A universal crossover in quantum circuits governed by a proximate classical error correction transition

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.

arXiv commentSubmitted to PRB; 8 pages, 6 figures; supplementary info in v1 merged into main text. (v1: 6+5 pages, 4+3 figures; extended supplementary info)

References in corpus (14)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Improved Simulation of Stabilizer Circuits
• Strong quantum computational advantage using a superconducting quantum processor
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Dynamical purification phase transitions induced by quantum measurements
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Measurement-induced phase transitions in quantum automaton circuits
• Entanglement on mixed stabiliser states--I: Normal Forms and Reduction Procedures
• Measurement-induced phase transition in a classical, chaotic many-body system

Cited by in corpus (6)

• Purification Timescales in Monitored Fermions
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Quantum and Classical Dynamics with Random Permutation Circuits
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
• Plaquette Models, Cellular Automata, and Measurement-induced Criticality