Monitored Quantum Dynamics and the Kitaev Spin Liquid
- URL: http://arxiv.org/abs/2207.02877v1
- Date: Wed, 6 Jul 2022 18:00:07 GMT
- Title: Monitored Quantum Dynamics and the Kitaev Spin Liquid
- Authors: Ali Lavasani, Zhu-Xi Luo, Sagar Vijay
- Abstract summary: Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter.
Motivated by the physics of the Kitaev quantum spin liquid, we study quantum circuit dynamics in (2+1)-dimensions involving local projective measurements.
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- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum circuit dynamics with local projective measurements can realize a
rich spectrum of entangled states of quantum matter. Motivated by the physics
of the Kitaev quantum spin liquid [1], we study quantum circuit dynamics in
(2+1)-dimensions involving local projective measurements, in which the
monitored trajectories realize (i) a phase with topological quantum order or
(ii) a "critical" phase with a logarithmic violation of area-law-scaling of the
entanglement entropy along with long range tripartite entanglement. A Majorana
parton description of these dynamics, which provides an out-of-equilibrium
generalization of the parton description of the Kitaev honeycomb model, permits
an analytic understanding of the universal properties of these two phases,
including the entanglement properties of the steady-state, the dynamics of the
system on the approach to equilibrium, and the phase transition between these
states. In the topologically-ordered phase, two logical qubits can be encoded
in an initial state and protected for a time which scales exponentially in the
linear dimension of the system, while no robust encoding of quantum information
persists in the critical phase. Extensive numerical simulations of these
monitored dynamics confirm our analytic predictions.
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