local-decoders

code relating to the construction and analysis of 1) Tsirelson's 1d memory [1] and its generalizations, and 2) a local Tsirelson-inspired decoder for the 2d toric code. work done jointly with Shankar Balasubramanian and Margarita Davydova [2].

main files

• circuit_simulator.jl main simulation code capable of computing the following quantities for the codes listed below:
  • time evolution of logical fidelity
  • relaxation times
  • spacetime trajectories under custom noise realizations
  • searches over low-weight noise realizations that lead to logical errors
  • statistical properties in long-time steady states (various moments of magnetization, statistics of domain wall sizes, etc.)
• gate_builder.jl builds circuits for below-listed codes
• gate_applier.jl applies circuits to states in the presence of various types of noise
• nilpotence_tester.jl used to verify the "nilpotence" property of gadgets used in the toric code automaton
• helper_functions.jl contains miscellaneous auxillary functions
• simulation_parameters.jl contains a repository of parameter values to be used by circuit_simulator.jl (threshold values, default number of samples, etc.)
• circuit_plotter.py plots data output (as .jld2 files) from circuit_simulator.jl
• 1d_circuit_visualizer.py draws diagrams of circuits (and spacetime spin configurations) for 1d codes
• 2d_circuit_visualizer.py an interactive visualizer for the toric code automaton
• scaling_plotter.py makes interactive plots for examining scaling collapses near critical points

currently supported codes

• 1d Tsirelson's automaton with base codes
  • 3- and 5-bit repetition codes
  • a [5, 2, 3] code
• A 2d version of Tsirelson's automaton based on 9-bit reptition codes
• 2d toric code

noise models

• "wire noise" (default): gates are implimented reliably, and iid noise is applied to each spin after the gates in a given layer have acted. for all but the toric code, the noise replaces a given spin by $\pm1$ with probability $p(1\pm \eta)/2$, and does nothing with probability $p$. for the toric code, a given spin is flipped with probability $p$.
• "measurement noise": each syndrome measurement independently gives the wrong outcome with probability $p$.
• "gadget noise": each gadget fails independently with probability $p$. when a gadget fails, its spacetime support incurrs a randomly chosen error from a pre-defined set (toric code), or the spins in the support are randomized (other codes). for the toric code, the supports of each gadget and the errors that occur when they fail can be modified in circuit_simulator.jl.
• each type of noise model also allows for a specific spacetime history of noise to be applied by appropriately modifying noise_hist in circuit_simulator.jl.

usage notes

• as written, circuit_simulator.jl is designed to be run in the REPL; changes to parameter values should be made by making direct edits to the relevant lines.
• the fps and length of animations produced by 2d_circuit_visualizer.py needed to be specified by hand by editing the relevant section of code.
• don't judge the lack of type declarations :)

to-do

• finish enumeration of threshold values in simuation_parameters.jl and default scaling exponents for critical points of different codes

references

1. Tsirelson's original paper (see page 26)
2. Our paper