Quantum variational optimization: The role of entanglement and problem hardness
Open accessAbstract
The authors investigate the ability of variational quantum algorithms to solve a combinatorial optimization problem, and demonstrate an advantage when the entanglement structure in the algorithm is chosen to mimic the structure of the problem. Notably, they find that when a certain cost function is used the depth of variational circuits is only moderately relevant, which suggests that new classical methods using product states may outperform existing quantum architectures.
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Investigations on the impact of different classical optimizers for parameter optimization in general advocate for gradient-free global optimizers when dealing with real quantum hardware.
“Investigations on the impact of different classical optimizers for parameter optimization in general advocate for gradient-free global optimizers when dealing with real quantum hardware [37, 47, 100, 121].”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [37]
The choice-of-classical-optimizer section (p. 6) finds that gradient-free methods perform well with stochastic, finite-measurement evaluations and uses SPSA in that setting. But the benchmarks used simulations rather than real hardware (p. 5), and the paper does not establish that the recommended methods are global optimizers. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe benefits of using RQAOA, CVar, and machine learning have been empirically validated in dedicated studies.
“The benefits of using RQAOA [22], CVar [37, 78], and machine learning [33] have been empirically validated in dedicated studies.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [37]
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“2-10 with 95% confidence intervals, which are obtained by resampling the output data with the bootstrap method [51,52].”
MethodQuantum Computing in the NISQ era and beyond
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“In the last years, quantum variational optimization [1,2] has emerged as a framework that exploits the computational power of near-term intermediate scale quantum circuits [3].”
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“In our study of the variational method we have tested seven different optimizers: modified Powell’s conjugate direction method [39], sequential least squares programming (SLSQP) [40], Broyden–Fletcher–Goldfarb–Shanno (BFGS) [41–44] and its limited-memory version (L-BFGS-B) [45], the simultaneous perturbation stochastic…”
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MethodA variational eigenvalue solver on a photonic quantum processor
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“In our research we address these questions with a focus on the Variational Quantum Eigensolver (VQE) method [32].”
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“As explained above, this also requires us to use the SPSA classical optimizer.”
MethodInfluentialAn Introduction to the Bootstrap
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The theory of variational hybrid quantum-classical algorithms
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“Entangled states We start by considering a set of entangled variational wavefunctions as originally proposed for the VQE method [2],”
BackgroundMethodA Quantum Approximate Optimization Algorithm
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“This result highlights the need to investigate further the existing algorithms for quantum optimization, including other alternatives such as QAOA [1].”
BackgroundMethodOn the coherence of expected shortfall
Acerbi, C., & Tasche, D. (2002) · Journal of Banking & Finance · doi:10.1016/s0378-4266(02)00283-2 · Cited by 1,632 · see citing works
Powell, M. J. D. (1994) · Advances in Optimization and Numerical Analysis · doi:10.1007/978-94-015-8330-5_4 · Cited by 1,369 · cited 1× · see citing works
“In our study of the variational method we have tested seven different optimizers: modified Powell’s conjugate direction method [39], Sequential Least Squares Programming (SLSQP) [40], Broyden–Fletcher–Goldfarb–Shanno (BFGS) [41–44] and its limited-memory version (L-BFGS-B) [45], Simultaneous Perturbation Stochastic Ap…”
MethodAn adaptive variational algorithm for exact molecular simulations on a quantum computer
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The convergence of a class of double-rank minimization algorithms
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Noise-induced barren plateaus in variational quantum algorithms
Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., & Coles, P. J. (2021) · Nature Communications · doi:10.1038/s41467-021-27045-6 · Cited by 773 · cited 1× · see citing works
“Hence, we cannot attribute the effect to vanishing gradients or barren plateaus [53,54], but to an intrinsic limitation of the algorithm.”
BackgroundQuantum optimization using variational algorithms on near-term quantum devices
Moll, N., Barkoutsos, P., Bishop, L. S., Chow, J. M., Cross, A., Egger, D. J., Filipp, S., Fuhrer, A., Gambetta, J. M., Ganzhorn, M., et al. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aab822 · Cited by 744 · cited 1× · see citing works
“In quantum variational algorithms [2, 35], the quantum computer is used to prepare and characterize a complex wavefunction, defined in terms of parameterized quantum operations”
MethodConnecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus
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“This circuit should be complete, and efficiently sample the Hilbert space, but it also should be as simple as possible, with the minimal number of entangling operations and quantum gates, to allow their use in NISQ architectures [19, 20].”
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“QUBO problems have been extensively studied in the literature [33,34].”
BackgroundAdvances in Optimization and Numerical Analysis
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“In our study of the variational method we have tested seven different optimizers: modified Powell’s conjugate direction method [39], sequential least squares programming (SLSQP) [40], Broyden–Fletcher–Goldfarb–Shanno (BFGS) [41–44] and its limited-memory version (LBFGS-B) [45], the simultaneous perturbation stochastic…”
MethodQubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer
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Improving Variational Quantum Optimization using CVaR
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Accelerated Variational Quantum Eigensolver
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Noisy intermediate-scale quantum (NISQ) algorithms
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Solving Vehicle Routing Problem Using Quantum Approximate Optimization Algorithm
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Performance of hybrid quantum-classical variational heuristics for combinatorial optimization
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Benchmarking the quantum approximate optimization algorithm
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Capacity and Quantum Geometry of Parametrized Quantum Circuits
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A unified modeling and solution framework for combinatorial optimization problems
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“QUBO problems have been extensively studied in the literature [33,34].”
BackgroundBenchmarking the quantum approximate optimization algorithm
Willsch, M., Willsch, D., Jin, F., Raedt, H. A. D., & Michielsen, K. F. L. (2020) · RWTH Publications (RWTH Aachen) · Cited by 109 · see citing works
Hybrid quantum-classical algorithms for approximate graph coloring
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“These questions also tie intimately to other aspects, such as the definition of the cost function [22, 23], and the hybrid quantum-classical algorithms which we use to optimize the variational state [24–31].”
MethodApplying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem
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How "Quantum" is the D-Wave Machine?
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“We can regard this family of states as a new type of classical algorithms, much like the spin-vector quantum Monte Carlo methods that have been used to benchmark quantum annealers [37, 38].”
MethodBengtsson, A., Vikstål, P., Warren, C., Svensson, M., Gu, X. Q., Kockum, A. F., Krantz, P., Križan, C., Shiri, D., Svensson, I.-M., et al. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.14.034010 · Cited by 81 · see citing works
HOW TO MAKE THE QUANTUM ADIABATIC ALGORITHM FAIL
FARHI, E., GOLDSTONE, J., GUTMANN, S., & NAGAJ, D. (2008) · International Journal of Quantum Information · doi:10.1142/s021974990800358x · Cited by 81 · see citing works
Classical signature of quantum annealing
Smolin, J. A., & Smith, G. (2014) · Frontiers in Physics · doi:10.3389/fphy.2014.00052 · Cited by 79 · cited 2× · see citing works
“Indeed, using product states, with CVaR or pure VQE, can be regarded as a new classical optimization algorithm, similar to other methods proposed in the last decade [37,38].”
MethodLayer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
Liu, X., Angone, A., Shaydulin, R., Safro, I., Alexeev, Y., & Cincio, L. (2022) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2021.3140190 · Cited by 78 · cited 1× · see citing works
“These questions also tie intimately to other aspects, such as the definition of the cost function [22, 23], and the hybrid quantum-classical algorithms which we use to optimize the variational state [24–31].”
MethodAdaptive pruning-based optimization of parameterized quantum circuits
Sim, S., Romero, J., Gonthier, J. F., & Kunitsa, A. A. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abe107 · Cited by 66 · see citing works
Finding spin glass ground states using quantum walks
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Quantum Approximation for Wireless Scheduling
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Finding spin glass ground states using quantum walks
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Lower bounds on circuit depth of the quantum approximate optimization algorithm
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Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing
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Max-independent set and the quantum alternating operator ansatz
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Addressing hard classical problems with Adiabatically Assisted Variational Quantum Eigensolvers
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Hybrid quantum–classical optimization with cardinality constraints and applications to finance
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Use Cases of Quantum Optimization for Finance
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Cited by
Sorted by citations
Filtering variational quantum algorithms for combinatorial optimization
Amaro, D., Modica, C., Rosenkranz, M., Fiorentini, M., Benedetti, M., & Lubasch, M. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac3e54 · Cited by 123 · see citing works
“F-VQE can readily be combined with the Conditional Value-at-Risk cost function [16, 44, 45] to provide new filtering operators with additional capabilities.”
BackgroundChallenges of variational quantum optimization with measurement shot noise
Scriva, G., Astrakhantsev, N., Pilati, S., & Mazzola, G. (2024) · Physical Review A · doi:10.1103/physreva.109.032408 · Cited by 49 · see citing works
Ajagekar, A., & You, F. (2024) · Advances in Applied Energy · doi:10.1016/j.adapen.2024.100179 · Cited by 37 · see citing works
Ajagekar, A., & You, F. (2024) · Applied Energy · doi:10.1016/j.apenergy.2024.123244 · Cited by 34 · see citing works
Constructing Optimal Bushy Join Trees by Solving QUBO Problems on Quantum Hardware and Simulators
Nayak, N., Rehfeld, J., Winker, T., Warnke, B., Çalıkyılmaz, U., & Groppe, S. (2023) · International Workshop on Big Data in Emergent Distributed Environments (BiDEDE) · doi:10.1145/3579142.3594298 · Cited by 28 · see citing works
“…the JOO problem as quadratic unconstrained binary optimization (QUBO) problem, which can be solved on quantum annealers [23] and gate-based quantum computers using approaches like the variational quantum eigensolver (VQE) [9] and the quantum approximation optimization algorithm (QAOA) [15].”
MethodCalibrating the role of entanglement in variational quantum circuits
Nakhl, A. C., Quella, T., & Usman, M. (2024) · Physical Review A · doi:10.1103/physreva.109.032413 · Cited by 22 · see citing works
Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study
Gemeinhardt, F., Garmendia, A., Wimmer, M., Weder, B., & Leymann, F. (2024) · ACM Computing Surveys · doi:10.1145/3620668 · Cited by 22 · see citing works
“Investigations on the impact of different classical optimizers for parameter optimization in general advocate for gradient-free global optimizers when dealing with real quantum hardware [37, 47, 100, 121].”
BackgroundMethodPractical Verification of Quantum Properties in Quantum-Approximate-Optimization Runs
Alam, M. S., Wudarski, F., Reagor, M. J., Sud, J., Grabbe, S. R., Wang, Z., Hodson, M. J., Lott, P. A., Rieffel, E. G., & Venturelli, D. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.024026 · Cited by 19 · see citing works
Evaluation of Parameterized Quantum Circuits With Cross-Resonance Pulse-Driven Entanglers
Ibrahim, M. M. A., Mohammadbagherpoor, H., Rios, C., Bronn, N. T., & Byrd, G. T. (2022) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2022.3231124 · Cited by 19 · see citing works
Leonidas, I. D., Dukakis, A., Tan, B. Y. L., & Angelakis, D. G. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202300309 · Cited by 24 · see citing works
Díez-Valle, P., Luis-Hita, J., Hernández-Santana, S., Martínez-García, F., Díaz-Fernández, Á., Andrés, E., García‐Ripoll, J. J., Sánchez-Martínez, E., & Porras, D. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace474 · Cited by 15 · see citing works
Self-citationSolving constrained optimization problems via the variational quantum eigensolver with constraints
Le, T. V., & Kekatos, V. (2024) · Physical Review A · doi:10.1103/physreva.110.022430 · Cited by 15 · see citing works
Mixer-phaser Ansätze for quantum optimization with hard constraints
LaRose, R., Rieffel, E. G., & Venturelli, D. (2022) · Quantum Machine Intelligence · doi:10.1007/s42484-022-00069-x · Cited by 14 · see citing works
“Metrics that are more focused on the high-quality solutions portion of the probability, such as our (11), or the Conditional Value at Risk (CVaR) [21, 22] or Gibbs averages [23], are suspected to have some desirable “trainability” properties to guide parameter setting, as opposed to”
BackgroundThe Role of Entanglement in Quantum-Relaxation Based Optimization Algorithms
Teramoto, K., Raymond, R., & Imai, H. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00068 · Cited by 12 · see citing works
“compatible, linear, and random are used like the previous research on VQE [7].”
BackgroundMethodResultLow-depth Clifford circuits approximately solve MaxCut
Muñoz-Arias, M. H., Kourtis, S., & Blais, A. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023294 · Cited by 12 · see citing works
“S In contrast, the QAOA solu-tion unitaries show E [ ] > 0 with a tendency towards the typical value, log(4 − N ), with increasing depth, in agreement with previous works using other indicators [84–86].”
ResultStochastic optimization algorithms for quantum applications
Gidi, J. A., Candia, B., Muñoz-Moller, A. D., Rojas, A. J., Pereira, L., Muñoz, M., Zambrano, L., & Delgado, A. (2023) · Physical Review A · doi:10.1103/physreva.108.032409 · Cited by 11 · see citing works
“SPSA has been successfully implemented in several experimental platforms and is one of the standards methods for training variational quantum eigensolvers (VQEs) [63–67], quantum neural networks (QNNs) [68–70], and quantum tomography [17, 18, 71].”
MethodKookani, A., Mafi, Y., Kazemikhah, P., Aghababa, H., Fouladi, K., & Barati, M. (2024) · Quantum Machine Intelligence · doi:10.1007/s42484-024-00183-y · Cited by 10 · see citing works
Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits
Ding, Z., Ko, T., Yao, J., Lin, L., & Li, X. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033029 · Cited by 9 · see citing works
“…such as finance, logistics, and machine learning, etc. Recognized as one prominent optimization model in quantum computing, QUBO consolidates a wide range of combinatorial optimization problems [20, 35, 4, 28] and translates them into identifying the ground state of classical Ising models [42].”
BackgroundGenuine multipartite entanglement in quantum optimization
Santra, G. C., Roy, S. S., Egger, D. J., & Hauke, P. (2025) · Physical Review A · doi:10.1103/physreva.111.022434 · Cited by 8 · see citing works
“The subtle role of bipartite entanglement is also observed in the variational quantum eigensolver (VQE), where distributing the entangling gates according to the problem’s topology increases success rates and reduces runtime [42].”
Shirai, T., & Togawa, N. (2024) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2024.3376721 · Cited by 9 · see citing works
“It relies on an optimization algorithm such as the gradient descent method or the Powell method to construct a progressively optimized sequence of variational parameters [22].”
MethodTsukayama, D., Shirakashi, J., Shibuya, T., & Imai, H. (2025) · AIP Advances · doi:10.1063/5.0236028 · Cited by 8 · see citing works
Exploring the neighborhood of 1-layer QAOA with instantaneous quantum polynomial circuits
Leontica, S., & Amaro, D. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013071 · Cited by 8 · see citing works
“This is only one example of a larger class of variational quantum optimization algorithms, which attempt to produce good solutions to combinatorial optimization problems by sampling a parameterized quantum circuit [4–8].”
BackgroundZhang, S., Zhou, Y., Qin, Z., Li, R., Du, C., Xiao, Z., & Zhang, Y. (2025) · Physical Review A · doi:10.1103/physreva.111.052403 · Cited by 6 · see citing works
“On the one hand, PQCs with high entanglement were required to capture non-trivial quantum correlations or ground states of interested quantum systems [37–40].”
Single entanglement connection architecture between multi-layer bipartite hardware efficient ansatz
Zhang, S., Qin, Z., Yang, Z., Li, R., Du, C., & Xiao, Z. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad64fb · Cited by 6 · see citing works
Accelerating feedback-based quantum algorithms through time rescaling
Rattighieri, L. A. M., Pexe, G. E. L., Bernardo, B. D. L., & Fanchini, F. F. (2025) · Physical Review A · doi:10.1103/qc91-5mj2 · Cited by 5 · see citing works
Sobhani, M., Chai, Y., Hartung, T., & Jansen, K. (2025) · Physical Review A · doi:10.1103/physreva.111.042413 · Cited by 5 · see citing works
“We refer to [31] for an in-depth explanation of the COBYLA optimizer.”
Non-Hermitian ground-state-searching algorithm enhanced by a variational toolbox
Chen, Y., Zhang, S., Hsieh, C., & Zhang, S. (2023) · Physical Review A · doi:10.1103/physreva.107.042418 · Cited by 5 · see citing works
The Questionable Influence of Entanglement in Quantum Optimisation Algorithms
Rohe, T., Schuman, D., Nüβlein, J., Sünkel, L., Stein, J., & Linnhoff–Popien, C. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00176 · Cited by 4 · see citing works
“…as it increases the ex-pressibility of the circuit and the non-locality of information in it, there seems to be a number of entangling layers l s at which the improvement in solution accuracy or convergence speed that can be gained by increasing entanglement “saturates” [4], [5], [15], [29], [30].”
InfluentialCrosstalk-Based Parameterized Quantum Circuit Approximation
Ibrahim, M. M. A., Bronn, N. T., & Byrd, G. T. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00014 · Cited by 4 · see citing works
“As previous work [46]–[49] states, different applications might require different levels of entanglement.”
BackgroundMultilingual multi-task quantum transfer learning
Buonaiuto, G., Guarasci, R., Pietro, G. D., & Esposito, M. (2025) · Quantum Machine Intelligence · doi:10.1007/s42484-025-00260-w · Cited by 3 · see citing works
Information scrambling and entanglement in quantum approximate optimization algorithm circuits
Qian, C., Zhuang, W.-F., Guo, R.-C., Hu, M., & Liu, D. E. (2024) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-023-04801-9 · Cited by 3 · see citing works
“Our aim is to find some correlation between complexity of the problems and tri-partite information.”
Shallow quantum circuits are robust hunters for quantum many-body scars
Cenedese, G., Bondani, M., Andreanov, A., Carrega, M., Benenti, G., & Rosa, D. (2025) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-025-06461-3 · Cited by 3 · see citing works
“At the same time, it has been argued that the resulting architecture is still able to show a quantum advantage over state-of-the-art implementations using purely classical algorithms [8]; though this last statement has been heavily debated [9, 10].”
Markazi, N., & Mirza, B. (2025) · Scientific Reports · doi:10.1038/s41598-025-22950-y · Cited by 3 · see citing works
“This choice is motivated by the fact that a linear entanglement strategy is both hardware-efficient and sufficiently expressive for our purposes, while also reducing circuit depth and avoiding unnecessary entanglement 30,31 .”
Alonso, M., Martínez, R., Díez-Valle, P., Garbayo, A., García‐Santiago, X., & Gil, G. B. (2025) · IEEE Access · doi:10.1109/access.2025.3578780 · Cited by 2 · see citing works
Self-citationMa, Q., Ma, Z., & Gao, M. Y. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad3710 · Cited by 1 · see citing works
“The difference in the success rates between the WPE and the SK model may be caused by their diverse distribution of the Hamming distance between excited states and the ground state [6, 7].”
BackgroundCVaR-Based Variational Quantum Optimization for User Association in Handoff-Aware Vehicular Networks
Yan, Z., Zhou, H., Pei, J., Kaushik, A., Tabassum, H., & Wang, P. (2025) · International Conference on Communications · doi:10.1109/icc52391.2025.11161596 · Cited by 1 · see citing works
“Variational quantum eigensolver (VQE) aims to find the minimum eigenvalue λ min and corresponding Hamiltonian H to solve the corresponding QUBO problem [15] in terms of parametrized quantum operations in Section IV-A.”
InfluentialChai, Y., Jansen, K., Kühn, S., Schwägerl, T., & Stollenwerk, T. (2025) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-025-00452-0 · Cited by 1 · see citing works
“For combinatorial optimization problems, the conditional value at risk (CVaR) [16] has been proposed as a cost function for the VQE, and it was been shown to significantly enhance VQE’s performance [5, 14, 17].”
Qubit‐Efficient Quantum Local Search for Combinatorial Optimization
Podobrii, M., Kuzmin, V., Voloshinov, V., Veshchezerova, M., & Perelshtein, M. R. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.202500438 · Cited by 1 · see citing works
“This limit is similar to algorithms that use the so-called complete encoding [ 8 ], such as VQE [ 14, 15 ] and QAOA [ 16, 17 ], where the number of qubits is equal to the number of classical variables.”
Modern Approaches to Topological Quantum Error Correction
Parrado-Rodríguez, P. (2022) · doi:10.23889/suthesis.60302
A design method for efficient variational quantum models based on specific Pauli axis
Li, B., Li, T., & Li, F. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04127-6
“…the use of quantum gates on NISQ devices introduces noise, so the circuit should be designed in such a way that it can efficiently sample the Hilbert space and minimize the quantum resources needed to search for the optimal solution so that it can operate efficiently on NISQ devices [22–26].”
Equality-Constrained Quadratic Programming with Quantum Computing
Gubaev, T., & Li, P. (2025) · Lecture notes in networks and systems · doi:10.1007/978-3-031-92602-0_7
Adiabatic dynamics of entanglement
Gabbassov, E., & Kempf, A. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/ae0364
Geometric and resource-theoretic characterization of nonstabilizerness in quantum algorithms
Krüger, T., & Mauerer, W. (2026) · Physical Review A · doi:10.1103/1f5p-rhy4
Experimental demonstration of entanglement forging for solving Max-Cut problem
Wang, T., Wu, Z., 陈, Y. 昱. C., Hou, Y., Li, Z., & Peng, X. (2026) · Physical Review Research · doi:10.1103/kk9v-5jk8
Rohe, T., Baumann, M., Ruiloba, F. H., Altmann, P., Stenzel, G., & Linnhoff-Popien, C. (2026) · 2026 IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw72780.2026.00014 · Cited by 1 · see citing works
“D ´ ıez-Valle et al. [11] investigated the relationship between entanglement structure and problem topology.”
Entanglement in the quantum volunteer's dilemma
Anonymous, & Koh, D. E. (2026) · Physical Review A · doi:10.1103/2lb4-m4bg
- Authors
- Díez-Valle, P., Porras, D., & García-Ripoll, J. J.
- Affiliations
- Consejo Superior de Investigaciones Científicas (ES)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2021-12-16
- Volume
- 104
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W3140392037
- Cited by
- 47
- References
- 62
- Citations by year
- 2026: 5 · 2025: 13 · 2024: 15 · 2023: 9 · 2022: 4 · 2021: 1
- FWCI
- 2.56
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Federación Española de Enfermedades Raras (S2018/TCS-4342, PGC2018-094792-B-I00)
- Consejo Superior de Investigaciones Científicas (PT-001)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- variational quantum algorithms, entanglement, combinatorial optimization, problem difficulty, entanglement structure, cost function design, product states, quantum advantage
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