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Quantum Algorithmic Measurement
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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 problem 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.
Forward citations
Cited by 2 Pith papers
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Information-Computation Gaps in Quantum Learning via Low-Degree Likelihood
A quantum extension of the low-degree method shows that state designs imply computational hardness for many single-copy quantum measurement strategies, yielding new information-computation gaps.
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Product testing with single-copy measurements
Testing whether a state is product across some bipartition costs Ω(d^{n/4}) copies with single-copy measurements versus O(n/ε²) with joint measurements — an exponential separation; full product testing has an O(n log ...
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