On the pseudorandomness of simple quantum processes
[quant-ph] Autorzy: Jesko Dujmovic, Jonas Haferkamp, Alexander Poremba
Can simple processes appear highly complex? Gowers (Comb. Prob. Comp. '96) conjectured that repeatedly composing local random reversible operations can yield global permutations that are indistinguishable from random. In this work, we study the unitary quantum analog of this question, in an attempt to make new progress on this longstanding conjecture. Our first result shows that statistical moment matching in the form of unitary designs does not generically lead to pseudorandomness---even for the simplest quantum processes: for every fixed $t$, we give an efficiently samplable family $\{ν_n\}_n$ of distributions on one- and two-qubit gates such that, after $T=O_t(n^2\log^2 n)$ independent steps, the resulting $n$-qubit ensemble is an approximate unitary $t$-design with negligible error $\exp(-Ω(\log^2 n))$, yet an efficient quantum algorithm distinguishes it from random using only $O_t(…
- Kategoria arxiv
- quant-ph
- Kategoria
- quant-ph