Oracle separations show proofs of quantumness coexist with P=NP
Original title: Quantum Advantage has Few Complexity Implications
Oracle relative to which P^O = NP^O, BQP^O = PSPACE^O and IP^O subset BQP^O is hard on average against P^O/poly.
The paper examines complexity implications of proofs of quantumness and quantum verifier oblivious state preparation. It constructs classical and unitary oracles where these objects exist even when P=NP and BQP=QCMA. A classical oracle satisfies P^O=NP^O, BQP^O=PSPACE^O and hosts an IP^O language hard on average against P^O/poly. A unitary oracle satisfies BQP^O=QCMA^O and enables quantum verifier oblivious state preparation. These separations imply proofs of quantumness cannot construct relativizing cryptography.
- P^O = NP^O with quantum proofs existing
- BQP^O = PSPACE^O
- IP^O subset BQP^O hard on average against P^O/poly
- Unitary oracle for BQP^O = QCMA^O
- Proofs of quantumness cannot yield relativizing cryptography
From the original article
1 min read at arxiv.orgWe consider the complexity implications of proofs of quantumness and (quantum verifier) oblivious state preparation. We show that both of these objects can coexist with the easiness of nondeterministic computation. That is, we give evidence that proofs of quantumness can exist when $\mathsf{P} = \mathsf{NP}$ and that (quantum verifier) oblivious state preparation can exist when $\mathsf{BQP} = \mathsf{QCMA}$.
By Eli Goldin · arxiv.org
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