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Quantum Machine Learning Entanglement Theory Quantum Correlations Quantum Simulation

A distribution testing oracle separation between QMA and QCMA

arXiv

Authors: Anand Natarajan, Chinmay Nirkhe

Year

2022

Paper ID

57952

Status

Preprint

Abstract Read

~2 min

Abstract Words

112

Citations

N/A

Abstract

It is a long-standing open question in quantum complexity theory whether the definition of textit{non-deterministic} quantum computation requires quantum witnesses \(textsf{QMA}\) or if classical witnesses suffice \(textsf{QCMA}\). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations [Aaronson-Kuperberg (CCC'07), Fefferman-Kimmel (MFCS'18)] required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over n-bit boolean functions.

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This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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It is a long-standing open question in quantum complexity theory whether the definition of non-deterministic quantum computation requires quantum witnesses (textsfQMA) or if...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2210.15380 [2] arXiv https://arxiv.org/abs/2210.15380 [3] Publisher https://arxiv.org/abs/2210.15380

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