Revisiting Nishimori multicriticality through the lens of information measures
arXiv:2511.02907 · doi:10.1103/b8y5-k3y6
Abstract
The quantum error correction threshold is closely related to the Nishimori physics of random statistical models. We extend quantum information measures such as coherent information beyond the Nishimori line and establish them as sharp indicators of phase transitions over the full - plane. These generalized measures admit a natural operational interpretation as diagnostics of inference mismatch for decoders operating at an effective temperature. We derive exact inequalities for several generalized measures, demonstrating that each attains its extremum along the Nishimori line. As a direct application, we study these measures in the 2d random-bond Ising model-corresponding to a surface code under bit-flip noise-and revisit the Nishimori multicritical point. Among all indicators, coherent information exhibits the weakest finite-size effects, enabling a high-precision estimate and the associated critical exponents.
arXiv comment5+13 pages, 7 figures
References in corpus (65)
- Fault-tolerant quantum computation by anyons
- Mixed State Entanglement and Quantum Error Correction
- Topological quantum memory
- Quantum Error Correction for Quantum Memories
- The capacity of the noisy quantum channel
- Quantum data processing and error correction
- Statistical physics of inference: Thresholds and algorithms
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- The XZZX Surface Code
- Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
- Ultrahigh Error Threshold for Surface Codes with Biased Noise
- Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
- Quantum criticality under decoherence or weak measurement
- Efficient classical simulation of random shallow 2D quantum circuits
- Solving the sampling problem of the Sycamore quantum circuits
- Strong Resilience of Topological Codes to Depolarization
- The two-dimensional random-bond Ising model, free fermions and the network model
- Error Threshold for Color Codes and Random 3-Body Ising Models
- The Nishimori line and Bayesian Statistics
- Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
- Tailoring surface codes for highly biased noise
- Nishimori point in the 2D +/- J random-bond Ising model
- Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
- Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
- Diagnostics of mixed-state topological order and breakdown of quantum memory
- Criticality in the two-dimensional random-bond Ising model
- Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
- Statistical mechanical models for quantum codes with correlated noise
- Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
- An efficient Markov chain Monte Carlo algorithm for the surface code
- Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
- Duality and Multicritical Point of Two-Dimensional Spin Glasses
- Intrinsic Mixed-state Topological Order
- Universality, frustration and conformal invariance in two-dimensional random Ising magnets
- Gapless Coulomb state emerging from a self-dual topological tensor-network state
- A Noisy Approach to Intrinsically Mixed-State Topological Order
- Towards a classification of mixed-state topological orders in two dimensions
- Strong disorder fixed points in the two-dimensional random-bond Ising model
- Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
- Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
- Coherent error threshold for surface codes from Majorana delocalization
- Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
- On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
- Direct Monte Carlo Measurement of the Surface Tension in Ising Models
- Tapestry of dualities in decohered quantum error correction codes
- Phase diagram and critical exponents of a Potts gauge glass
- Robust teleportation of a surface code and cascade of topological quantum phase transitions
- Negative scaling dimensions and conformal invariance at the Nishimori point in the +/-J random-bond Ising model
- Efficient sampling of noisy shallow circuits via monitored unraveling
- Duality in finite-dimensional spin glasses
- Accurate optimal quantum error correction thresholds from coherent information
- Coherent information for CSS codes under decoherence
- High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
- Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold
- Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model
- Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition
- Coherent information as a mixed-state topological order parameter of fermions
- Properties of the multicritical point of +/- J Ising spin glasses on the square lattice
- Critical exponents at the Nishimori point
- Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
- Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line
- Exact results on finite size corrections for surface codes tailored to biased noise
- Temperature chaos as a logical consequence of the reentrant transition in spin glasses
- Monitored Fluctuating Hydrodynamics
- Fundamental thresholds for computational and erasure errors via the coherent information