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2012/12/06, McConnell 320, 10:00 - 11:00

Scrambling speed of random quantum circuits
Winton Brown , University of Sherbrooke

Abstract:

Random transformations are typically good at "scrambling" information. Specifically, in the quantum setting, scrambling refers to the process of mapping most initial pure product states under a unitary transformation to states which are macroscopically entangled, in the sense of being close to completely mixed on all or most subsystems containing a fraction fn of all n particles for some constant f. While the term scrambling is used in the context of the black hole information paradox, scrambling is related to problems involving decoupling in general, and to the question of how large isolated many-body systems reach local thermal equilibrium under their own unitary dynamics. I will discuss the speed at which various notions of scrambling/decoupling occur in a simplified but natural model of random two-particle interactions: random quantum circuits. For a circuit representing the dynamics generated by a local Hamiltonian, the depth of the circuit corresponds to time. We resolve a conjecture raised in the context of the black hole information paradox with respect to the depth at which a typical quantum circuit generates an entanglement assisted encoding against the erasure channel. In addition, we prove that typical quantum circuits of poly(log n) depth satisfy a stronger notion of scrambling and can be used to encode r1 n qubits into n qubits so that up to r2 n errors can be corrected, for finite rates r1 and r2 > 0.