A universal crossover in quantum circuits governed by a proximate
classical error correction transition
- URL: http://arxiv.org/abs/2208.02217v2
- Date: Thu, 11 May 2023 16:03:52 GMT
- Title: A universal crossover in quantum circuits governed by a proximate
classical error correction transition
- Authors: Anasuya Lyons, Soonwon Choi, Ehud Altman
- Abstract summary: We define a random circuit model with nearest neighbor classical gates interrupted by erasure errors.
We show that this phase transition is in the directed percolation class, consistent with the fact that having zero entropy is an absorbing state of the dynamics.
We describe the universal properties of this instability in an effective model of the semi-classical circuit.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We formulate a semi-classical circuit model to clarify the role of quantum
entanglement in the recently discovered encoding phase transitions in quantum
circuits with measurements. As a starting point we define a random circuit
model with nearest neighbor classical gates interrupted by erasure errors. In
analogy with the quantum setting, this system undergoes a purification
transition at a critical error rate above which the classical information
entropy in the output state vanishes. We show that this phase transition is in
the directed percolation universality class, consistent with the fact that
having zero entropy is an absorbing state of the dynamics; this classical
circuit cannot generate entropy. Adding an arbitrarily small density of quantum
gates in the presence of errors eliminates the transition by destroying the
absorbing state: the quantum gates generate internal entanglement, which can be
effectively converted to classical entropy by the errors. We describe the
universal properties of this instability in an effective model of the
semi-classical circuit. Our model highlights the crucial differences between
information dynamics in classical and quantum circuits.
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