Abstract
Quantum computational chemistry has emerged as a potential application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers, have been designed as promising solutions to quantum chemistry problems. Nonetheless, challenges due to theoretical complexity and experimental imperfections hinder progress in achieving reliable and accurate results. Experimental works for solving electronic structures are consequently still restricted to non-scalable or classically simulable ansatz or limited to a few qubits with large errors. Here, we address the critical challenges associated with solving molecular electronic structures using noisy quantum processors. Our protocol presents improvements in the circuit depth and running time, key metrics for chemistry simulation. Through systematic hardware enhancements and the integration of error-mitigation techniques, we overcome theoretical and experimental limitations and successfully scale up the implementation of variational quantum eigensolvers with an optimized unitary coupled cluster ansatz to 12 qubits. We produce high-precision results of the ground-state energy for molecules with error suppression by around two orders of magnitude. Our work demonstrates a feasible path towards a scalable solution to electronic structure calculation.
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Data availability
Source data are provided with this paper. All other data that support the findings of this study are available from the corresponding author upon reasonable request.
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The code for this paper is available from the corresponding authors upon reasonable request.
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Acknowledgements
We thank W. Li, V. Vedral, M.S. Kim, H. Shen, C. Cao, D. Lv and J. Liu for useful related discussions on the theoretical scheme. We thank the USTC Center for Micro- and Nanoscale Research and Fabrication for supporting the sample fabrication. We also thank QuantumCTek Co., Ltd. for supporting the fabrication and maintenance of room-temperature electronics. This research was supported by the Innovation Programme for Quantum Science and Technology (grant nos. 2021ZD0300200, 2023ZD0300200), Shanghai Municipal Science and Technology Major Project (grant no. 2019SHZDZX01), Anhui Initiative in Quantum Information Technologies, National Natural Science Foundation of China (grant nos. 12175003 and 12361161602), NSAF (grant no. U2330201), Natural Science Foundation of Shandong Province, China (grant no. ZR202209080019), the Key-Area Research and Development Programme of Guangdong Province (grant no. 2020B0303060001) and special funds from Jinan Science and Technology Bureau and Jinan High Tech Zone Management Committee. H.-L.H. acknowledges support from the Youth Talent Lifting Project (grant no. 2020-JCJQ-QT-030), National Natural Science Foundation of China (grant nos. 11905294, 12274464), China Postdoctoral Science Foundation and the Open Research Fund from State Key Laboratory of High Performance Computing of China (grant no. 201901-01). J.S. acknowledges the Samsung GRC grant for financial support. M.G. was supported by the National Science Foundation of China (grant no. T2322024), Shanghai Rising-Star Programme (grant no. 23QA1410000) and the Youth Innovation Promotion Association of CAS (grant no. 2022460). X.Z. acknowledges support from THE XPLORER PRIZE.
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Contributions
X.Y, M.G and J.S. initiated the project. J.S. developed the theoretical aspect of the project and built up the source code for numerical simulation with input from X.Y. and Y. Zhang. J.S., Y. Zhang and K.L. carried out the numerical simulation under the supervision of X.Y., Y. Zhang and K.L. generated the measurement bases with the algorithm developed by J.S. S.G., H.Q., M.G., F.C. and S.C. performed the measurements. S.G., J.S., H.Q., M.G. and Y. Zhao analysed the experimental data. Q.Z., Y.Y., C.Y., F.C. and S.L. designed the processor. S.C., Y.L., K.Z., S.G., H.Q., T.-H.C., H.R., H.D. and Y.-H.H. fabricated the processor. M.G., S.W., C.Z., Y. Zhao, S.L., C.Y., J.Y., D.F., D.W. and H.S. contributed to the construction of the ultracold and low-noise measurement system. J.L., Y.X., F.L., C.G., L.S., N.L. and C.-Z.P. developed the room-temperature electronics. Experiments were performed using a quantum processor that was developed and fabricated with a large effort from the experimental team. J.S., S.G., Y.Z., X.Y. and M.G. wrote the paper with input from all authors. X.Y., X.Z. and J.-W.P. supervised the project.
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Extended data
Extended Data Fig. 1 Benchmark of multi-qubit Pauli rotation gate.
The comparison of the operation quality before and after optimization with qubit number being four (a), six (b), eight (c) and ten (d). The error rate of each sequence, as a characteristic of the averaged fidelity, can be obtained by measuring the probability of \({\left\vert 0\right\rangle }^{\otimes n}\). The data points are the average values at each sequence length.
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Guo, S., Sun, J., Qian, H. et al. Experimental quantum computational chemistry with optimized unitary coupled cluster ansatz. Nat. Phys. 20, 1240–1246 (2024). https://doi.org/10.1038/s41567-024-02530-z
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DOI: https://doi.org/10.1038/s41567-024-02530-z
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