Quantum algorithmic measurement

Journal Article · 15 February 2022 · Nature Communications

DOI: https://doi.org/10.1038/s41467-021-27922-0 · OSTI ID:1904469

Aharonov, Dorit ^[1]; Cotler, Jordan  ^[2]; Qi, Xiao-Liang ^[3]

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1. Hebrew University of Jerusalem (Israel); OSTI
2. Harvard University, Cambridge, MA (United States); Stanford University, CA (United States)
3. Stanford University, CA (United States)

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.

• Research Organization: Harvard University, Cambridge, MA (United States); Massachusetts Institute of Technology (MIT), Cambridge, MA (United States); University of California, Oakland, CA (United States)
• Sponsoring Organization: Fannie and John Hertz Foundation; Israel Science Foundation (ISF); Simons Foundation; USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0012567; SC0019380
• OSTI ID: 1904469
• Journal Information: Nature Communications, Journal Name: Nature Communications Journal Issue: 1 Vol. 13; ISSN 2041-1723
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United States
• Language: English