multitree

Self-contained repository for multitree state preparation of the generalized Shor (GS) code, also called the Bell tree. Additional code and data available upon request; please contact gsommers@princeton.edu.

To use the modules included in this repo (in the subdirectory src/), execute the following from the command line:

export JULIA_LOAD_PATH="~/path/to/repo:"

or, inside a Julia session, do:

push!(LOAD_PATH, "~/path/to/repo")

Then you can access the functions in these modules through the command using <module name>.

External dependencies

• QuantumClifford (for stabilizer formalism)
• Nemo (for finite fields)

The module TensorExtensions.jl is mostly copied from the code here, a Julia implementation of the MATLAB function NCON, modified to allow for alternative definitions of "multiplication" (see the functions tropical_matrix_mult, normalize_mult).

Code

The modules contained in src/ fall into three broad groups:

• Functions for (stacked) probability passing of the GS code:
  • Higher-level functions: BellPrepErrorDecoder.jl for classical simulations of state prep (generating error patterns on the fly, BellPrepSyndromeDecoder.jl for decoding state prep given a syndrome (used on experimental data), BellMemoryDecoder.jl for decoding the Steane EC gadget. QuantinuumRuns.jl calls functions in BellPrepSyndromeDecoder.jl to process raw data for Quantinuum System H2.
  • Lower-level functions: BellTreeFaults.jl (propagating faults, initializing error nodes in the tensor network), BellTreeTensors.jl (basic data structures for the stacked decoder of state prep and probability passing decoder of EC; marginal updates of error probabilities), StackedTree.jl (tensor and index lists for stacked decoder), PauliNoise.jl (error tensors for Pauli channels, not specific to Bell tree)
• Functions for optimal decoding of fully heralded errors:
  • Higher-level functions: SteaneRuns.jl.
  • Lower-level functions: SteanePrep.jl (for state preparation) and SteaneSyndrome.jl (for syndrome extraction/Steane EC)
• General utilities
  • StabilizerTree.jl (track operators in binary tree with arbitrary gates)
  • BinaryFields.jl (boolean linear algebra)
  • TensorExtensions.jl (tensor network contraction)

Data

The folder dat/ contains data used to produce the figures in the main text:

• dat/heralded/ contains state preparation data for fully heralded errors (Fig. 3a)
• dat/unheralded/ contains state preparation data for unheralded errors, stacked decoder (Fig. 3b)
• dat/H2/erasures/ contains data from Quantinuum System H2, with added erasure errors (Fig. 4a)
• dat/H2/coherent/ contains data from Quantinuum System H2, with added heralded coherent errors (Fig. 4b)
• dat/memory/ contains data for one round and d rounds of syndrome measurement (Fig. 5)