Non-uniformity and Quantum Advice in the Quantum Random Oracle Model

Liu, Qipeng

doi:10.1007/978-3-031-30545-0_5

Cited by 7 publications

(11 citation statements)

References 24 publications

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“…Our work is based on the previous works on quantum advantages with unstructured oracles, by Yamakawa and Zhandry [YZ22] and recent separation by Liu [Liu22]. Our work improves [Liu22] in two aspects: first, Liu only proved the separation of their relational variants, instead of the original decision classes; second, the separation by Liu does not allow algorithms to have access to the oracle (either classically, or quantumly), but only the advice can depend on the oracle.…”

Section: Our Resultsmentioning

confidence: 99%

“…On the other hand, they showed a quantum algorithm that uses quantum queries to invert images. Liu [Liu22] observed that the inversion quantum algorithm only needs to make non-adaptive quantum queries that are independent of the image y. Therefore, the algorithm with quantum access can be easily cast into a quantum algorithm with quantum advice but no queries; on the other hand, he showed that, if an algorithm has no access to the random oracle, it can not invert even with a piece of exponentially large classical advice.…”

Section: Overviewmentioning

confidence: 99%

“…To see that L is decidable by a BQP/qpoly machine, we can just take the quantum advice as in [Liu22]. On an input x, an algorithm generates v such that f H C (v) = x using the quantum advice.…”

Section: Overviewmentioning

confidence: 99%

“…To see that the two distributions can be distinguished using a QMA machine, notice that we can take the quantum advice as in [Liu22], and generate v such that f H C (v) = r. By querying O at v, we can distinguish whether the oracle belongs to the YES distribution or the NO distribution.…”

Section: Overviewmentioning

confidence: 99%

“…QCMA, Aaronson and Kuperberg [AK07] in the same paper showed an oracle separation between these two classes, leaving the separation with respect to a classical oracle as an open question. Recently, Liu [Liu22] showed the separation for its relational variants (i.e., FBQP/qpoly and FBQP/poly) under a special case, where the oracle is never given to the algorithms 3 . Despite all the efforts, the separation between BQP/poly and BQP/qpoly relative to a classical oracle remains obscure.…”

Section: Introductionmentioning

confidence: 99%

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Classical vs Quantum Advice under Classically-Accessible Oracle

Li¹,

Liu²,

Angelos³

et al. 2023

Preprint

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It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly = BQP/poly or QMA = QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly = BQP/poly and QMA = QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.

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Section: Our Resultsmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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