From dual-unitary to quantum Bernoulli circuits: Role of the entangling
power in constructing a quantum ergodic hierarchy
- URL: http://arxiv.org/abs/2101.04580v2
- Date: Mon, 12 Jul 2021 14:36:01 GMT
- Title: From dual-unitary to quantum Bernoulli circuits: Role of the entangling
power in constructing a quantum ergodic hierarchy
- Authors: S. Aravinda, Suhail Ahmad Rather, Arul Lakshminarayan
- Abstract summary: We study the apex of a putative quantum ergodic hierarchy which is Bernoulli.
We derive a condition based on the entangling power $e_p(U)$ of the basic two-particle unitary building block.
We construct a coupled quantum cat map which is dual-unitary for all local dimensions and a 2-unitary or perfect tensor for odd local dimensions.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Deterministic classical dynamical systems have an ergodic hierarchy, from
ergodic through mixing, to Bernoulli systems that are "as random as a
coin-toss". Dual-unitary circuits have been recently introduced as solvable
models of many-body nonintegrable quantum chaotic systems having a hierarchy of
ergodic properties. We extend this to include the apex of a putative quantum
ergodic hierarchy which is Bernoulli, in the sense that correlations of single
and two-particle observables vanish at space-time separated points. We derive a
condition based on the entangling power $e_p(U)$ of the basic two-particle
unitary building block, $U$, of the circuit, that guarantees mixing, and when
maximized, corresponds to Bernoulli circuits. Additionally we show, both
analytically and numerically, how local-averaging over random realizations of
the single-particle unitaries, $u_i$ and $v_i$ such that the building block is
$U^\prime = (u_1 \otimes u_2 ) U (v_1 \otimes v_2 )$ leads to an identification
of the average mixing rate as being determined predominantly by the entangling
power $e_p(U)$. Finally we provide several, both analytical and numerical, ways
to construct dual-unitary operators covering the entire possible range of
entangling power. We construct a coupled quantum cat map which is dual-unitary
for all local dimensions and a 2-unitary or perfect tensor for odd local
dimensions, and can be used to build Bernoulli circuits.
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