QuantumACES.jl is a package for designing and simulating scalable and performant Pauli noise characterisation experiments for stabiliser circuits with averaged circuit eigenvalue sampling (ACES). It is particularly interested in characterising the noise associated with fault-tolerant gadgets in the context of topological quantum error correcting codes, such as surface code syndrome extraction circuits.

The methods used in this package are detailed in arXiv:2404.06545, and the code generating the data for this paper can be found in the scalable_aces folder on the scalable_aces branch. These methods build on the original ACES protocol presented in arXiv:2108.05803. This package relies on Stim for stabiliser circuit simulations.

First parameterise a depolarising noise model with single-qubit gate infidelity r_1, two-qubit gate infidelity r_2, and measurement infidelity r_m, and a log-normal random Pauli noise model with the same gate infidelities and a standard deviation of the underlying normal distributions total_std_log, alongside a random seed used when generating the noise model.

r_1 = 0.075 / 100
r_2 = 0.5 / 100
r_m = 2.0 / 100
total_std_log = sqrt(log(10 / 9))
seed = UInt(0)
dep_param = get_dep_param(r_1, r_2, r_m)
log_param = get_log_param(r_1, r_2, r_m, total_std_log; seed = seed)

Then generate the syndrome extraction circuit for a distance dist (rotated) surface code.

dist = 3
rotated_param = get_rotated_param(dist)
rotated_planar = get_circuit(rotated_param, dep_param)

Next, generate an experimental design for this circuit.

d = generate_design(rotated_planar)

Alternatively, optimise an experimental design to improve its sample efficiency.

d = optimise_design(rotated_planar, options = OptimOptions(; ls_type = :wls, seed = seed))

Create a copy of the optimised design that associates log-normal random Pauli noise with the circuit, and simulate repetitions rounds of an ACES noise characterisation experiment across all of the supplied measurement budgets in budget_set, which are measurement shots normalised by the time taken to perform the experiment.

d_log = update_noise(d, log_param)
budget_set = [10^6; 10^7; 10^8]
repetitions = 20
aces_data = simulate_aces(d_log, budget_set; repetitions = repetitions)

We can compare the performance to performance predictions at the largest measurement budget, although we note that the z-scores will not be normally distributed as the underlying distribution is not quite normal.

wls_merit_log = calc_wls_merit(d_log)
fgls_z_scores =
    (aces_data.fgls_gate_norm_coll[:, 3] .- wls_merit_log.expectation) /
    sqrt(wls_merit_log.variance)

Next, calculate the performance scaling of this design as a fuction of the code distance up to some large distance dist_max with the weighted least squares (WLS) estimator, for both depolarising and log-normal random Pauli noise.

dist_max = 9
dep_planar_scaling = calc_depolarising_planar_scaling(d, dist_max; ls_type = :wls)
log_planar_scaling = calc_lognormal_planar_scaling(d_log, dist_max; ls_type = :wls, seed = seed)

Next, transfer the optimised experimental design to the syndrome extraction circuit for a distance dist_big surface code with log-normal random Pauli noise.

dist_big = 13
rotated_param_big = get_rotated_param(dist_big)
rotated_planar_big = get_circuit(rotated_param_big, log_param)
d_big = generate_design(rotated_planar_big, d.tuple_set_data)

We can simulate a large-scale ACES noise characterisation experiment across the supplied measurement budgets.

budget_set_big = [10^6; 10^7; 10^8; 10^9]
aces_data_big = simulate_aces(d_big, budget_set_big)

Finally, we compare the performance to predictions across the measurement budgets, although note that we would not expect the z-scores here to actually correspond to a normal distribution as the underlying distribution is not quite normal, and there is a substantive amount of uncertainty associated with the fit.

pred_expectation = log_planar_scaling.expectation_fit(dist_big)
pred_variance = log_planar_scaling.variance_fit(dist_big)
fgls_z_scores_big =
    (aces_data_big.fgls_gate_norm_coll[1, :] .- pred_expectation) / sqrt(pred_variance)

To install this package, run the following command in the Julia REPL.

] add QuantumACES

This package relies on the Python package Stim to perform stabiliser circuit simulations. It calls Stim with PythonCall. By default, PythonCall creates its own Python environment, but you may wish to use an existing Python installation.

One helpful method for managing Python versions is pyenv, or for Windows, pyenv-win; these are analogous to Juliaup for Julia. The following assumes you are using pyenv or pyenv-win.

On Windows, to instruct PythonCall to use the Python version set by pyenv, configure PythonCall's environment variables by adding the following to your ~/.julia/config/startup.jl file

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"
python_exe = readchomp(`cmd /C pyenv which python`)
ENV["JULIA_PYTHONCALL_EXE"] = python_exe

On Unix systems, shell commands are parsed directly by Julia and appear to be unaware of your PATH variable, and I am not sure how to work around this. Therefore, you may need to manually supply python_exe for the Python version <version> as

python_exe = homedir() * "/.pyenv/versions/<version>/bin/python"

Then ensure Stim is installed by running pip install stim in your terminal.