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Quantum algorithmic measurement

Author

Listed:
  • Dorit Aharonov

    (The Hebrew University of Jerusalem)

  • Jordan Cotler

    (Harvard University
    Stanford University)

  • Xiao-Liang Qi

    (Stanford University)

Abstract

There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system’s Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.

Suggested Citation

  • Dorit Aharonov & Jordan Cotler & Xiao-Liang Qi, 2022. "Quantum algorithmic measurement," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-021-27922-0
    DOI: 10.1038/s41467-021-27922-0
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    References listed on IDEAS

    as
    1. Sisi Zhou & Mengzhen Zhang & John Preskill & Liang Jiang, 2018. "Achieving the Heisenberg limit in quantum metrology using quantum error correction," Nature Communications, Nature, vol. 9(1), pages 1-11, December.
    2. Yosi Atia & Dorit Aharonov, 2017. "Fast-forwarding of Hamiltonians and exponentially precise measurements," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    3. Ben W. Reichardt & Falk Unger & Umesh Vazirani, 2013. "Classical command of quantum systems," Nature, Nature, vol. 496(7446), pages 456-460, April.
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    Cited by:

    1. Supanut Thanasilp & Samson Wang & M. Cerezo & Zoë Holmes, 2024. "Exponential concentration in quantum kernel methods," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    2. Matthias C. Caro & Hsin-Yuan Huang & M. Cerezo & Kunal Sharma & Andrew Sornborger & Lukasz Cincio & Patrick J. Coles, 2022. "Generalization in quantum machine learning from few training data," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    3. Matthias C. Caro & Hsin-Yuan Huang & Nicholas Ezzell & Joe Gibbs & Andrew T. Sornborger & Lukasz Cincio & Patrick J. Coles & Zoë Holmes, 2023. "Out-of-distribution generalization for learning quantum dynamics," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    4. Laura Lewis & Hsin-Yuan Huang & Viet T. Tran & Sebastian Lehner & Richard Kueng & John Preskill, 2024. "Improved machine learning algorithm for predicting ground state properties," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    5. Sitan Chen & Jordan Cotler & Hsin-Yuan Huang & Jerry Li, 2023. "The complexity of NISQ," Nature Communications, Nature, vol. 14(1), pages 1-6, December.

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