On the pseudorandomness of simple quantum processes
Simple local quantum processes can match unitary designs yet remain efficiently distinguishable from truly random unitaries.
The paper studies whether simple local quantum processes can be pseudorandom, as a unitary analog of Gowers' conjecture on random reversible operations. For every fixed t, the authors give efficiently samplable one- and two-qubit gate distributions that, after T=O_t(n^2 log^2 n) steps, form an approximate unitary t-design with error exp(-Omega(log^2 n)), yet an efficient quantum algorithm distinguishes them from Haar-random unitaries with O_t(log^2 n) queries. A second, more structured separation holds at polynomially bounded moments, and the authors propose new conjectures for random quantum circuits.
- Local one- and two-qubit gates form an approximate unitary t-design after O(n^2 log^2 n) steps.
- An efficient quantum algorithm distinguishes that ensemble with only O(log^2 n) queries.
- The result refutes the unitary analog of the Hoory-Magen-Myers-Rackoff conjecture.
- Authors propose new conjectures for pseudorandomness emerging in random quantum circuits.
From the original article
1 min read at arxiv.orgCan simple processes appear highly complex? Gowers (Comb. Prob.
By Jesko Dujmovic · arxiv.org
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