Quantum Advantage has Few Complexity Implications
[quant-ph] Autorzy: Eli Goldin, Alex Lombardi, Tomoyuki Morimae
We 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 $\mathsf{BQP} = \mathsf{QCMA}$. In particular, we give a classical oracle relative to which (1) $\mathsf{P}^\mathcal{O} = \mathsf{NP}^\mathcal{O}$ (2) $\mathsf{BQP}^\mathcal{O} = \mathsf{PSPACE}^\mathcal{O}$ (3) Proofs of quantumness exist. In particular, there exists a language in $\mathsf{IP}^\mathcal{O} \subseteq \mathsf{BQP}^\mathcal{O}$ which is hard on average against $\mathsf{P}^\mathcal{O}/poly$. We give a unitary oracle such that (1) $\mathsf{BQP}^\mathcal{O} = \mathsf{QCMA}^\mathcal{O}$ (2) Quantum veri…
- Kategoria arxiv
- quant-ph
- Kategoria
- quant-ph