Edge Estimation with Independent Set Oracles

Beame, Paul; Har-Peled, Sariel; Ramamoorthy, Sivaramakrishnan Natarajan; Rashtchian, Cyrus; Sinha, Makrand

doi:10.48550/arxiv.1711.07567

Cited by 1 publication

(1 citation statement)

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“…In different applications, we apply different queries, and the OR query is important for problems in computational biology. This type of query is also known as independent set query [13] and edgedetection query [8]. Many classical algorithms were discovered to learn graphs using OR queries in the past decades.…”

Section: Prior Workmentioning

confidence: 99%

Quantum algorithms for learning a hidden graph and beyond

Montanaro,

Shao

2020

Preprint

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We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any edges. In the second ("parity queries"), the oracle returns the parity of the number of edges in a subset. In the third model, we are given copies of the graph state corresponding to the graph.We give quantum algorithms that achieve speedups over the best possible classical algorithms in the OR and parity query models, for some families of graphs, and give quantum algorithms in the graph state model whose complexity is similar to the parity query model. For some parameter regimes, the speedups can be exponential in the parity query model. On the other hand, without any promise on the graph, no speedup is possible in the OR query model.A main technique we use is the quantum algorithm for solving the combinatorial group testing problem, for which a query-efficient quantum algorithm was given by Belovs. Here we additionally give a time-efficient quantum algorithm for this problem, based on the algorithm of Ambainis et al. for a "gapped" version of the group testing problem. We also give simple time-efficient quantum algorithms based on Fourier sampling and amplitude amplification for learning the exact-half and majority functions, which almost match the optimal complexity of Belovs' algorithms.

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Section: Prior Workmentioning

confidence: 99%