Journal articles: 'Quantum optimization'

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Hogg, Tad, and Dmitriy Portnov. "Quantum optimization." Information Sciences 128, no. 3-4 (October 2000): 181–97. http://dx.doi.org/10.1016/s0020-0255(00)00052-9.

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Berta, Mario, Omar Fawzi, and Volkher B. Scholz. "Quantum Bilinear Optimization." SIAM Journal on Optimization 26, no. 3 (January 2016): 1529–64. http://dx.doi.org/10.1137/15m1037731.

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Malossini, A., E. Blanzieri, and T. Calarco. "Quantum Genetic Optimization." IEEE Transactions on Evolutionary Computation 12, no. 2 (April 2008): 231–41. http://dx.doi.org/10.1109/tevc.2007.905006.

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Apolloni, B., C. Carvalho, and D. de Falco. "Quantum stochastic optimization." Stochastic Processes and their Applications 33, no. 2 (December 1989): 233–44. http://dx.doi.org/10.1016/0304-4149(89)90040-9.

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Egger, Daniel J., Jakub Mareček, and Stefan Woerner. "Warm-starting quantum optimization." Quantum 5 (June 17, 2021): 479. http://dx.doi.org/10.22331/q-2021-06-17-479.

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There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

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Li, Yangyang, Mengzhuo Tian, Guangyuan Liu, Cheng Peng, and Licheng Jiao. "Quantum Optimization and Quantum Learning: A Survey." IEEE Access 8 (2020): 23568–93. http://dx.doi.org/10.1109/access.2020.2970105.

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Sayed, Gehad Ismail, Ashraf Darwish, and Aboul Ella Hassanien. "Quantum multiverse optimization algorithm for optimization problems." Neural Computing and Applications 31, no. 7 (November 1, 2017): 2763–80. http://dx.doi.org/10.1007/s00521-017-3228-9.

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van Apeldoorn, Joran, András Gilyén, Sander Gribling, and Ronald de Wolf. "Convex optimization using quantum oracles." Quantum 4 (January 13, 2020): 220. http://dx.doi.org/10.22331/q-2020-01-13-220.

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We study to what extent quantum algorithms can speed up solving convex optimization problems. Following the classical literature we assume access to a convex set via various oracles, and we examine the efficiency of reductions between the different oracles. In particular, we show how a separation oracle can be implemented using O~(1) quantum queries to a membership oracle, which is an exponential quantum speed-up over the Ω(n) membership queries that are needed classically. We show that a quantum computer can very efficiently compute an approximate subgradient of a convex Lipschitz function. Combining this with a simplification of recent classical work of Lee, Sidford, and Vempala gives our efficient separation oracle. This in turn implies, via a known algorithm, that O~(n) quantum queries to a membership oracle suffice to implement an optimization oracle (the best known classical upper bound on the number of membership queries is quadratic). We also prove several lower bounds: Ω(n) quantum separation (or membership) queries are needed for optimization if the algorithm knows an interior point of the convex set, and Ω(n) quantum separation queries are needed if it does not.

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Krotov, V. F. "Quantum system control optimization." Doklady Mathematics 78, no. 3 (December 2008): 949–52. http://dx.doi.org/10.1134/s1064562408060380.

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Maron, Adriano, Renata Reiser, Maurício Pilla, and Adenauer Yamin. "Quantum Processes: A Novel Optimization for Quantum Simulation." TEMA (São Carlos) 14, no. 3 (November 24, 2013): 399. http://dx.doi.org/10.5540/tema.2013.014.03.0399.

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The simulation of quantum algorithms in classic computers is a task which requires high processing and storing capabilities, limiting the size of quantum systems supported by the simulators. However, optimizations for reduction of temporal and spatial complexities are promising and expanding the capabilities of some simulators. The main contribution of this work consists in designing optimizations by the description of quantum transformations using Quantum Processes and Partial Quantum Processes conceived in the qGM theoretical model. These processes, when computed on the VPE-qGM execution environment, result in lower execution time and better performance, allowing the simulation of more complex quantum algorithms. The performance evaluation of this proposal was carried out by benchmarks used in similar works and included the sequential simulation of quantum algorithms up to 24 qubits. The results show a great improvement when compared to the previous version of the environment and indicate possibilities of advances in this research.

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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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Urgelles, Helen, Pablo Picazo-Martinez, David Garcia-Roger, and Jose F. Monserrat. "Multi-Objective Routing Optimization for 6G Communication Networks Using a Quantum Approximate Optimization Algorithm." Sensors 22, no. 19 (October 6, 2022): 7570. http://dx.doi.org/10.3390/s22197570.

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Sixth-generation wireless (6G) technology has been focused on in the wireless research community. Global coverage, massive spectrum usage, complex new applications, and strong security are among the new paradigms introduced by 6G. However, realizing such features may require computation capabilities transcending those of present (classical) computers. Large technology companies are already exploring quantum computers, which could be adopted as potential technological enablers for 6G. This is a promising avenue to explore because quantum computers exploit the properties of quantum states to perform certain computations significantly faster than classical computers. This paper focuses on routing optimization in wireless mesh networks using quantum computers, explicitly applying the quantum approximate optimization algorithm (QAOA). Single-objective and multi-objective examples are presented as robust candidates for the application of quantum machine learning. Moreover, a discussion about quantum supremacy estimation for this problem is provided.

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RAMOS, RUBENS V., and PAULO B. M. SOUSA. "QUANTUM ALGORITHMS FOR OPTIMIZATION USING ASYMPTOTIC QUANTUM SEARCH." International Journal of Quantum Information 06, no. 04 (August 2008): 935–44. http://dx.doi.org/10.1142/s021974990800416x.

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Problems of optimization are very common in several areas like engineering, physics, economics and mathematics and usually, they are very difficult to solve. Basically, one has to find the minimum or maximum of an objective function. In this work, we chose two optimization problems and we present quantum algorithms to solve them. The problems are: (1) to find the best decomposition of a unitary operation achievable by a programmable quantum circuit; (2) to find the minimal distance of a linear code. The quantum algorithms used are asymptotic quantum search and their main property is the fact that only one measurement is required.

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Xin, Gang, Peng Wang, and Yuwei Jiao. "Multiscale quantum harmonic oscillator optimization algorithm with multiple quantum perturbations for numerical optimization." Expert Systems with Applications 185 (December 2021): 115615. http://dx.doi.org/10.1016/j.eswa.2021.115615.

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Sack, Stefan H., and Maksym Serbyn. "Quantum annealing initialization of the quantum approximate optimization algorithm." Quantum 5 (July 1, 2021): 491. http://dx.doi.org/10.22331/q-2021-07-01-491.

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The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.

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Epelde, M. ,., E. F. Combarro,, and I. F. R ́ua,. "DECODING M-ARY LINEAR CODES WITH THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM." Eurasian Journal of Mathematical and Computer Applications 10, no. 1 (March 2022): 4–25. http://dx.doi.org/10.32523/2306-6172-2022-10-1-4-25.

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Abstract The NP-hardness of the Minimum Distance Decoding Problem (MDDP) is the core of the McEliece cryptosystem. The difficulty of decoding a received word to the closest codeword in a given arbitrary code is key to its security. Related to the MDDP is the Coset Leader Problem (CLP), which consists in finding a word of a given syndrome and minimum Hamming weight. Both can be modelled as optimization problems, and solved using the Quantum Approximate Optimization Algorithm (QAOA), a well-known hybrid quantum- classical algorithm. In this paper, we model both the MDDP and CLP for linear codes over arbitrary m−ary alphabets, we make the theoretical analysis of the first level for the binary CLP problem, and introduce some experiments to test its performance. The experiments were carried out on both quantum computer simulators and real quantum devices, and use codes of different lengths and different depths of the QAOA.

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Dong, Yulong, Xiang Meng, Lin Lin, Robert Kosut, and K. Birgitta Whaley. "Robust Control Optimization for Quantum Approximate Optimization Algorithms." IFAC-PapersOnLine 53, no. 2 (2020): 242–49. http://dx.doi.org/10.1016/j.ifacol.2020.12.130.

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V. "Reactive Power Optimization Using Quantum Particle Swarm Optimization." Journal of Computer Science 8, no. 10 (October 1, 2012): 1644–48. http://dx.doi.org/10.3844/jcssp.2012.1644.1648.

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Sarvari, Samira, Nor Fazlida Mohd. Sani, Zurina Mohd Hanapi, and Mohd Taufik Abdullah. "An efficient quantum multiverse optimization algorithm for solving optimization problems." International Journal of Advances in Applied Sciences 9, no. 1 (March 1, 2020): 27. http://dx.doi.org/10.11591/ijaas.v9.i1.pp27-33.

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<p>Due to the recent trend of technologies to use the network-based systems, detecting them from threats become a crucial issue. Detecting unknown or modified attacks is one of the recent challenges in the field of intrusion detection system (IDS). In this research, a new algorithm called quantum multiverse optimization (QMVO) is investigated and combined with an artificial neural network (ANN) to develop advanced detection approaches for an IDS. QMVO algorithm depends on adopting a quantum representation of the quantum interference and operators in the multiverse optimization to obtain the optimal solution. The QMVO algorithm determining the neural network weights based on the kernel function, which can improve the accuracy and then optimize the training part of the artificial neural network. It is demonstrated 99.98% accuracy with experimental results that the proposed QMVO is significantly improved optimization compared with multiverse optimizer (MVO) algorithms.</p>

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Ostaszewski, Mateusz, Edward Grant, and Marcello Benedetti. "Structure optimization for parameterized quantum circuits." Quantum 5 (January 28, 2021): 391. http://dx.doi.org/10.22331/q-2021-01-28-391.

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We propose an efficient method for simultaneously optimizing both the structure and parameter values of quantum circuits with only a small computational overhead. Shallow circuits that use structure optimization perform significantly better than circuits that use parameter updates alone, making this method particularly suitable for noisy intermediate-scale quantum computers. We demonstrate the method for optimizing a variational quantum eigensolver for finding the ground states of Lithium Hydride and the Heisenberg model in simulation, and for finding the ground state of Hydrogen gas on the IBM Melbourne quantum computer.

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Dong, Yumin, Jianshe Xie, Wanbin Hu, Cheng Liu, and Yi Luo. "Variational algorithm of quantum neural network based on quantum particle swarm." Journal of Applied Physics 132, no. 10 (September 14, 2022): 104401. http://dx.doi.org/10.1063/5.0098702.

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Most models of quantum neural networks are optimized based on gradient descent, and like classical neural networks, gradient descent suffers from the barren plateau phenomenon, which reduces the effectiveness of optimization. Therefore, this paper establishes a new QNN model, the optimization process adopts efficient quantum particle swarm optimization, and tentatively adds a quantum activation circuit to our QNN model. Our model will inherit the superposition property of quantum and the random search property of quantum particle swarm. Simulation experiments on some classification data show that the model proposed in this paper has higher classification performance than the gradient descent-based QNN.

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He, Jianhao, Feidiao Yang, Jialin Zhang, and Lvzhou Li. "Quantum algorithm for online convex optimization." Quantum Science and Technology 7, no. 2 (March 17, 2022): 025022. http://dx.doi.org/10.1088/2058-9565/ac5919.

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Abstract We explore whether quantum advantages can be found for the zeroth-order online convex optimization (OCO) problem, which is also known as bandit convex optimization with multi-point feedback. In this setting, given access to zeroth-order oracles (that is, the loss function is accessed as a black box that returns the function value for any queried input), a player attempts to minimize a sequence of adversarially generated convex loss functions. This procedure can be described as a T round iterative game between the player and the adversary. In this paper, we present quantum algorithms for the problem and show for the first time that potential quantum advantages are possible for problems of OCO. Specifically, our contributions are as follows. (i) When the player is allowed to query zeroth-order oracles O(1) times in each round as feedback, we give a quantum algorithm that achieves O ( T ) regret without additional dependence of the dimension n, which outperforms the already known optimal classical algorithm only achieving O ( n T ) regret. Note that the regret of our quantum algorithm has achieved the lower bound of classical first-order methods. (ii) We show that for strongly convex loss functions, the quantum algorithm can achieve O(log T) regret with O(1) queries as well, which means that the quantum algorithm can achieve the same regret bound as the classical algorithms in the full information setting.

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Chen, Samuel Yen-Chi, Chih-Min Huang, Chia-Wei Hsing, Hsi-Sheng Goan, and Ying-Jer Kao. "Variational quantum reinforcement learning via evolutionary optimization." Machine Learning: Science and Technology 3, no. 1 (February 15, 2022): 015025. http://dx.doi.org/10.1088/2632-2153/ac4559.

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Abstract Recent advances in classical reinforcement learning (RL) and quantum computation point to a promising direction for performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in modern quantum devices. Here, we present two frameworks for deep quantum RL tasks using gradient-free evolutionary optimization. First, we apply the amplitude encoding scheme to the Cart-Pole problem, where we demonstrate the quantum advantage of parameter saving using amplitude encoding. Second, we propose a hybrid framework where the quantum RL agents are equipped with a hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs of dimensions exceeding the number of qubits. This allows us to perform quantum RL in the MiniGrid environment with 147-dimensional inputs. The hybrid TN-VQC architecture provides a natural way to perform efficient compression of the input dimension, enabling further quantum RL applications on noisy intermediate-scale quantum devices.

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Barkoutsos, Panagiotis Kl, Giacomo Nannicini, Anton Robert, Ivano Tavernelli, and Stefan Woerner. "Improving Variational Quantum Optimization using CVaR." Quantum 4 (April 20, 2020): 256. http://dx.doi.org/10.22331/q-2020-04-20-256.

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Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the expectation of the problem Hamiltonian for a parameterized trial quantum state. The expectation is estimated as the sample mean of a set of measurement outcomes, while the parameters of the trial state are optimized classically. This procedure is fully justified for quantum mechanical observables such as molecular energies. In the case of classical optimization problems, which yield diagonal Hamiltonians, we argue that aggregating the samples in a different way than the expected value is more natural. In this paper we propose the Conditional Value-at-Risk as an aggregation function. We empirically show -- using classical simulation as well as quantum hardware -- that this leads to faster convergence to better solutions for all combinatorial optimization problems tested in our study. We also provide analytical results to explain the observed difference in performance between different variational algorithms.

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Korolyov, Vyacheslav, and Oleksandr Khodzinskyi. "Solving Combinatorial Optimization Problems on Quantum Computers." Cybernetics and Computer Technologies, no. 2 (July 24, 2020): 5–13. http://dx.doi.org/10.34229/2707-451x.20.2.1.

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Introduction. Quantum computers provide several times faster solutions to several NP-hard combinatorial optimization problems in comparison with computing clusters. The trend of doubling the number of qubits of quantum computers every year suggests the existence of an analog of Moore's law for quantum computers, which means that soon they will also be able to get a significant acceleration of solving many applied large-scale problems. The purpose of the article is to review methods for creating algorithms of quantum computer mathematics for combinatorial optimization problems and to analyze the influence of the qubit-to-qubit coupling and connections strength on the performance of quantum data processing. Results. The article offers approaches to the classification of algorithms for solving these problems from the perspective of quantum computer mathematics. It is shown that the number and strength of connections between qubits affect the dimensionality of problems solved by algorithms of quantum computer mathematics. It is proposed to consider two approaches to calculating combinatorial optimization problems on quantum computers: universal, using quantum gates, and specialized, based on a parameterization of physical processes. Examples of constructing a half-adder for two qubits of an IBM quantum processor and an example of solving the problem of finding the maximum independent set for the IBM and D-wave quantum computers are given. Conclusions. Today, quantum computers are available online through cloud services for research and commercial use. At present, quantum processors do not have enough qubits to replace semiconductor computers in universal computing. The search for a solution to a combinatorial optimization problem is performed by achieving the minimum energy of the system of coupled qubits, on which the task is mapped, and the data are the initial conditions. Approaches to solving combinatorial optimization problems on quantum computers are considered and the results of solving the problem of finding the maximum independent set on the IBM and D-wave quantum computers are given. Keywords: quantum computer, quantum computer mathematics, qubit, maximal independent set for a graph.

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Choi, Vicky. "Different adiabatic quantum optimization algorithms." Quantum Information and Computation 11, no. 7&8 (July 2011): 638–48. http://dx.doi.org/10.26421/qic11.7-8-7.

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One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001) proposed the adiabatic quantum optimization (AQO), a paradigm that directly attacks NP-hard optimization problems. How powerful is AQO? Early on, van-Dam and Vazirani claimed that AQO failed (i.e. would take exponential time) for a family of 3SAT instances they constructed. More recently, Altshuler, et al. (Proc Natl Acad Sci USA, 107(28): 12446--12450, 2010) claimed that AQO failed also for random instances of the NP-complete Exact Cover problem. In this paper, we make clear that all these negative results are only for a specific AQO algorithm. We do so by demonstrating different AQO algorithms for the same problem for which their arguments no longer hold. Whether AQO fails or succeeds for solving the NP-complete problems (either the worst case or the average case) requires further investigation. Our AQO algorithms for Exact Cover and 3SAT are based on the polynomial reductions to the NP-complete Maximum-weight Independent Set (MIS) problem.

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Fawzi, Hamza, and Omar Fawzi. "Defining quantum divergences via convex optimization." Quantum 5 (January 26, 2021): 387. http://dx.doi.org/10.22331/q-2021-01-26-387.

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We introduce a new quantum Rényi divergenceDα#forα∈(1,∞)defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property. An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum Rényi divergence. This allows us to prove several results. First, we use it to get a converging hierarchy of upper bounds on the regularized sandwichedα-Rényi divergence between quantum channels forα>1. Second it allows us to prove a chain rule property for the sandwichedα-Rényi divergence forα>1which we use to characterize the strong converse exponent for channel discrimination. Finally it allows us to get improved bounds on quantum channel capacities.

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Xu, Yu Fa, Jie Gao, Guo Chu Chen, and Jin Shou Yu. "Quantum Particle Swarm Optimization Algorithm." Applied Mechanics and Materials 63-64 (June 2011): 106–10. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.106.

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Based on the problem of traditional particle swarm optimization (PSO) easily trapping into local optima, quantum theory is introduced into PSO to strengthen particles’ diversities and avoid the premature convergence effectively. Experimental results show that this method proposed by this paper has stronger optimal ability and better global searching capability than PSO.

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Trugenberger, C. A. "Quantum optimization for combinatorial searches." New Journal of Physics 4 (April 19, 2002): 26. http://dx.doi.org/10.1088/1367-2630/4/1/326.

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Boixo, S., G. Ortiz, and R. Somma. "Fast quantum methods for optimization." European Physical Journal Special Topics 224, no. 1 (February 2015): 35–49. http://dx.doi.org/10.1140/epjst/e2015-02341-5.

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BERMAN, GENNADY P., and ALEXANDER I. NESTEROV. "NON-HERMITIAN ADIABATIC QUANTUM OPTIMIZATION." International Journal of Quantum Information 07, no. 08 (December 2009): 1469–78. http://dx.doi.org/10.1142/s0219749909005961.

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We propose a novel non-Hermitian adiabatic quantum optimization algorithm. One of the new ideas is to use a non-Hermitian auxiliary "initial" Hamiltonian that provides an effective level repulsion for the main Hamiltonian. This effect enables us to develop an adiabatic theory which determines ground state much more efficiently than Hermitian methods.

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Liu, Peng, Shaohan Hu, Marco Pistoia, ChunFu Richard Chen, and Jay M. Gambetta. "Stochastic Optimization of Quantum Programs." Computer 52, no. 6 (June 2019): 58–67. http://dx.doi.org/10.1109/mc.2019.2909711.

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Donaldson, Laurie. "Quantum processor solves optimization problems." Materials Today 16, no. 7-8 (July 2013): 261. http://dx.doi.org/10.1016/j.mattod.2013.07.017.

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Shukla, Alok, and Prakash Vedula. "Trajectory optimization using quantum computing." Journal of Global Optimization 75, no. 1 (February 21, 2019): 199–225. http://dx.doi.org/10.1007/s10898-019-00754-5.

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Amin, Mohammad H. S., Neil G. Dickson, and Peter Smith. "Adiabatic quantum optimization with qudits." Quantum Information Processing 12, no. 4 (October 17, 2012): 1819–29. http://dx.doi.org/10.1007/s11128-012-0480-x.

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Brandt, Howard E. "Optimization problem in quantum cryptography." Journal of Optics B: Quantum and Semiclassical Optics 5, no. 6 (October 16, 2003): S557—S560. http://dx.doi.org/10.1088/1464-4266/5/6/003.

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Raychev, Nikolay. "Quantum circuit for spatial optimization." International Journal of Scientific and Engineering Research 6, no. 6 (June 25, 2015): 1365–68. http://dx.doi.org/10.14299/ijser.2015.06.004.

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Tannous, Charbel, and Jacques Langlois. "Quantum Key Distribution Protocol Optimization." Annalen der Physik 531, no. 4 (February 10, 2019): 1800334. http://dx.doi.org/10.1002/andp.201800334.

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Niroula, Pradeep. "Conquering the challenge of quantum optimization." Physics World 35, no. 2 (February 1, 2022): 25–29. http://dx.doi.org/10.1088/2058-7058/35/02/32.

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Hyped as the solution to many problems – both hard and easy – quantum-enhanced optimization is a burgeoning research field. But with untrainable circuits, “barren plateaus” and deceptive local minimas, nature itself may prevent the use of quantum solutions for hard problems, as Pradeep Niroula explains.

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CALARCO, T., M. A. CIRONE, M. COZZINI, A. NEGRETTI, A. RECATI, and E. CHARRON. "QUANTUM CONTROL THEORY FOR DECOHERENCE SUPPRESSION IN QUANTUM GATES." International Journal of Quantum Information 05, no. 01n02 (February 2007): 207–13. http://dx.doi.org/10.1142/s0219749907002645.

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We show how quantum optimal control theory can help achieve high-fidelity quantum gates in real experimental settings. We discuss several optimization methods (from iterative algorithms to optimization by interference and to impulsive control) and different physical scenarios (from optical lattices to atom chips and to Rydberg atoms).

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Truger, Felix, Martin Beisel, Johanna Barzen, Frank Leymann, and Vladimir Yussupov. "Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem." Electronics 11, no. 7 (March 25, 2022): 1033. http://dx.doi.org/10.3390/electronics11071033.

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Today’s quantum computers are limited in their capabilities, e.g., the size of executable quantum circuits. The Quantum Approximate Optimization Algorithm (QAOA) addresses these limitations and is, therefore, a promising candidate for achieving a near-term quantum advantage. Warm-starting can further improve QAOA by utilizing classically pre-computed approximations to achieve better solutions at a small circuit depth. However, warm-starting requirements often depend on the quantum algorithm and problem at hand. Warm-started QAOA (WS-QAOA) requires developers to understand how to select approach-specific hyperparameter values that tune the embedding of classically pre-computed approximations. In this paper, we address the problem of hyperparameter selection in WS-QAOA for the maximum cut problem using the classical Goemans–Williamson algorithm for pre-computations. The contributions of this work are as follows: We implement and run a set of experiments to determine how different hyperparameter settings influence the solution quality. In particular, we (i) analyze how the regularization parameter that tunes the bias of the warm-started quantum algorithm towards the pre-computed solution can be selected and optimized, (ii) compare three distinct optimization strategies, and (iii) evaluate five objective functions for the classical optimization, two of which we introduce specifically for our scenario. The experimental results provide insights on efficient selection of the regularization parameter, optimization strategy, and objective function and, thus, support developers in setting up one of the central algorithms of contemporary and near-term quantum computing.

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Amaro, David, Carlo Modica, Matthias Rosenkranz, Mattia Fiorentini, Marcello Benedetti, and Michael Lubasch. "Filtering variational quantum algorithms for combinatorial optimization." Quantum Science and Technology 7, no. 1 (January 1, 2022): 015021. http://dx.doi.org/10.1088/2058-9565/ac3e54.

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Abstract Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the filtering variational quantum eigensolver which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the quantum approximate optimization algorithm. We also demonstrate the experimental feasibility of our algorithms on a Quantinuum trapped-ion quantum processor powered by Honeywell.

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Cutugno, Massimiliano, Annarita Giani, Paul Alsing, Laura Wessing, and Austar Schnore. "Quantum Computing Approaches for Mission Covering Optimization." Algorithms 15, no. 7 (June 27, 2022): 224. http://dx.doi.org/10.3390/a15070224.

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Quantum computing has the potential to revolutionize the way hard computational problems are solved in terms of speed and accuracy. Quantum hardware is an active area of research and different hardware platforms are being developed. Quantum algorithms target each hardware implementation and bring advantages to specific applications. The focus of this paper is to compare how well quantum annealing techniques and the QAOA models constrained optimization problems. As a use case, a constrained optimization problem called mission covering optimization is used. Quantum annealing is implemented in adiabatic hardware such as D-Wave, and QAOA is implemented in gate-based hardware such as IBM. This effort provides results in terms of cost, timing, constraints held, and qubits used.

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Thakral, Shaveta, and Dipali Bansal. "Improved ant colony optimization for quantum cost reduction." Bulletin of Electrical Engineering and Informatics 9, no. 4 (August 1, 2020): 1525–32. http://dx.doi.org/10.11591/eei.v9i4.1657.

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Heuristic algorithms play a significant role in synthesize and optimization of digital circuits based on reversible logic yet suffer with multiple disadvantages for multiqubit functions like scalability, run time and memory space. Synthesis of reversible logic circuit ends up with trade off between number of gates, quantum cost, ancillary inputs and garbage outputs. Research on optimization of quantum cost seems intractable. Therefore post synthesis optimization needs to be done for reduction of quantum cost. Many researchers have proposed exact synthesis approaches in reversible logic but focussed on reduction of number of gates yet quantum cost remains undefined. The main goal of this paper is to propose improved Ant Colony Optimization (ACO) algorithm for quantum cost reduction. The research efforts reported in this paper represent a significant contribution towards synthesis and optimization of high complexity reversible function via swarm intelligence based approach. The improved ACO algorithm provides low quantum cost based toffoli synthesis of reversible logic function without long computation overhead.

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Sun, Jia Ze, Guo Hua Geng, Hao Chen, and Ming Quan Zhou. "An Improved Social Cognitive Optimization Algorithm." Applied Mechanics and Materials 427-429 (September 2013): 2580–83. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.2580.

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To improve the global convergence speed of classical social cognitive optimization (SCO) algorithm, a novel hybrid social cognitive optimization algorithm based on quantum behavior (QSCO) is proposed. In the proposed algorithm, learning agents learn in a quantum multi-dimensional space and establish a quantum delta potential well model. A quantum search process is incorporated into local searching operation so as to enhance the local searching efficiency in the neighboring areas of the feasible solutions. Simulation results on a set of benchmark problems show that the proposed algorithm has high optimization efficiency and good global performance.

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Stokes, James, Josh Izaac, Nathan Killoran, and Giuseppe Carleo. "Quantum Natural Gradient." Quantum 4 (May 25, 2020): 269. http://dx.doi.org/10.22331/q-2020-05-25-269.

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A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.

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Ganguly, Kaushik. "Quantum AI: Deep Learning optimization using Hybrid Quantum Filters." International Journal for Research in Applied Science and Engineering Technology 10, no. 9 (September 30, 2022): 1720–33. http://dx.doi.org/10.22214/ijraset.2022.46914.

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Abstract: Deep learning algorithms have shown promising results for different image processing tasks, particularly in remote sensing & image recognition. Till now many studies have been carried out on image processing, which brings a new paradigm of innovative capabilities under the umbrella of intelligent remote sensing and computer vision. Accordingly, quantum processing algorithms have proved to efficiently solve some issues that are undetectable to classical algorithms and processors. Keeping that in mind, a Quantum Convolutional Neural Network (QCNN) architecture along with Hybrid Quantum filters would be utilized supported by cloud computing infrastructures and data centers to provide a broad range of complex AI services and high data availability. This research summaries the conventional techniques of Classical and Quantum Deep Learning and it’s research progress on realworld problems in remote sensing image processing as a comparative demonstration. Last but not least, we evaluate our system by training on Street View House Numbers datasets in order to highlight the feasibility and effectiveness of using Quantum Deep Learning approach in image recognition and other similar applications. Upcoming challenges and future research areas on this spectrum are also discussed.

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Guodong Wang, Guodong Wang, Shoule Dai Shoule Dai, and Hui Zhang Hui Zhang. "Optimization of top coupling grating for mid-wave quantum well infrared photodetector." Chinese Optics Letters 10, s1 (2012): S12501–312502. http://dx.doi.org/10.3788/col201210.s12501.

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Xue, Cheng, Zhao-Yun Chen, Yu-Chun Wu, and Guo-Ping Guo. "Effects of Quantum Noise on Quantum Approximate Optimization Algorithm." Chinese Physics Letters 38, no. 3 (March 1, 2021): 030302. http://dx.doi.org/10.1088/0256-307x/38/3/030302.

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Tosatti, Giuseppe E. Santoro and Erio. "Optimization using quantum mechanics: quantum annealing through adiabatic evolution." Journal of Physics A: Mathematical and Theoretical 41, no. 20 (May 6, 2008): 209801. http://dx.doi.org/10.1088/1751-8121/41/20/209801.

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Journal articles on the topic 'Quantum optimization'

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