Unitary complexity in polynomial space
[quant-ph] Autorzy: William Kretschmer, Ewin Tang
We show that if quantum commitments exist, then either there is no polynomial-time solution to the unitary synthesis problem, or $\mathsf{BPP} \neq \mathsf{NEXP}$. Thus, showing unconditionally that quantum commitments exist would require answering at least one of two longstanding open questions in complexity theory. We prove our main result as a consequence of a more general lemma, which shows that every unitary in $\mathsf{unitaryPSPACE}$ either cannot be synthesized efficiently relative to any classical oracle, or can be synthesized efficiently with an oracle for $\mathsf{NEXP}$ search problems. Our lemma has other noteworthy consequences, including that certain oracle separations involving $\mathsf{unitaryPSPACE}$ would imply breakthrough classical lower bounds such as $\mathsf{NC} \neq \mathsf{NP}$. Along the way, we propose new definitions for the unitary complexity classes $\math…
- Kategoria arxiv
- quant-ph
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- quant-ph