The tricritical point at the learning transition of deformed toric codes is a higher Nishimori critical point where the Edwards-Anderson correlation exponent exactly matches the clean Ising spin exponent and c_eff is greater than 1/2, decreasing under RG flow.
Learning transitions in classical Ising models and deformed toric codes
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Conditional probability distributions describe the effect of learning an initially unknown classical state through Bayesian inference. Here we demonstrate the existence of a \textit{learning transition}, having signatures in the long distance behavior of conditional correlation functions, in the two-dimensional classical Ising model. This transition, which arises when learning local energy densities, extends all the way from the infinite-temperature paramagnetic state down to the thermal critical state. The intersection of the line of learning transitions and the thermal Ising transition is a new tricritical point. Our model for learning also exactly describes the effects of weak measurements on ground states of frustration-free quantum Hamiltonians, which interpolate between the toric code and a paramagnet. Notably, the location of the above tricritical point implies that the quantum memory defined by the degenerate ground states in the topological phase is robust to weak measurement, even when the initial state is arbitrarily close to the quantum phase transition separating topological and trivial phases. Our analysis uses a replica field theory combined with the renormalization group, and we chart out the phase diagram using a combination of tensor network and Monte Carlo techniques. Our methods can be extended to study the more general effects of learning on both classical and quantum states. The learning induced critical states can be realized in classical or quantum devices.
verdicts
UNVERDICTED 4representative citing papers
Measurement phases in the critical Ising model exhibit an enlarged replica symmetry, analogous to the Nishimori phenomenon, that exactly determines the Edwards-Anderson correlator exponent in 2D and near six dimensions.
Generalized coherent information acts as a sharp phase-transition indicator over the entire p-T plane in the 2D ±J random-bond Ising model, yielding a high-precision multicritical point estimate p_c=0.1092212(4) with reduced finite-size effects.
Introduces statistical dynamical quantum phase transitions via Born-rule sampling of post-measurement states in quenched Ising chains, recovering DQPT features in high moments and proposing a measurement-based simulation protocol.
citing papers explorer
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Higher Nishimori Criticality and Exact Results at the Learning Transition of Deformed Toric Codes
The tricritical point at the learning transition of deformed toric codes is a higher Nishimori critical point where the Edwards-Anderson correlation exponent exactly matches the clean Ising spin exponent and c_eff is greater than 1/2, decreasing under RG flow.
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Bayesian phase transition for the critical Ising model: Enlarged replica symmetry in the epsilon expansion and in 2D
Measurement phases in the critical Ising model exhibit an enlarged replica symmetry, analogous to the Nishimori phenomenon, that exactly determines the Edwards-Anderson correlator exponent in 2D and near six dimensions.
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Revisiting Nishimori multicriticality through the lens of information measures
Generalized coherent information acts as a sharp phase-transition indicator over the entire p-T plane in the 2D ±J random-bond Ising model, yielding a high-precision multicritical point estimate p_c=0.1092212(4) with reduced finite-size effects.
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Born-rule statistical dynamical quantum phase transitions under measurement
Introduces statistical dynamical quantum phase transitions via Born-rule sampling of post-measurement states in quenched Ising chains, recovering DQPT features in high moments and proposing a measurement-based simulation protocol.