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1

Skopec, Robert. "Hybrid Quantum Computing Apocalypse." American International Journal of Multidisciplinary Scientific Research 1, no. 1 (August 22, 2018): 31–38. http://dx.doi.org/10.46281/aijmsr.v1i1.181.

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Chinese scientists won a major victory, by proving that the Majorana fermions – a particle we’ve found tantalizing hints for years – genuinely exists. This discovery has huge implications for quantum computing, and it might change the world. Don Lincoln, a senior physicist at Fermi lab, does research using the Large Hadrons Collider. He is the author of “The Large Hadrons Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind”, and produces a series of science education videos. To the question: Why is there (in our Universe) something including cancer, rather than nothing? He is giving the simplest scientific answer: We shouldn’t exist at all.
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Proctor, Timothy J., and Viv Kendon. "Hybrid quantum computing with ancillas." Contemporary Physics 57, no. 4 (March 15, 2016): 459–76. http://dx.doi.org/10.1080/00107514.2016.1152700.

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Li, Yu, and Liang Ma. "A Hybrid Ant Algorithm for the Vehicle Routing Problem." Applied Mechanics and Materials 182-183 (June 2012): 2118–22. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.2118.

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A hybrid algorithm for solving the vehicle routing problem is proposed based upon the combination of Ant Colony Optimization and quantum computing. The algorithm takes the advantage of the principles in quantum computing, such as the qubit, quantum gate, and the quantum superposition of states. It can search the best solution by quantum walk and can further improve the search capability of the algorithm for the best solution. Numerical examples are tested and verified, that show the good performances.
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Frank, Jodi Ackerman. "Hybrid quantum computing circuit combines quantum devices with readout amplifier." Scilight 2020, no. 49 (December 4, 2020): 491108. http://dx.doi.org/10.1063/10.0002863.

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Ingber, Lester. "Hybrid classical-quantum computing: Applications to statistical mechanics of financial markets." E3S Web of Conferences 307 (2021): 04001. http://dx.doi.org/10.1051/e3sconf/202130704001.

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Hybrid Classical-Quantum computing is now offered by several commercial quantum computers. In this project, a model of financial options, Statistical Mechanics of Financial Markets (SMFM), uses this approach. However, only Classical (super-)computers are used to include the quantum features of these models. Since 1989, Adaptive Simulated Annealing (ASA), an optimization code using importance-sampling, has fit parameters in such models. Since 2015, PATHINT, a path-integral numerical agorithm, has been used to describe several systems in several disciplines. PATHINT has been generalized from 1 dimension to N dimensions, and from classical to quantum systems into qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space modeled by SMFM fits parameters in conditional short-time probability distributions of nonlinear nonequilibrium multivariate statistical mechanics, while the quantum space modeled by qPATHINT describes quantum money. This project demonstrates how some hybrid classical-quantum systems may be calculated using only classical (super-)computers.
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Kendon, Viv, Angelika Sebald, and Susan Stepney. "Heterotic computing: exploiting hybrid computational devices." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2046 (July 28, 2015): 20150091. http://dx.doi.org/10.1098/rsta.2015.0091.

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Current computational theory deals almost exclusively with single models: classical, neural, analogue, quantum, etc. In practice, researchers use ad hoc combinations, realizing only recently that they can be fundamentally more powerful than the individual parts. A Theo Murphy meeting brought together theorists and practitioners of various types of computing, to engage in combining the individual strengths to produce powerful new heterotic devices. ‘Heterotic computing’ is defined as a combination of two or more computational systems such that they provide an advantage over either substrate used separately. This post-meeting collection of articles provides a wide-ranging survey of the state of the art in diverse computational paradigms, together with reflections on their future combination into powerful and practical applications.
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Iyer, Vijayasri, Bhargava Ganti, A. M. Hima Vyshnavi, P. K. Krishnan Namboori, and Sriram Iyer. "Hybrid quantum computing based early detection of skin cancer." Journal of Interdisciplinary Mathematics 23, no. 2 (February 17, 2020): 347–55. http://dx.doi.org/10.1080/09720502.2020.1731948.

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Zhao, Yujing, Xiongwen Chen, Zhengang Shi, Fang Zhou, Shaohua Xiang, and Kehui Song. "Implementation of One-Way Quantum Computing with a Hybrid Solid-State Quantum System." Chinese Journal of Electronics 26, no. 1 (January 1, 2017): 27–34. http://dx.doi.org/10.1049/cje.2016.11.004.

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Wei, Shijie, Hang Li, and GuiLu Long. "A Full Quantum Eigensolver for Quantum Chemistry Simulations." Research 2020 (March 23, 2020): 1–11. http://dx.doi.org/10.34133/2020/1486935.

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Quantum simulation of quantum chemistry is one of the most compelling applications of quantum computing. It is of particular importance in areas ranging from materials science, biochemistry, and condensed matter physics. Here, we propose a full quantum eigensolver (FQE) algorithm to calculate the molecular ground energies and electronic structures using quantum gradient descent. Compared to existing classical-quantum hybrid methods such as variational quantum eigensolver (VQE), our method removes the classical optimizer and performs all the calculations on a quantum computer with faster convergence. The gradient descent iteration depth has a favorable complexity that is logarithmically dependent on the system size and inverse of the precision. Moreover, the FQE can be further simplified by exploiting a perturbation theory for the calculations of intermediate matrix elements and obtaining results with a precision that satisfies the requirement of chemistry application. The full quantum eigensolver can be implemented on a near-term quantum computer. With the rapid development of quantum computing hardware, the FQE provides an efficient and powerful tool to solve quantum chemistry problems.
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Li, Yiwei, Edison Tsai, Marek Perkowski, and Xiaoyu Song. "Grover-based Ashenhurst-Curtis decomposition using quantum language quipper." Quantum Information and Computation 19, no. 1&2 (February 2019): 35–66. http://dx.doi.org/10.26421/qic19.1-2-4.

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Functional decomposition plays a key role in several areas such as system design, digital circuits, database systems, and Machine Learning. This paper presents a novel quantum computing approach based on Grover’s search algorithm for a generalized Ashenhurst-Curtis decomposition. The method models the decomposition problem as a search problem and constructs the oracle circuit based on the set-theoretic partition algebra. A hybrid quantum-based algorithm takes advantage of the quadratic speedup achieved by Grover’s search algorithm with quantum oracles for finding the minimum-cost decomposition. The method is implemented and simulated in the quantum programming language Quipper. This work constitutes the first attempt to apply quantum computing to functional decomposition.
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Choudhary, Renu, Rana Biswas, Bicai Pan, and Durga Paudyal. "Defects in SiC for Quantum Computing." MRS Advances 4, no. 40 (2019): 2217–22. http://dx.doi.org/10.1557/adv.2019.301.

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AbstractMany novel materials are being actively considered for quantum information science and for realizing high-performance qubit operation at room temperature. It is known that deep defects in wide-band gap semiconductors can have spin states and long coherence times suitable for qubit operation. We theoretically investigate from ab-initio density functional theory (DFT) that the defect states in the hexagonal silicon carbide (4H-SiC) are potential qubit materials. The DFT supercell calculations were performed with the local-orbital and pseudopotential methods including hybrid exchange-correlation functionals. Di-vacancies in SiC supercells yielded defect levels in the gap consisting of closely spaced doublet just above the valence band edge, and higher levels in the band gap. The divacancy with a spin state of 1 is charge neutral. The divacancy is characterized by C-dangling bonds and a Si-dangling bonds. Jahn-teller distortions and formation energies as a function of the Fermi level and single photon interactions with these defect levels will be discussed. In contrast, the anti-site defects where C, Si are interchanged have high formation energies of 5.4 eV and have just a single shallow defect level close to the valence band edge, with no spin. We will compare results including the defect levels from both the electronic structure approaches.
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Nembrini, Riccardo, Maurizio Ferrari Dacrema, and Paolo Cremonesi. "Feature Selection for Recommender Systems with Quantum Computing." Entropy 23, no. 8 (July 28, 2021): 970. http://dx.doi.org/10.3390/e23080970.

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The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last few years that small but functional quantum computers have become available to the broader research community. One paradigm in particular,quantum annealing, can be used to sample optimal solutions for a number of NP-hard optimization problems represented with classical operations research tools, providing an easy access to the potential of this emerging technology. One of the tasks that most naturally fits in this mathematical formulation is feature selection. In this paper, we investigate how to design a hybrid feature selection algorithm for recommender systems that leverages the domain knowledge and behavior hidden in the user interactions data. We represent the feature selection as an optimization problem and solve it on a real quantum computer, provided by D-Wave. The results indicate that the proposed approach is effective in selecting a limited set of important features and that quantum computers are becoming powerful enough to enter the wider realm of applied science.
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BÉNY, CÉDRIC, DAVID W. KRIBS, and ARON PASIEKA. "ALGEBRAIC FORMULATION OF QUANTUM ERROR CORRECTION." International Journal of Quantum Information 06, supp01 (July 2008): 597–603. http://dx.doi.org/10.1142/s0219749908003839.

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We give a brief introduction to the algebraic formulation of error correction in quantum computing called operator algebra quantum error correction (OAQEC). Then we extend one of the basic results for subsystem codes in operator quantum error correction (OQEC) to the OAQEC setting: Every hybrid classical-quantum code is shown to be unitarily recoverable in an appropriate sense. The algebraic approach of the proof yields a new, less technical proof for the OQEC case.
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Moll, Maximilian, and Leonhard Kunczik. "Comparing quantum hybrid reinforcement learning to classical methods." Human-Intelligent Systems Integration 3, no. 1 (March 2021): 15–23. http://dx.doi.org/10.1007/s42454-021-00025-3.

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AbstractIn recent history, reinforcement learning (RL) proved its capability by solving complex decision problems by mastering several games. Increased computational power and the advances in approximation with neural networks (NN) paved the path to RL’s successful applications. Even though RL can tackle more complex problems nowadays, it still relies on computational power and runtime. Quantum computing promises to solve these issues by its capability to encode information and the potential quadratic speedup in runtime. We compare tabular Q-learning and Q-learning using either a quantum or a classical approximation architecture on the frozen lake problem. Furthermore, the three algorithms are analyzed in terms of iterations until convergence to the optimal behavior, memory usage, and runtime. Within the paper, NNs are utilized for approximation in the classical domain, while in the quantum domain variational quantum circuits, as a quantum hybrid approximation method, have been used. Our simulations show that a quantum approximator is beneficial in terms of memory usage and provides a better sample complexity than NNs; however, it still lacks the computational speed to be competitive.
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15

Colucci, Giuseppe, and Francesco Giacosa. "Quantum algorithmic differentiation." Quantum Information and Computation 21, no. 1&2 (February 2021): 0080–94. http://dx.doi.org/10.26421/qic21.1-2-5.

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In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid approach). Since the implementation of elementary functions is already possible on quantum computers, the scheme that we propose can be easily applied. Moreover, since some steps (such as the CNOT operator) can (or will be) faster on a quantum computer than on a classical one, our procedure may ultimately emonstrate that quantum algorithmic differentiation has an advantage relative to its classical counterpart.
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Mueller, Niklas, Andrey Tarasov, and Raju Venugopalan. "Computing real time correlation functions on a hybrid classical/quantum computer." Nuclear Physics A 1005 (January 2021): 121889. http://dx.doi.org/10.1016/j.nuclphysa.2020.121889.

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17

Ushijima-Mwesigwa, Hayato, Ruslan Shaydulin, Christian F. A. Negre, Susan M. Mniszewski, Yuri Alexeev, and Ilya Safro. "Multilevel Combinatorial Optimization across Quantum Architectures." ACM Transactions on Quantum Computing 2, no. 1 (April 2021): 1–29. http://dx.doi.org/10.1145/3425607.

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Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore’s law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this article, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. To demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave’s quantum annealer and IBM’s gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitude larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution. Reproducibility : Our code and data are available at Reference [1].
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Atchade-Adelomou, Parfait, Guillermo Alonso-Linaje, Jordi Albo-Canals, and Daniel Casado-Fauli. "qRobot: A Quantum Computing Approach in Mobile Robot Order Picking and Batching Problem Solver Optimization." Algorithms 14, no. 7 (June 26, 2021): 194. http://dx.doi.org/10.3390/a14070194.

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This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating a quantum combinatorial optimization algorithm that saves the distance travelled and the batch of orders to be made. In case of computational need, the robot will be able to parallelize part of the operations in hybrid computing (quantum + classical), accessing CPUs and QPUs distributed in a public or private cloud. We developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave), and Pennylane locally or remotely. The proof of concept, when run in the above stated quantum environments, showed the execution time of our algorithm with different public access simulators on the market, computational results of our picking and batching algorithm, and analyze the quantum real-time execution. Our findings are that the behavior of the Amazon Braket D-Wave is better than Gate-based Quantum Computing over 20 qubits, and that AWS-Braket has better time performance than Qiskit or Pennylane.
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19

Nielsen, Ida M. B., and Curtis L. Janssen. "Multicore Challenges and Benefits for High Performance Scientific Computing." Scientific Programming 16, no. 4 (2008): 277–85. http://dx.doi.org/10.1155/2008/450818.

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Until recently, performance gains in processors were achieved largely by improvements in clock speeds and instruction level parallelism. Thus, applications could obtain performance increases with relatively minor changes by upgrading to the latest generation of computing hardware. Currently, however, processor performance improvements are realized by using multicore technology and hardware support for multiple threads within each core, and taking full advantage of this technology to improve the performance of applications requires exposure of extreme levels of software parallelism. We will here discuss the architecture of parallel computers constructed from many multicore chips as well as techniques for managing the complexity of programming such computers, including the hybrid message-passing/multi-threading programming model. We will illustrate these ideas with a hybrid distributed memory matrix multiply and a quantum chemistry algorithm for energy computation using Møller–Plesset perturbation theory.
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20

Chakraborty, Sanjay, Soharab Hossain Shaikh, Sudhindu Bikash Mandal, Ranjan Ghosh, and Amlan Chakrabarti. "A study and analysis of a discrete quantum walk-based hybrid clustering approach using d-regular bipartite graph and 1D lattice." International Journal of Quantum Information 17, no. 02 (March 2019): 1950016. http://dx.doi.org/10.1142/s0219749919500163.

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Traditional machine learning shares several benefits with quantum information processing field. The study of machine learning with quantum mechanics is called quantum machine learning. Data clustering is an important tool for machine learning where quantum computing plays a vital role in its inherent speed up capability. In this paper, a hybrid quantum algorithm for data clustering (quantum walk-based hybrid clustering (QWBHC)) is introduced where one-dimensional discrete time quantum walks (DTQW) play the central role to update the positions of data points according to their probability distributions. A quantum oracle is also designed and it is mainly implemented on a finite [Formula: see text]-regular bipartite graph where data points are initially distributed as a predefined set of clusters. An overview of a quantum walk (QW) based clustering algorithm on 1D lattice structure is also introduced and described in this paper. In order to search the nearest neighbors, a unitary and reversible DTQW gives a quadratic speed up over the traditional classical random walk. This paper also demonstrates the comparisons of our proposed hybrid quantum clustering algorithm with some state-of-the-art clustering algorithms in terms of clustering accuracy and time complexity analysis. The proposed quantum oracle needs [Formula: see text] queries to mark the nearest data points among clusters and modify the existing clusters. Finally, the proposed QWBHC algorithm achieves [Formula: see text] performance.
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Wu, Xin, Axel Koslowski, and Walter Thiel. "Semiempirical Quantum Chemical Calculations Accelerated on a Hybrid Multicore CPU–GPU Computing Platform." Journal of Chemical Theory and Computation 8, no. 7 (June 7, 2012): 2272–81. http://dx.doi.org/10.1021/ct3001798.

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Ajagekar, Akshay, Travis Humble, and Fengqi You. "Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems." Computers & Chemical Engineering 132 (January 2020): 106630. http://dx.doi.org/10.1016/j.compchemeng.2019.106630.

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23

Wang, Ling, Fang Tang, and Hao Wu. "Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation." Applied Mathematics and Computation 171, no. 2 (December 2005): 1141–56. http://dx.doi.org/10.1016/j.amc.2005.01.115.

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Ajagekar, Akshay, and Fengqi You. "Quantum computing based hybrid deep learning for fault diagnosis in electrical power systems." Applied Energy 303 (December 2021): 117628. http://dx.doi.org/10.1016/j.apenergy.2021.117628.

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Guan, Ji, Yuan Feng, and Mingsheng Ying. "Super-activating quantum memory with entanglement." Quantum Information and Computation 18, no. 13&14 (November 2018): 1115–24. http://dx.doi.org/10.26421/qic18.13-14-3.

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Noiseless subsystems were proved to be an efficient and faithful approach to preserve fragile information against decoherence in quantum information processing and quantum computation. They were employed to design a general (hybrid) quantum memory cell model that can store both quantum and classical information. In this paper, we find an interesting new phenomenon that the purely classical memory cell can be super-activated to preserve quantum states, whereas the null memory cell can only be super-activated to encode classical information. Furthermore, necessary and sufficient conditions for this phenomenon are discovered so that the super-activation can be easily checked by examining certain eigenvalues of the quantum memory cell without computing the noiseless subsystems explicitly. In particular, it is found that entangled and separable stationary states are responsible for the super-activation of storing quantum and classical information, respectively.
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YEPEZ, JEFFREY. "TYPE-II QUANTUM COMPUTERS." International Journal of Modern Physics C 12, no. 09 (November 2001): 1273–84. http://dx.doi.org/10.1142/s0129183101002668.

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This paper discusses a computing architecture that uses both classical parallelism and quantum parallelism. We consider a large parallel array of small quantum computers, connected together by classical communication channels. This kind of computer is called a type-II quantum computer, to differentiate it from a globally phase-coherent quantum computer, which is the first type of quantum computer that has received nearly exclusive attention in the literature. Although a hybrid, a type-II quantum computer retains the crucial advantage allowed by quantum mechanical superposition that its computational power grows exponentially in the number of phase-coherent qubits per node, only short-range and short time phase-coherence is needed, which significantly reduces the level of engineering facility required to achieve its construction. Therefore, the primary factor limiting its computational power is an economic one and not a technological one, since the volume of its computational medium can in principle scale indefinitely.
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Watabe, Masaya, Kodai Shiba, Chih-Chieh Chen, Masaru Sogabe, Katsuyoshi Sakamoto, and Tomah Sogabe. "Quantum Circuit Learning with Error Backpropagation Algorithm and Experimental Implementation." Quantum Reports 3, no. 2 (May 28, 2021): 333–49. http://dx.doi.org/10.3390/quantum3020021.

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Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and high-dimensional state or function approximation. Quantum–classical hybrid algorithms have been proposed in recent years for this purpose under the noisy intermediate-scale quantum computer (NISQ) environment. Under this scheme, the role played by the classical computer is the parameter tuning, parameter optimization, and parameter update for the quantum circuit. In this paper, we propose a gradient descent-based backpropagation algorithm that can efficiently calculate the gradient in parameter optimization and update the parameter for quantum circuit learning, which outperforms the current parameter search algorithms in terms of computing speed while presenting the same or even higher test accuracy. Meanwhile, the proposed theoretical scheme was successfully implemented on the 20-qubit quantum computer of IBM Q, ibmq_johannesburg. The experimental results reveal that the gate error, especially the CNOT gate error, strongly affects the derived gradient accuracy. The regression accuracy performed on the IBM Q becomes lower with the increase in the number of measurement shot times due to the accumulated gate noise error.
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Tohari, Mariam M., Moteb M. Alqahtani, and Andreas Lyras. "Optical Multistability in the Metal Nanoparticle–Graphene Nanodisk–Quantum Dot Hybrid Systems." Nanomaterials 10, no. 9 (August 27, 2020): 1687. http://dx.doi.org/10.3390/nano10091687.

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Hybrid nanoplasmonic systems can provide a promising platform of potential nonlinear applications due to the enhancement of optical fields near their surfaces in addition to the control of strong light–matter interactions they can afford. We theoretically investigated the optical multistability of a probe field that circulated along a unidirectional ring cavity containing a metal nanoparticle–graphene nanodisk–quantum dot hybrid system; the quantum dot was modeled as a three-level atomic system of Lambda configuration interacting with probe and control fields in the optical region of the electromagnetic spectrum. We show that the threshold and degree of multistability can be controlled by the geometry of the setup, the size of metal nanoparticles, the carrier mobility in the graphene nanodisk and the detunings of probe and control fields. We found that under electromagnetically-induced transparency conditions the system exhibits enhanced optical multistability with an ultralow threshold in the case of two-photon resonance with high carrier mobility in the graphene nanodisk. Moreover, we calculated the limits of the controllable parameters within which the switching between optical multistability and bistability can occur. We show that our proposed hybrid plasmonic system can be useful for efficient all-optical switches and logic-gate elements for quantum computing and quantum information processing.
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Cerezo, Marco, Alexander Poremba, Lukasz Cincio, and Patrick J. Coles. "Variational Quantum Fidelity Estimation." Quantum 4 (March 26, 2020): 248. http://dx.doi.org/10.22331/q-2020-03-26-248.

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Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ,σ) based on the ``truncated fidelity'' F(ρm,σ), which is evaluated for a state ρm obtained by projecting ρ onto its m-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ, (2) compute matrix elements of σ in the eigenbasis of ρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.
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Yan, Fei, Abdullah M. Iliyasu, Sihao Jiao, and Huamin Yang. "Quantum Structure for Modelling Emotion Space of Robots." Applied Sciences 9, no. 16 (August 15, 2019): 3351. http://dx.doi.org/10.3390/app9163351.

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Utilising the properties of quantum mechanics, i.e., entanglement, parallelism, etc., a quantum structure is proposed for representing and manipulating emotion space of robots. This quantum emotion space (QES) provides a mechanism to extend emotion interpretation to the quantum computing domain whereby fewer resources are required and, by using unitary transformations, it facilitates easier tracking of emotion transitions over different intervals in the emotion space. The QES is designed as an intuitive and graphical visualisation of the emotion state as a curve in a cuboid, so that an “emotion sensor” could be used to track the emotion transition as well as its manipulation. This ability to use transition matrices to convey manipulation of emotions suggests the feasibility and effectiveness of the proposed approach. Our study is primarily influenced by two developments. First, the massive amounts of data, complexity of control, planning and reasoning required for today’s sophisticated automation processes necessitates the need to equip robots with powerful sensors to enable them adapt and operate in all kinds of environments. Second, the renewed impetus and inevitable transition to the quantum computing paradigm suggests that quantum robots will have a role to play in future data processing and human-robot interaction either as standalone units or as part of larger hybrid systems. The QES proposed in this study provides a quantum mechanical formulation for quantum emotion as well as a platform to process, track, and manipulate instantaneous transitions in a robot’s emotion. The new perspective will open broad areas, such as applications in emotion recognition and emotional intelligence for quantum robots.
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Tomesh, Teague, Pranav Gokhale, Eric R. Anschuetz, and Frederic T. Chong. "Coreset Clustering on Small Quantum Computers." Electronics 10, no. 14 (July 15, 2021): 1690. http://dx.doi.org/10.3390/electronics10141690.

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Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.
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Kirke, Alexis. "Programming gate-based hardware quantum computers for music." Muzikologija, no. 24 (2018): 21–37. http://dx.doi.org/10.2298/muz1824021k.

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There have been significant attempts previously to use the equations of quantum mechanics for generating sound, and to sonify simulated quantum processes. For new forms of computation to be utilized in computer music, eventually hardware must be utilized. This has rarely happened with quantum computer music. One reason for this is that it is currently not easy to get access to such hardware. A second is that the hardware available requires some understanding of quantum computing theory. This paper moves forward the process by utilizing two hardware quantum computation systems: IBMQASM v1.1 and a D-Wave 2X. It also introduces the ideas behind the gate-based IBM system, in a way hopefully more accessible to computerliterate readers. This is a presentation of the first hybrid quantum computer algorithm, involving two hardware machines. Although neither of these algorithms explicitly utilize the promised quantum speed-ups, they are a vital first step in introducing QC to the musical field. The article also introduces some key quantum computer algorithms and discusses their possible future contribution to computer music.
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Kumar, Yogesh, Shashi Kant Verma, and Sandeep Sharma. "An ensemble approach of improved quantum inspired gravitational search algorithm and hybrid deep neural networks for computational optimization." International Journal of Modern Physics C 32, no. 08 (April 7, 2021): 2150100. http://dx.doi.org/10.1142/s012918312150100x.

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In this paper, an autonomous ensemble approach of improved quantum inspired gravitational search algorithm (IQI-GSA) and hybrid deep neural networks (HDNN) is proposed for the optimization of computational problems. The IQI-GSA is a combinational variant of gravitational search algorithm (GSA) and quantum computing (QC). The improved variant enhances the diversity of mass collection for retaining the stochastic attributes and handling the local trapping of mass agents. Further, the hybrid deep neural network encompasses the convolutional and recurrent neural networks (HDCR-NN) which analyze the relational & temporal dependencies among the different computational components for optimization. The proposed ensemble approach is evaluated for the application of facial expression recognition by experimentation on Karolinska Directed Emotional Faces (KDEF) and Japanese Female Facial Expression (JAFFE) datasets. The experimentation evaluations evidently exhibit the outperformed recognition rate of the proposed ensemble approach in comparison with state-of-the-art techniques.
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34

Lo, Shih-Che, and Yi-Cheng Shih. "A Genetic Algorithm with Quantum Random Number Generator for Solving the Pollution-Routing Problem in Sustainable Logistics Management." Sustainability 13, no. 15 (July 27, 2021): 8381. http://dx.doi.org/10.3390/su13158381.

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The increase of greenhouse gases emission, global warming, and even climate change is an ongoing issue. Sustainable logistics and distribution management can help reduce greenhouse gases emission and lighten its influence against our living environment. Quantum computing has become more and more popular in recent years for advancing artificial intelligence into the next generation. Hence, we apply quantum random number generator to provide true random numbers for the genetic algorithm to solve the pollution-routing problems (PRPs) in sustainable logistics management in this paper. The objective of the PRPs is to minimize carbon dioxide emissions, following one of the seventeen sustainable development goals set by the United Nations. We developed a two-phase hybrid model combining a modified k-means algorithm as a clustering method and a genetic algorithm with quantum random number generator as an optimization engine to solve the PRPs aiming to minimize the pollution produced by trucks traveling along delivery routes. We also compared the computation performance with another hybrid model by using a different optimization engine, i.e., the tabu search algorithm. From the experimental results, we found that both hybrid models can provide good solution quality for CO2 emission minimization for 29 PRPs out of a total of 30 instances (30 runs each for all problems).
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Nakaji, Kouhei, and Naoki Yamamoto. "Expressibility of the alternating layered ansatz for quantum computation." Quantum 5 (April 19, 2021): 434. http://dx.doi.org/10.22331/q-2021-04-19-434.

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The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.
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36

Tribollet, Jérôme. "Hybrid nanophotonic-nanomagnonic SiC-YiG quantum sensor: II/dark spins quantum sensing with V2 spins and fiber based OP-PELDOR/ODMR." European Physical Journal Applied Physics 90, no. 2 (May 2020): 20103. http://dx.doi.org/10.1051/epjap/2020200063.

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First experiments like optically detected (OD) electron paramagnetic resonance (ODMR), photoluminescence detected RABI oscillations, and optical pumping (OP) assisted pulsed EPR measurements of T2 and T1 of V2 spins in bulk SiC, which were previously demonstrated on various home build EPR spectrometers with free space optics, are here all demonstrated for the first time using a commercial X band pulsed EPR spectrometer combined with a single optical fiber and a standard external photoluminescence setup. Quantum sensing of bulk dark spins dipolar coupled to V2 spins in SiC is also demonstrated here for the first time using single fiber based OP assisted pulsed electron electron double resonance spectroscopy (PELDOR). A spin wave resonance study of model permalloy nanostripes is also presented allowing to check the ferromagnetic nanostripes design. These experiments are first key steps towards the fiber-based integration of the recently proposed SiC-YiG quantum sensor device [J. Tribollet, Eur. Phys. J. Appl. Phys. 90, 20102 (2020)], to a commercially available and worldwide used pulsed EPR spectrometer, with important applications expected in structural biology, surface chemistry, and quantum computing.
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Palacio-Morales, Alexandra, Eric Mascot, Sagen Cocklin, Howon Kim, Stephan Rachel, Dirk K. Morr, and Roland Wiesendanger. "Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system." Science Advances 5, no. 7 (July 2019): eaav6600. http://dx.doi.org/10.1126/sciadv.aav6600.

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Topological superconductors are predicted to harbor exotic boundary states—Majorana zero-energy modes—whose non-Abelian braiding statistics present a new paradigm for the realization of topological quantum computing. Using low-temperature scanning tunneling spectroscopy, here, we report on the direct real-space visualization of chiral Majorana edge states in a monolayer topological superconductor, a prototypical magnet-superconductor hybrid system composed of nanoscale Fe islands of monoatomic height on a Re(0001)-O(2 × 1) surface. In particular, we demonstrate that interface engineering by an atomically thin oxide layer is crucial for driving the hybrid system into a topologically nontrivial state as confirmed by theoretical calculations of the topological invariant, the Chern number.
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38

Kübler, Jonas M., Andrew Arrasmith, Lukasz Cincio, and Patrick J. Coles. "An Adaptive Optimizer for Measurement-Frugal Variational Algorithms." Quantum 4 (May 11, 2020): 263. http://dx.doi.org/10.22331/q-2020-05-11-263.

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Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient descent. We numerically simulate the performance of iCANS for the variational quantum eigensolver and for variational quantum compiling, with and without noise. In all cases, and especially in the noisy case, iCANS tends to out-perform state-of-the-art optimizers for VHQCAs. We therefore believe this adaptive optimizer will be useful for realistic VHQCA implementations, where the number of measurements is limited.
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39

Chekletsov, V. V. "Dialogs of a hybrid world." Philosophical Problems of Information Technologies and Cyberspace, no. 1 (July 14, 2021): 99–116. http://dx.doi.org/10.17726/philit.2021.1.6.

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The article is based on reports and discussions held during three online events organized by the Russian Research Center for the Internet of Things together with the Department of Philosophy and Sociology of South-West State University during 2021: an open discussion with the famous transhumanist philosopher David Pearce dedicated to the birthday of Jeremiah Bentham on February 15, a round table dedicated to the World Internet of Things Day on April 9, and a session within the first IoT Hot Spots conference on June 16.The main topics for discussion this year were the consideration of the following philosophical and socio-cultural problems and concepts in the light of the development of cyberphysical systems: anthropological differences between the «posthuman» and «metahuman» projects, epistemological aspects of bio- and cybersemiotics in modern hybrid techno-social networks, the cultural dimension of remote proximity in the digital age, the ontology of the quantum complexity of the digital multiverse, the ethical dimensions of the digital economy in the post-covid period, the aesthetics of metamodernism in the smart city, the anthropocene effects of silicon addiction and the race of computing, socio-philosophical problems of management in situations of high uncertainty, political strategies for sustainable development.
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40

Faheem, Muhammad, and Andreas Heyden. "Hybrid Quantum Mechanics/Molecular Mechanics Solvation Scheme for Computing Free Energies of Reactions at Metal–Water Interfaces." Journal of Chemical Theory and Computation 10, no. 8 (June 10, 2014): 3354–68. http://dx.doi.org/10.1021/ct500211w.

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41

Vallury, Harish J., Michael A. Jones, Charles D. Hill, and Lloyd C. L. Hollenberg. "Quantum computed moments correction to variational estimates." Quantum 4 (December 15, 2020): 373. http://dx.doi.org/10.22331/q-2020-12-15-373.

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The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer quantum circuit steps and are robust to device errors. Here we present an approach in which problem complexity is transferred to dynamic quantities computed on the quantum processor – Hamiltonian moments, ⟨Hn⟩. From these quantum computed moments, an estimate of the ground-state energy can be obtained using the ``infimum'' theorem from Lanczos cumulant expansions which manifestly corrects the associated variational calculation. With higher order effects in Hilbert space generated via the moments, the burden on the trial-state quantum circuit depth is eased. The method is introduced and demonstrated on 2D quantum magnetism models on lattices up to 5×5 (25 qubits) implemented on IBM Quantum superconducting qubit devices. Moments were quantum computed to fourth order with respect to a parameterised antiferromagnetic trial-state. A comprehensive comparison with benchmark variational calculations was performed, including over an ensemble of random coupling instances. The results showed that the infimum estimate consistently outperformed the benchmark variational approach for the same trial-state. These initial investigations suggest that the quantum computed moments approach has a high degree of stability against trial-state variation, quantum gate errors and shot noise, all of which bodes well for further investigation and applications of the approach.
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42

Gokhale, Angelina, Mandaar B. Pande, and Dhanya Pramod. "Implementation of a quantum transfer learning approach to image splicing detection." International Journal of Quantum Information 18, no. 05 (August 2020): 2050024. http://dx.doi.org/10.1142/s0219749920500240.

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In this paper, we present an implementation of quantum transfer learning to blind and passive detection of image splicing forgeries. Though deep learning models are becoming increasingly popular for various computer vision use cases, they depend on powerful classical machines and GPUs for dealing with complex problem solving and also to reduce the time taken for computation. The quantum computing research community has demonstrated elegant solutions to complex use cases in deep learning and computer vision for reducing storage space and increasing the accuracy of results compared to those obtained on a classical computer. We extend the quantum transfer learning approach formerly applied to image classification, for solving the growing problem of image manipulation, specifically, image splicing detection. A hybrid model is built using the ResNet50 pre-trained classical deep learning network and a quantum variational circuit to classify spliced versus authentic images. We present a comparative empirical study of classical versus quantum transfer learning approach using Xanadu’s pennylane quantum simulator and the pytorch deep learning framework. The model was also evaluated on the actual quantum processor ibmqx2 provided by IBM. Results obtained by execution on the quantum processor ([Formula: see text]%, [Formula: see text]%) and simulator ([Formula: see text]%, [Formula: see text]%) showed improvements in comparison to those obtained from classical computers ([Formula: see text]%, [Formula: see text]%).
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43

Gao, Min, Xiaowen Han, Wenjing Liu, Ziao Tian, Yongfeng Mei, Miao Zhang, Paul K. Chu, et al. "Graphene-mediated ferromagnetic coupling in the nickel nano-islands/graphene hybrid." Science Advances 7, no. 30 (July 2021): eabg7054. http://dx.doi.org/10.1126/sciadv.abg7054.

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Nanoscale magnetic structures are fundamental to the design and fabrication of spintronic devices and have exhibited tremendous potential superior to the conventional semiconductor devices. However, most of the magnetic moments in nanostructures are unstable due to size effect, and the possible solution based on exchange coupling between nanomagnetism is still not clear. Here, graphene-mediated exchange coupling between nanomagnets is demonstrated by depositing discrete superparamagnetic Ni nano-islands on single-crystal graphene. The heterostructure exhibits ideal two-dimensional (2D) ferromagnetism with clear hysteresis loops and Curie temperature up to 80 K. The intrinsic ferromagnetism in graphene and antiferromagnetic exchange coupling between graphene and Ni nano-islands are revealed by x-ray magnetic circular dichroism and density functional theory calculations. The artificial 2D ferromagnets constitute a platform to study the coupling mechanism between complex correlated electronic systems and magnetism on the nanoscale, and the results and concept provide insights into the realization of spin manipulation in quantum computing.
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44

Xu, Mengying, Jie Zhou, and Yi Lu. "A Chaotic Hybrid Immune Genetic Algorithm for Spectrum Allocation Optimization in ICRSN." Journal of Sensors 2020 (September 23, 2020): 1–13. http://dx.doi.org/10.1155/2020/8827512.

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The growing usage of the industrial cognitive radio sensor network (ICRSN) brings profound changes to the Internet of Things. The ICRSN is an emerging technique to transfer industrial data, which has strict and accurate communication requirements in a large number of areas such as environmental surveillance, building monitoring, control, and many other areas. The problem of maximizing the sum bandwidth by using a spectrum allocation algorithm has been extensively studied in this paper. Inspired by chaos theory and quantum computing, this work presents a new chaotic hybrid immune genetic algorithm (CHIGA). We then introduce a spectrum allocation model that considers both network reward, throughput, and convergence time. The improvement of CHIGA performance through experimental simulations is evaluated in terms of the sum network reward compared to methods based on simulated annealing (SA), ant colony optimization (ACO), and particle swarm optimization (PSO). Simulation results show that the CHIGA has a higher network reward and throughput existing optimized algorithms while maintaining total system throughput.
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45

Rahmat, M. Sidik Augi, and Pekik Nurwantoro. "Kajian Komputasi Algoritma Kuantum Quantum V ariational Eigensolver untuk Simulasi Molekul H2." Jurnal Fisika Indonesia 24, no. 1 (April 7, 2020): 17. http://dx.doi.org/10.22146/jfi.v24i1.52011.

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Telah dilakukan telaah teoritis dan komputasi mengenai algoritma kuantum variational quantum eigensolver simulasi molekul H2. Algoritma variational quantum eigensolver (VQE) adalah salah satu algoritma yang dapat diterapkan pada komputer kuantum sederhana pada masa kini dan merupakan algoritma yang cukup stabil dan efek dekoherensi. Algoritma VQE disebut sebagai hybrid quantum-classical karena sebagian algoritma dikerjakan pada komputer klasik. Prinsip dasar algoritma VQE adalah prinsip variasi, yaitu pencarian fungsi gelombang yang akan mengakibatkan energi sistem kuantum memiliki energi terendah. Fungsi gelombang dan Hamiltonan pada algoritma VQE disimulasikan dengan menggunakan gerbang-gerbang kuantum. Untuk dapat dioperasikan oleh gerbang kuantum. Hamiltonan dan fungsi gelombang pada penelitian ini menggunakan wakilan kuantisasi kedua. Penelitian ini menggunakan transformasi Jordan-Wigner dan Bravyi-Kitaev dari operator fermionik menjadi operator kubit (qubit) atau gerbang kuantum.Perhitungan atau komputasi energi sistem dilakukan menggunakan komputer kuantum, namun optimasi dilakukan pada komputer klasik menggunakan algoritma optimasi seperti Nelder-Mead, Powell dan BFGS. Penelitian ini akan mendekati fungsi gelombang sistem dengan beberapa basis fungsi dan metode, kemudian dari hasil yang diperoleh akan dilihat pendekatan seperti apa yang paling cocok untuk simulasi molekul H2. Simulasi numerik pada penelitian ini menggunakan paket pemrograman OpenFermion dan layanan komputasi awan kuantum Rigetti Computing.
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46

Minati, Gianfranco. "A Note on the Reality of Incomputable Real Numbers and Its Systemic Significance." Systems 9, no. 2 (June 12, 2021): 44. http://dx.doi.org/10.3390/systems9020044.

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We discuss mathematical and physical arguments contrasting continuous and discrete, limitless discretization as arbitrary granularity. In this regard, we focus on Incomputable (lacking an algorithm that computes in finite time) Real Numbers (IRNs). We consider how, for measurements, the usual approach to dealing with IRNs is to approximate to avoid the need for more detailed, unrealistic surveys. In this regard, we contrast effective computation and emergent computation. Furthermore, we consider the alternative option of taking into account the properties of the decimal part of IRNs, such as the occurrence, distribution, combinations, quasi-periodicities, and other contextual properties, e.g., topological. For instance, in correspondence with chaotic behaviors, quasi-periodic solutions, quasi-systems, uniqueness, and singularities, non-computability represents and corresponds to theoretically incomplete properties of the processes of complexity, such as emergence and quantum-like properties. We elaborate upon cases of equivalences and symmetries, characterizing complexity and infiniteness as corresponding to the usage of multiple non-equivalent models that are constructively and theoretically incomplete due to the non-exhaustive nature of the multiplicity of complexity. Finally, we detail alternative computational approaches, such as hypercomputation, natural computing, quantum computing, and analog and hybrid computing. The reality of IRNs is considered to represent the theoretical incompleteness of complex phenomena taking place through collapse from equivalences and symmetries. A world of precise finite values, even if approximated, is assumed to have dynamics that are zippable in analytical formulae and to be computable and symbolically representable in the way it functions. A world of arbitrary precise infinite values with dynamics that are non-zippable in analytical formulae, non-computable, and, for instance, sub-symbolically representable, is assumed to be almost compatible with the coherence of emergence. The real world is assumed to be a continuous combination of the two—functioning and emergent—where the second dominates and is the norm, and the first is the locus of primarily epistemic extracts. Research on IRNs should focus on properties representing and corresponding to those that are detectable in real, even if extreme, phenomena, such as emergence and quantum phenomena.
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Khairy, Sami, Ruslan Shaydulin, Lukasz Cincio, Yuri Alexeev, and Prasanna Balaprakash. "Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (April 3, 2020): 2367–75. http://dx.doi.org/10.1609/aaai.v34i03.5616.

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Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.
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Fatemeh, D. B., C. K. Loo, G. Kanagaraj, and S. G. Ponnambalam. "A hybrid SP-QPSO algorithm with parameter free adaptive penalty method for constrained global optimization problems." Journal of Modern Manufacturing Systems and Technology 1, no. 1 (September 13, 2018): 15–26. http://dx.doi.org/10.15282/jmmst.v1i1.195.

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Most real-life optimization problems involve constraints which require a specialized mechanism to deal with them. The presence of constraints imposes additional challenges to the researchers motivated towards the development of new algorithm with efficient constraint handling mechanism. This paper attempts the suitability of newly developed hybrid algorithm, Shuffled Complex Evolution with Quantum Particle Swarm Optimization abbreviated as SP-QPSO, extended specifically designed for solving constrained optimization problems. The incorporation of adaptive penalty method guides the solutions to the feasible regions of the search space by computing the violation of each one. Further, the algorithm’s performance is improved by Centroidal Voronoi Tessellations method of point initialization promise to visit the entire search space. The effectiveness and the performance of SP-QPSO are examined by solving a broad set of ten benchmark functions and four engineering case study problems taken from the literature. The experimental results show that the hybrid version of SP-QPSO algorithm is not only overcome the shortcomings of the original algorithms but also outperformed most state-of-the-art algorithms, in terms of searching efficiency and computational time.
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49

Mohsin, Sayed A., Ahmed Younes, and Saad M. Darwish. "Dynamic Cost Ant Colony Algorithm to Optimize Query for Distributed Database Based on Quantum-Inspired Approach." Symmetry 13, no. 1 (January 2, 2021): 70. http://dx.doi.org/10.3390/sym13010070.

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A distributed database model can be effectively optimized through using query optimization. In such a model, the optimizer attempts to identify the most efficient join order, which minimizes the overall cost of the query plan. Successful query processing largely relies on the methodology implemented by the query optimizer. Many researches are concerned with the fact that query processing is considered an NP-hard problem especially when the query becomes bigger. Regarding large queries, it has been found that heuristic methods cannot cover all search spaces and may lead to falling in a local minimum. This paper examines how quantum-inspired ant colony algorithm, a hybrid strategy of probabilistic algorithms, can be devised to improve the cost of query joins in distributed databases. Quantum computing has the ability to diversify and expand, and thus covering large query search spaces. This enables the selection of the best trails, which speeds up convergence and helps avoid falling into a local optimum. With such a strategy, the algorithm aims to identify an optimal join order to reduce the total execution time. Experimental results show that the proposed quantum-inspired ant colony offers a faster convergence with better outcome when compared with the classic model.
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Vasant, Pandian, Fahad Parvez Mahdi, Jose Antonio Marmolejo-Saucedo, Igor Litvinchev, Roman Rodriguez Aguilar, and Junzo Watada. "Quantum-Behaved Bat Algorithm for Solving the Economic Load Dispatch Problem Considering a Valve-Point Effect." International Journal of Applied Metaheuristic Computing 11, no. 3 (July 2020): 41–57. http://dx.doi.org/10.4018/ijamc.2020070102.

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Quantum computing-inspired metaheuristic algorithms have emerged as a powerful computational tool to solve nonlinear optimization problems. In this paper, a quantum-behaved bat algorithm (QBA) is implemented to solve a nonlinear economic load dispatch (ELD) problem. The objective of ELD is to find an optimal combination of power generating units in order to minimize total fuel cost of the system, while satisfying all other constraints. To make the system more applicable to the real-world problem, a valve-point effect is considered here with the ELD problem. QBA is applied in 3-unit, 10-unit, and 40-unit power generation systems for different load demands. The obtained result is then presented and compared with some well-known methods from the literature such as different versions of evolutionary programming (EP) and particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), simulated annealing (SA) and hybrid ABC_PSO. The comparison of results shows that QBA performs better than the above-mentioned methods in terms of solution quality, convergence characteristics and computational efficiency. Thus, QBA proves to be an effective and a robust technique to solve such nonlinear optimization problem.
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