Analyticity in some models of quantum statistical mechanics

Renato Calleja, Rafael de la Llave

Ola Bratteli, Derek W. Robinson

Garnet N. Ord

The Dirac equation, usually obtained by ‘quantizing’ a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space‐time geometry of the random walk replaces the missing analytic continuation, making the model ‘self‐quantizing’. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics.

Lucas English, Dominic J. Williamson, Stephen D. Bartlett

We identify regimes where postselection can be used scalably in quantum error correction (QEC) to improve performance. We use statistical mechanical models to analytically quantify the performance and thresholds of postselected QEC, with a focus on the surface code. Based on the nonequilibrium magnetization of these models, we identify a simple heuristic technique for postselection that determines whether to abort without requiring a decoder. Along with performance gains, this heuristic allows us to derive analytic expressions for postselected conditional logical thresholds and abort thresholds of surface codes. We find that such postselected QEC is characterized by four distinct thermodynamic phases and detail the implications of this phase space for practical, scalable quantum computation.

浩 市村

Lester Ingber

Several commerical quantum computers are now available that offer Hybrid Classical-Quantum computing. Application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers.Since 2015, PATHINT, has been used as a numerical algorithm for folding path-integrals. Applications in several systems in several disciplines has generalized been from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Papers have applied qPATHINT to neocortical interactions and financial options.The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites.Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the author. However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets.This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks to fit EEG data to the SMNI model, with previous analytic forms for the quantum processes replaced by qPATHINT. The classical-quantum system is fit using the author's Adaptive Simulated Annealing (ASA) importance-sampling optimization code. Gaussian Quadratures are used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions.This project demonstrates how some hybrid classical-quantum systems may be calculated using only classical (super-)computers.Recent calculations also are reported using the closed-form expression, with and without shocks.