoir on quantum communication depends on its spectral density. The efficiency of quantum teleportation and dense coding is explored when each one of the channel qubits is coupled simultaneously to multiple bosonic reservoirs. It is shown that the non-Markovianity [...] Read more.

The effect of a reservoir on quantum communication depends on its spectral density. The efficiency of quantum teleportation and dense coding is explored when each one of the channel qubits is coupled simultaneously to multiple bosonic reservoirs. It is shown that the non-Markovianity triggered by increasing the reservoir number can induce revivals of quantum advantages of the two protocols after their disappearance. However, the backflow of information to the system that signifies non-Markovianity does not always induce immediate revivals of the quantum advantages. There may be a delayed effect for some initial states, and only as the backflow of information accumulates to a certain extent can the revivals of quantum advantages be triggered. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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33 pages, 8365 KiB

Open AccessFeature PaperArticle

Gaussian Amplitude Amplification for Quantum Pathfinding

by Daniel Koch, Massimiliano Cutugno, Samuel Karlson, Saahil Patel, Laura Wessing and Paul M. Alsing

Entropy 2022, 24(7), 963; https://doi.org/10.3390/e24070963 - 11 Jul 2022

Cited by 3 | Viewed by 1769

Abstract

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which [...] Read more.

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by Gaussian distributions. We then demonstrate how an oracle that encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases that are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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18 pages, 459 KiB

Open AccessArticle

A NISQ Method to Simulate Hermitian Matrix Evolution

by Keren Li and Pan Gao

Entropy 2022, 24(7), 899; https://doi.org/10.3390/e24070899 - 29 Jun 2022

Viewed by 1452

Abstract

As a universal quantum computer requires millions of error-corrected qubits, one of the current goals is to exploit the power of noisy intermediate-scale quantum (NISQ) devices. Based on a NISQ module–layered circuit, we propose a heuristic protocol to simulate Hermitian matrix evolution, which [...] Read more.

As a universal quantum computer requires millions of error-corrected qubits, one of the current goals is to exploit the power of noisy intermediate-scale quantum (NISQ) devices. Based on a NISQ module–layered circuit, we propose a heuristic protocol to simulate Hermitian matrix evolution, which is widely applied as the core for many quantum algorithms. The two embedded methods, with their own advantages, only require shallow circuits and basic quantum gates. Capable to being deployed in near future quantum devices, we hope it provides an experiment-friendly way, contributing to the exploitation of power of current devices. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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14 pages, 747 KiB

Open AccessArticle

Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems

by Chao Zheng

Entropy 2022, 24(7), 867; https://doi.org/10.3390/e24070867 - 24 Jun 2022

Cited by 4 | Viewed by 1636

Abstract

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian [...] Read more.

Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-

φ

-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices. Full article

(This article belongs to the Special Issue Quantum Computing for Complex Dynamics)

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