The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all information encoded in the calculation. Even if the technology advances fast within the next years, any use of quantum computers will be limited to short and simple tasks, serving as subroutines of more complex classical procedures. Even for these applications the resource efficiency, measured in the number of quantum computer runs, will be a key parameter. Here we suggest a general meta-optimization procedure for hybrid quantum-classical algorithms that allows finding the optimal approach with limited quantum resources. This method optimizes the usage of resources of an existing method by testing its capabilities and setting the optimal resource utilization. We demonstrate this procedure on a specific example of variational quantum algorithm used to find the ground state energy of a hydrogen molecule.

Faculty of Natural sciences and Informatics Constantine the Philosopher University Tr A Hlinku 1 949 01 Nitra Slovak Republic

Faculty of Natural Sciences Matej Bel University Tajovského 40 974 01 Banská Bystrica Slovakia

Institute of Physics of Materials Czech Academy of Sciences Žižkova 513 22 616 00 Brno Czech Republic

Institute of Physics Slovak Academy of Sciences Dúbravská cesta 9 841 04 Bratislava Slovak Republic

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Benioff P. The computer as a physical system: A microscopic quantum mechanical hamiltonian model of computers as represented by turing machines. J. Stat. Phys. 1980;22:563–591. doi: 10.1007/BF01011339. DOI

Manin Y. Computable and Uncomputable. Sovetskoye Radio; 1980.

Feynman RP. Simulating physics with computers. Int. J. Theor. Phys. 1982;21:467–488. doi: 10.1007/BF02650179. DOI

Nielsen MA, Chuang IL. Quantum Computation and Quantum Information. Cambridge University Press; 2000.

Shor PW. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 1997;26:1484–1509. doi: 10.1137/S0097539795293172. DOI

Grover, L. K. A fast quantum mechanical algorithm for database search. In Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, STOC ’96 212–219 (Association for Computing Machinery, 1996) 10.1145/237814.237866

Preskill J. Quantum computing in the NISQ era and beyond. Quantum. 2018;2:79. doi: 10.22331/q-2018-08-06-79. DOI

Cerezo M, et al. Variational quantum algorithms. Nat. Rev. Phys. 2021;3:625–644. doi: 10.1038/s42254-021-00348-9. DOI

Bharti K, et al. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 2022;94:015004. doi: 10.1103/RevModPhys.94.015004. DOI

McCaskey AJ, et al. Quantum chemistry as a benchmark for near-term quantum computers. npj Quantum Inf. 2019;5:99. doi: 10.1038/s41534-019-0209-0. DOI

McArdle S, Endo S, Aspuru-Guzik A, Benjamin SC, Yuan X. Quantum computational chemistry. Rev. Mod. Phys. 2020;92:015003. doi: 10.1103/RevModPhys.92.015003. DOI

Dunjko V, Briegel HJ. Machine learning & artificial intelligence in the quantum domain: A review of recent progress. Rep. Prog. Phys. 2018;81:074001. doi: 10.1088/1361-6633/aab406. PubMed DOI

Biamonte J, et al. Quantum machine learning. Nature. 2017;549:195–202. doi: 10.1038/nature23474. PubMed DOI

Orús R, Mugel S, Lizaso E. Quantum computing for finance: Overview and prospects. Rev. Phys. 2019;4:100028. doi: 10.1016/j.revip.2019.100028. DOI

Peruzzo A, et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 2014;5:1–7. doi: 10.1038/ncomms5213. PubMed DOI PMC

Spall JC. An overview of the simultaneous perturbation method for efficient optimization. J. Hopkins APL Tech. Dig. 1998;19:482–492.

Tilly, J. et al. The variational quantum eigensolver: A review of methods and best practices, 10.48550/ARXIV.2111.05176 (2021).

Kübler JM, Arrasmith A, Cincio L, Coles PJ. An adaptive optimizer for measurement-frugal variational algorithms. Quantum. 2020;4:263. doi: 10.22331/q-2020-05-11-263. DOI

Arrasmith, A., Cincio, L., Somma, R. D. & Coles, P. J. Operator sampling for shot-frugal optimization in variational algorithms. 10.48550/ARXIV.2004.06252 (2020).

Sweke R, et al. Stochastic gradient descent for hybrid quantum-classical optimization. Quantum. 2020;4:314. doi: 10.22331/q-2020-08-31-314. DOI

Schuld M, Bergholm V, Gogolin C, Izaac J, Killoran N. Evaluating analytic gradients on quantum hardware. Phys. Rev. A. 2019;99:032331. doi: 10.1103/PhysRevA.99.032331. DOI

Tamiya S, Yamasaki H. Stochastic gradient line bayesian optimization for efficient noise-robust optimization of parameterized quantum circuits. npj Quantum Inf. 2022;8:90. doi: 10.1038/s41534-022-00592-6. DOI

Miháliková I, et al. The cost of improving the precision of the variational quantum eigensolver for quantum chemistry. Nanomaterials. 2022;12:243. doi: 10.3390/nano12020243. PubMed DOI PMC

Yen T-C, Izmaylov AF. Cartan subalgebra approach to efficient measurements of quantum observables. PRX Quantum. 2021;2:040320. doi: 10.1103/PRXQuantum.2.040320. DOI

Yen, T.-C., Ganeshram, A. & Izmaylov, A. F. Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates. arXiv preprint arXiv:2201.01471 (2022). PubMed PMC

Gonthier JF, et al. Measurements as a roadblock to near-term practical quantum advantage in chemistry: Resource analysis. Phys. Rev. Res. 2022;4:033154. doi: 10.1103/PhysRevResearch.4.033154. DOI