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.
Bayesian critical points in classical lattice models
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian. If we acquire further information about the configuration from measurement, our knowledge is updated according to Bayes' theorem. We examine the resulting "conditioned ensembles", finding that they show many new phase transitions and new renormalization-group fixed points. (Similar conditioned ensembles also describe "partial quenches" in which some of the system's degrees of freedom are instantaneously frozen, while the others continue to evolve.) After describing general features of the replica field theories for these problems, we analyze the effect of measurement on illustrative critical systems, including: critical Ising and Potts models, which show surprisingly rich phase diagrams, with RG fixed points at weak, intermediate, and infinite measurement strength; various models involving free fields, XY spins, or flux lines in 2D or 3D; and geometrical models such as polymers or clusters. We make connections with quantum dynamics, in particular with "charge sharpening" in 1D, by giving a formalism for measurement of classical stochastic processes: e.g. we give a purely hydrodynamic derivation of the known effective field theory for charge sharpening. We discuss qualitative differences between RG flows for the above measured systems, described by $N\to 1$ replica limits, and those for disordered systems, described by $N\to 0$ limits. In addition to discussing measurement of critical states, we give a unifying treatment of a family of inference problems for non-critical states. These are related to the Nishimori line in the phase diagram of the random-bond Ising model, and are relevant to various quantum error correction problems. We describe distinct physical interpretations of conditioned ensembles and note interesting open questions.
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Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.
Learning transitions exist in the 2D Ising model when inferring local energies via Bayesian methods, intersecting the thermal transition at a new tricritical point and implying robustness of quantum memory in deformed toric codes under weak measurements.
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.
Measurement-induced entanglement in Tomonaga-Luttinger liquids is universal, conformally invariant, and arises from Born-rule averaging over conformally invariant boundary conditions in the CFT.
In the monitored symmetric exclusion process, the local Markovianization timescale tracks the global-charge learnability timescale and diverges in the charge-fuzzy phase.
In U(1)-symmetric monitored random circuits, symmetry-breaking measurements drive the entanglement transition to the non-symmetric universality class and keep the charge correlation length finite at any measurement rate.
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.
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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Holographically Emergent Gauge Theory in Symmetric Quantum Circuits
Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.
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Learning transitions in classical Ising models and deformed toric codes
Learning transitions exist in the 2D Ising model when inferring local energies via Bayesian methods, intersecting the thermal transition at a new tricritical point and implying robustness of quantum memory in deformed toric codes under weak measurements.
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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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Measurement-Induced Entanglement in Conformal Field Theory
Measurement-induced entanglement in Tomonaga-Luttinger liquids is universal, conformally invariant, and arises from Born-rule averaging over conformally invariant boundary conditions in the CFT.
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Local Markov Order and Global Inference in Many-Body Dynamics
In the monitored symmetric exclusion process, the local Markovianization timescale tracks the global-charge learnability timescale and diverges in the charge-fuzzy phase.
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Universality of Measurement-Induced Criticality under Symmetry-Breaking Measurements
In U(1)-symmetric monitored random circuits, symmetry-breaking measurements drive the entanglement transition to the non-symmetric universality class and keep the charge correlation length finite at any measurement rate.
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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.