Variational quantum eigenvalue solver algorithm utilizing bridge-inspired quantum circuits and a gradient filter module. (English) Zbl 07833775
Summary: The complexity of theoretical simulation for drug molecule synthesis increases exponentially with the growth in system dimensions, posing a challenging task for precise solutions. Currently, the quantum algorithm capable of accurately simulating chemical molecule properties in the era of Noisy Intermediate-Scale Quantum (NISQ) devices is the Variational Quantum Eigensolver (VQE) algorithm. This paper introduces a variational quantum eigensolver based on the bridge-inspired quantum circuits and gradient filter module (BG), using Unitary Coupled Cluster Singles and Doubles (UCCSD) as the foundation (BG-VQE). The primary contributions are as follows: (1) The design of bridge rules among Hamiltonian quantum terms and rules for reordering Hamiltonian quantum terms based on similarity. By constructing a B-UCCSD ansatz according to the bridge rules and the new Hamiltonian pool, the quantum gate count and circuit depth are reduced without compromising the representative capacity of the original UCCSD ansatz; (2) The design of a variational parameter filtering module based on gradient values, which efficiently eliminates ineffective variational parameters based on their gradients. This reduction in the parameter counts of the B-UCCSD ansatz, at the cost of minimal precision loss, accelerates the calculation. Furthermore, we validate the transferability of the strategies proposed in this paper by empowering ADAPT-VQE with the BG strategy. Experimental calculations of ground state energies for H2, H3, H4, and H6 molecules were conducted using BG-VQE. By comparing the results with the UCCSD-VQE, ADAPT-VQE and BG-ADAPT-VQE, the effectiveness and superiority of BG-VQE are demonstrated. Furthermore, by performing BG-VQE calculations with different Trotter decomposition slice numbers, we demonstrate the feasibility of BG-VQE in computing the ground-state energies of HeH+, \(\mathrm{BeH}_2\), and \(\mathrm{H_2O}\) molecules. The proposed approach won the championship in the Quantum Biochemical Engineering track of the 2nd CCF Origin Pilot Cup Quantum Computing Challenge in the professional group.
MSC:
| 81-08 | Computational methods for problems pertaining to quantum theory |
| 81-04 | Software, source code, etc. for problems pertaining to quantum theory |
| 81P65 | Quantum gates |
| 81P68 | Quantum computation |
| 81V55 | Molecular physics |
| 82M37 | Computational molecular dynamics in statistical mechanics |
References:
| [1] | Preskill, J., Quantum computing in the NISQ era and beyond, Quantum, 2, 79, 2018 |
| [2] | Brooks, M., Beyond quantum supremacy: the hunt for useful quantum computers, Nature, 574, 7776, 19, 2019 |
| [3] | Arute, F., Quantum supremacy using a programmable superconducting processor, Nature, 574, 7779, 505, 2019 |
| [4] | Zhong, H., Quantum computational advantage using photons, Science, 370, 6523, 1460, 2020, (1979) |
| [5] | Wu, Y., Strong quantum computational advantage using a superconducting quantum processor, Phys. Rev. Lett., 127, 18, Article 180501 pp., 2021 |
| [6] | Madsen, L. S., Quantum computational advantage with a programmable photonic processor, Nature, 606, 7912, 75, 2022 |
| [7] | Brown, K. L., Using quantum computers for quantum simulation, Entropy, 12, 11, 2268, 2010 · Zbl 1229.81062 |
| [8] | Singh, J., Contemporary quantum computing use cases: taxonomy, review and challenges, Arch. Comput. Method E, 30, 1, 615, 2023 |
| [9] | Huggins, W. J.; McClean, J. R.; Rubin, N. C., Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers, NPJ Quantum Inf., 7, 1, 23, 2021 |
| [10] | Bravyi, S., The future of quantum computing with superconducting qubits, J. Appl. Phys., 132, Article 160902 pp., 2022 |
| [11] | Asano, M., A model of differentiation in quantum bioinformatics, Prog. Biophys. Mol. Bio., 130, 88, 2017 |
| [12] | Cheng, H., Application of quantum computing to biochemical systems: a look to the future, Front. Chem., 8, Article 587143 pp., 2020 |
| [13] | Reiher, M., Elucidating reaction mechanisms on quantum computers, P. Natl. Acad. Sci., 114, 29, 7555, 2017 |
| [14] | Peruzzo, A., A variational eigenvalue solver on a photonic quantum processor, Nat. Commun., 5, 1, 4213, 2014 |
| [15] | Cao, Y., Quantum chemistry in the age of quantum computing, Chem. Rev., 119, 19, 10856, 2019 |
| [16] | McArdle, S.; Endo, S.; Aspuru-Guzik, A.; Benjamin, S. C.; Yuan, X., Quantum computational chemistry, Rev. Mod. Phys., 92, 1, Article 015003 pp., 2020 |
| [17] | Bauer, B., Quantum algorithms for quantum chemistry and quantum materials science, Chem. Rev., 120, 22, 12685, 2020 |
| [18] | Weber, M.; Anand, A.; Cervera-Lierta, A.; Kottmann, J. S.; Kyaw, T. H.; Li, B.; Aspuru-Guzik, A.; Zhang, C.; Zhao, Z., Toward reliability in the NISQ era: robust interval guarantee for quantum measurements on approximate states, Phys. Rev. Res., 4, 3, Article 033217 pp., 2022 |
| [19] | Feng, Q. K., Recent progress and future prospects on all-organic polymer dielectrics for energy storage capacitors, Chem. Rev., 122, 3, 3820, 2021 |
| [20] | Tilly, J.; Jones, G.; Chen, H.; Wossnig, L.; Grant, E., Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver, Phys. Rev. A, 102, 6, Article 062425 pp., 2020 |
| [21] | Jones, T.; Endo, S.; McArdle, S.; Yuan, X.; Benjamin, S. C., Variational quantum algorithms for discovering hamiltonian spectra, Phys. Rev. A, 99, 6, Article 062304 pp., 2019 |
| [22] | Kuroiwa, K.; Yuya, O., Penalty methods for a variational quantum eigensolver, Phys. Rev. Res., 3, 1, Article 013197 pp., 2021 |
| [23] | Wen, J., Variational quantum packaged deflation for arbitrary excited states, Quantum Eng., 3, 4, e80, 2021 |
| [24] | Higgott, O.; Wang, D.; Brierley, S., Variational quantum computation of excited states, Quantum, 3, 156, 2019 |
| [25] | McClean, J. R.; Kimchi-Schwartz, M. E.; Carter, J.; de Jong, W. A., Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states, Phys. Rev. A, 95, 4, Article 042308 pp., 2017 |
| [26] | Kottmann, J., A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers, Chem. Sci., 12, 10, 3497, 2021 |
| [27] | Ollitrault, P. J.; Kandala, A.; Chen, C. F.; Barkoutsos, P. K.; Mezzacapo, A.; Pistoia, M.; Sheldon, S.; Woerner, S.; Gambetta, J. M.; Tavernelli, I., Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor, Phys. Rev. Res., 2, 4, Article 043140 pp., 2020 |
| [28] | Xie, Y., Construction of vibronic diabatic hamiltonian for excited-state electron and energy transfer processes, J. Phys. Chem. A, 121, 50, 9567, 2017 |
| [29] | Deglmann, P.; Schäfer, A.; Lennartz, C., Application of quantum calculations in the chemical industry-an overview, Int. J. Quantum Chem., 115, 3, 107, 2014 |
| [30] | Williams-Noonan, B. J., Free energy methods in drug design: prospects of ‘‘alchemical perturbation’’ in medicinal chemistry, J. Med. Chem., 61, 3, 638, 2017 |
| [31] | Heifetz, A., Quantum Mechanics in Drug Discovery, 2020, Humana Press: Humana Press New York |
| [32] | Continentino, M., Key Methods and Concepts in Condensed Matter Physics, 2021, IOP Publishing · Zbl 1517.82002 |
| [33] | Ven, A. V.; Deng, Z.; Banerjee, S.; Ong, S. P., Rechargeable Alkali-ion battery materials: theory and computation, Chem. Rev., 120, 14, 6977, 2020 |
| [34] | Cao, Y.; Romero, J.; Aspuru-Guzik, A., Potential of quantum computing for drug discovery, IBM J. Res. Dev., 62, 6, 1, 2018, 6 |
| [35] | Blunt, N. S., Perspective on the current state-of-the-art of quantum computing for drug discovery applications, J. Chem. Theory Comput., 18, 12, 7001, 2022 |
| [36] | Lordi, V.; Nichol, J. M., Advances and opportunities in materials science for scalable quantum computing, MRS Bull, 46, 589, 2021 |
| [37] | Georgescu, I. . M., Quantum simulation, Rev. Mod. Phys., 86, 1, 153, 2014 |
| [38] | Magann, A. B.; Arenz, C.; Grace, M. D.; Ho, T. S.; Kosut, R. L.; McClean, J. R.; Rabitz, H. A.; Sarovar, M., From pulses to circuits and back again: a quantum optimal control perspective on variational quantum algorithms, PRX Quantum, 2, 1, Article 010101 pp., 2021 |
| [39] | Anselmetti, G. L.R., Local, expressive, quantum-number-preserving VQE ansätze for fermionic systems, New J. Phys., 23, 11, Article 113010 pp., 2021 |
| [40] | Pavošević, F.; Ivano, T.; Angel, R., Spin-flip unitary coupled cluster method: toward accurate description of strong electron correlation on quantum computers, J. Phys. Chem. Lett., 14, 35, 7876, 2023 |
| [41] | Choquette, A.; Di Paolo, A.; Barkoutsos, P. K.; Sénéchal, D.; Tavernelli, I.; Blais, A., Quantum-optimal-control-inspired ansatz for variational quantum algorithms, Phys. Rev. Res., 3, 2, Article 023092 pp., 2021 |
| [42] | Grimsley, H. R., Is the trotterized UCCSD ansatz chemically well-defined?, J. Chem. Theory Comput., 16, 1, 2019, 1 |
| [43] | B. O’Gorman, et al., Generalized swap networks for near-term quantum computing, https://doi.org/10.48550/arXiv.1905.05118, (2019), arXiv:1905.05118. |
| [44] | Nielsen, M. A., Quantum Computation and Quantum Information, 2010, Cambridge university press · Zbl 1288.81001 |
| [45] | Sokolov, I. O., Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: can quantum algorithms outperform their classical equivalents?, J. Chem. Phys., 152, 12, Article 124107 pp., 2020 |
| [46] | Greene-Diniz, G.; Ramo, D. M., Generalized unitary coupled cluster excitations for multireference molecular states optimized by the variational quantum eigensolver, Int. J. Quantum Chem., 121, 4, e26352, 2020 |
| [47] | Evangelista, F. A.; Chan, G. K.; Scuseria, G. E., Exact parameterization of fermionic wave functions via unitary coupled cluster theory, J. Chem. Phys., 151, 24, Article 244112 pp., 2019 |
| [48] | Bartlett, R. J.; Kucharski, S. A.; Noga, J., Alternative coupled-cluster ansätze II. The unitary coupled-cluster method, Chem. Phys. Lett., 155, 1, 133, 1989 |
| [49] | Taube, A. G.; Bartlett, R. J., New perspectives on unitary coupled-cluster theory, Int. J. Quantum Chem., 106, 15, 3393, 2006 |
| [50] | Filip, M. A.; Thom, A. J.W., A stochastic approach to unitary coupled cluster, J. Chem. Phys., 153, 21, Article 214106 pp., 2020 |
| [51] | Mehendale, S. G.; Peng, B.; Govind, N.; Alexeev, Y., Exploring parameter redundancy in the unitary coupled-cluster ansätze for hybrid variational quantum computing, J. Phys. Chem. A, 127, 20, 4526, 2023 |
| [52] | Sugisaki, K., Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: a case study of the C 2v quasi-reaction pathway of beryllium insertion into a H 2 molecule, Phys. Chem. Chem. Phys., 24, 14, 8439, 2022 |
| [53] | Lee, J.; Huggins, W. J.; Head-Gordon, M., Generalized unitary coupled cluster wave functions for quantum computation, J. Chem. Theory Comput., 15, 1, 311, 2018 |
| [54] | Grimsley, H. R.; Economou, S. E.; Barnes, E.; Mayhall, N. J., An adaptive variational algorithm for exact molecular simulations on a quantum computer, Nat. Commun., 10, 1, 3007, 2019 |
| [55] | Claudino, D.; Wright, J.; McCaskey, A. J.; Humble, T. S., Benchmarking adaptive variational quantum eigensolvers, Front. Chem., 8, Article 606863 pp., 2020 |
| [56] | Kökcü, E., Algebraic compression of quantum circuits for Hamiltonian evolution, Phys. Rev. A, 105, 3, Article 032420 pp., 2022 |
| [57] | Peng, B., Quantum time dynamics employing the Yang-Baxter equation for circuit compression, Phys. Rev. A, 106, 1, Article 012412 pp., 2022 |
| [58] | Wecker, D.; Hastings, M. B.; Troyer, M., Progress towards practical quantum variational algorithms, Phys. Rev. A, 92, 4, Article 042303 pp., 2015 |
| [59] | Romero, J., Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz, Quantum Sci. Technol., 4.1, Article 014008 pp., 2018 |
| [60] | Jordan, P.; Wigner, E. P., Über Das Paulische äquivalenzverbot, 1993, Springer Berlin Heidelberg · JFM 54.0983.03 |
| [61] | Sim, S.; Sukin, D. J.P; Alan, A., Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, Adv. Quantum. Technol., 2, 12, Article 1900070 pp., 2019 |
| [62] | Wang, Y., Stochastic zeroth-order optimization in high dimensions, Int. Conf. Artif. Intell. Stat., 84, 1356-1365, 2018, PMLR |
| [63] | Wiersema, R.; Zhou, C., Exploring entanglement and optimization within the Hamiltonian variational ansatz, PRX Quantum, 2.1, Article 010101 pp., 2021 |
| [64] | Wecker, D.; Hastings, M. B.; Troyer, M., Progress towards practical quantum variational algorithms, Phys. Rev. A, 92, 4, Article 042303 pp., 2015 |
| [65] | Mele, A. A.; Mbeng, G. B., Avoiding barren plateaus via transferability of smooth solutions in a Hamiltonian variational ansatz, Phys. Rev. A, 106, 6, Article L060401 pp., 2022 |
| [66] | Barkoutsos, P.; Gonthier, J., Quantum algorithms for electronic structure calculations: particle-hole Hamiltonian and optimized wave-function expansions, Phys. Rev. A, 98, 2, Article 022322 pp., 2018 |
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