Speaker: Claudio Chamon (Boston University)

Time: 9:00-10:00 a.m., June 16, 2023, GMT+8

Venue: Zoom ID:963 5796 8034 Password:125125

Abstract:

Black holes are conjectured to be the fastest scramblers ofinformation in nature, with a scrambling time,tsc, that scaleslogarithmically with the number of degrees of freedom of the system,.c~ logn. At the same time, recent work suggests that resolving someof the long-standing information paradoxes inherent in the quantumdescription of evaporating black holes requires cryptographic levelscrambling of information. The implication is that black holes areeffective generators of computational pseudorandomness, i.e, that theygenerate pseudorandom quantum states that cannot be distinguishedfrom Haar-random by an observer with polynomial resources. The simple point made and explicitly justified in this paper is that, when analyzed in the context of universal 2-qubit-gate-based randomquantum circuits - which are generally employed as simple models ofblack hole dynamics - these two conjectures are inconsistent with oneanother. More precisely, we argue that log n-depth 2-qubit-gate-based random quantum circuits that match the speed limit for scrambling,conjectured for black holes, cannot produce computationally pseudo random quantum states. However, producing such states withshallow logn -depth quantum circuits can be accomplished if oneemploys universal families of “inflationary” quantum gates implemented either as a subset of 2-qudit-gates in U(d2) with d > 3 and d prime, oras special 3-qubit gates.

Source: School of Physics