Overlapped grouping measurement: A unified framework for measuring quantum states

Overlapped grouping measurement: A unified framework for measuring quantum states

Overlapped grouping measurement: A unified framework for measuring quantum states PlatoAiStream Data Intelligence. Vertical Search. Ai.

Bujiao Wu1,2, Jinzhao Sun3,1, Qi Huang4,1, and Xiao Yuan1,2

1Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
2School of Computer Science, Peking University, Beijing 100871, China
3Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
4School of Physics, Peking University, Beijing 100871, China

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Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as importance sampling, observable compatibility, or classical shadows of quantum states, different advanced measurement schemes have been proposed to greatly reduce the large measurement cost. Yet, the underline cost reduction mechanisms seem distinct from each other, and how to systematically find the optimal scheme remains a critical challenge. Here, we address this challenge by proposing a unified framework of quantum measurements, incorporating advanced measurement methods as special cases. Our framework allows us to introduce a general scheme – overlapped grouping measurement, which simultaneously exploits the advantages of most existing methods. An intuitive understanding of the scheme is to partition the measurements into overlapped groups with each one consisting of compatible measurements. We provide explicit grouping strategies and numerically verify its performance for different molecular Hamiltonians with up to 16 qubits. Our numerical result shows significant improvements over existing schemes. Our work paves the way for efficient quantum measurement and fast quantum processing with current and near-term quantum devices.

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[8] Ting Zhang, Jinzhao Sun, Xiao-Xu Fang, Xiao-Ming Zhang, Xiao Yuan, and He Lu, “Experimental Quantum State Measurement with Classical Shadows”, Physical Review Letters 127 20, 200501 (2021).

[9] Tzu-Ching Yen, Aadithya Ganeshram, and Artur F. Izmaylov, “Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates”, arXiv:2201.01471.

[10] Kaifeng Bu, Dax Enshan Koh, Roy J. Garcia, and Arthur Jaffe, “Classical shadows with Pauli-invariant unitary ensembles”, arXiv:2202.03272.

[11] Weitang Li, Zigeng Huang, Changsu Cao, Yifei Huang, Zhigang Shuai, Xiaoming Sun, Jinzhao Sun, Xiao Yuan, and Dingshun Lv, “Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers”, arXiv:2109.08062.

[12] Ariel Shlosberg, Andrew J. Jena, Priyanka Mukhopadhyay, Jan F. Haase, Felix Leditzky, and Luca Dellantonio, “Adaptive estimation of quantum observables”, arXiv:2110.15339.

[13] Zi-Jian Zhang, Jinzhao Sun, Xiao Yuan, and Man-Hong Yung, “Low-depth Hamiltonian Simulation by Adaptive Product Formula”, arXiv:2011.05283.

[14] Yusen Wu, Bujiao Wu, Jingbo Wang, and Xiao Yuan, “Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron”, arXiv:2111.07553.

[15] Daniel Miller, Laurin E. Fischer, Igor O. Sokolov, Panagiotis Kl. Barkoutsos, and Ivano Tavernelli, “Hardware-Tailored Diagonalization Circuits”, arXiv:2203.03646.

[16] Zhenhuan Liu, Pei Zeng, You Zhou, and Mile Gu, “Characterizing correlation within multipartite quantum systems via local randomized measurements”, Physical Review A 105 2, 022407 (2022).

[17] William Kirby, Mario Motta, and Antonio Mezzacapo, “Exact and efficient Lanczos method on a quantum computer”, arXiv:2208.00567.

[18] Marco Majland, Rasmus Berg Jensen, Mads Greisen Højlund, Nikolaj Thomas Zinner, and Ove Christiansen, “Runtime optimization for vibrational structure on quantum computers: coordinates and measurement schemes”, arXiv:2211.11615.

[19] Seonghoon Choi, Ignacio Loaiza, and Artur F. Izmaylov, “Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver”, arXiv:2208.14490.

[20] Tianren Gu, Xiao Yuan, and Bujiao Wu, “Efficient measurement schemes for bosonic systems”, arXiv:2210.13585.

[21] You Zhou and Qing Liu, “Performance analysis of multi-shot shadow estimation”, arXiv:2212.11068.

[22] Xiao-Ming Zhang, Zixuan Huo, Kecheng Liu, Ying Li, and Xiao Yuan, “Unbiased random circuit compiler for time-dependent Hamiltonian simulation”, arXiv:2212.09445.

[23] Alexander Gresch and Martin Kliesch, “Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping”, arXiv:2301.03385.

[24] Andrew Jena, Scott N. Genin, and Michele Mosca, “Optimization of variational-quantum-eigensolver measurement by partitioning Pauli operators using multiqubit Clifford gates on noisy intermediate-scale quantum hardware”, Physical Review A 106 4, 042443 (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-01-13 11:36:07). The list may be incomplete as not all publishers provide suitable and complete citation data.

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