Verifying Fault-Tolerance of Quantum Error Correction Codes

Prerequisite

• docker is required to perform artifact evaluation.
• x86 or amd64 CPU.

Build

1. Build and run the corresponding Docker image. It will handle all dependencies and packages:

docker build -t vftqecc .
docker run -it vftqecc

2. Inside Docker, you will be at the project directory /workspace/QuantumSE.jl. Install the necessary Julia packages by using the following script.

julia instantiate.jl

Then, follow the Case Study section to test different examples.

Case Study

Cat State Preparation

The following steps produce the verification results of cat state preparation shown in Fig. 5 in the paper.

Run example/CatPreparation.jl with one parameter. The parameter is the number of faults to be tolerated, taking value in $[1, 2, 3, \ldots]$. After the run is completed, the last two lines of output are the verification result ("Pass" or "Fail") and the running time. For example:

When the number of faults is no more than $2$, it is fault-tolerant. For example, if you run:

julia example/CatPreparation.jl 2

then the results should be like

>>> Pass!
Cat State Preparation, num_faults=2, time=2.1842598915100098

When the number of faults is larger than $2$, it is non-fault-tolerant. For example, if you run:

julia example/CatPreparation.jl 3

then the results should be like

>>> Fail!
Cat State Preparation, num_faults=3, time=2.1932621002197266

Fault Tolerance Verification

The results of fault tolerance verification (see Table 1 in the paper) are produced by the following steps.

Run example/ColorCode.jl, example/RotatedSurfaceCode.jl, or example/ToricCode.jl with two parameters. The first parameter is the type of gadget, taking value in [prep, cnot, meas, ec]. The second parameter is the code distance, taking values in odd numbers (Color code only supports distances $3$ and $5$).

Here are some examples:

julia example/ColorCode.jl ec 5

julia example/RotatedSurfaceCode.jl meas 3

julia example/ToricCode.jl prep 3

Then, Run example/QuantumReedMullerCode.jl without parameters.

julia example/QuantumReedMullerCode.jl

After the run is completed, the last two lines of output are the verification result (should be "Pass") and the running time. For example:

>>> Pass!
Color Code, ec, [n,k,d]=[17,1,5], time=20.980690174102783

Reproducing Table 1

For the reader's convenience, we provide here the parameters corresponding to the results in Table 1.

QECC	[n,k,d]	Prep.	CNOT	Meas.	EC
Color Code	[7,1,3]	prep 3	cnot 3	meas 3	ec 3
Color Code	[17,1,5]	prep 5	cnot 5	meas 5	ec 5
Rotated Surface Code	[9,1,3]	prep 3	cnot 3	meas 3	ec 3
Rotated Surface Code	[25,1,5]	prep 5	cnot 5	meas 5	ec 5
Rotated Surface Code	[49,1,7]	prep 7	cnot 7	meas 7	ec 7
Toric Code	[18,2,3]	prep 3	cnot 3	meas 3	ec 3
Toric Code	[50,2,5]	prep 5	cnot 5	meas 5	ec 5
Quantum Reed-Muller Code	[15,1,3]	N.A.	N.A.	N.A.	no parameter

The first parameter is the type of gadget to be verified (i.e., Preparation, CNOT, Measurement and Error Correction). The second parameter is the code distance $d$ of the QECC (there is no need to specify $n$ and $k$ since they are determined by $d$). You can set $d$ to any odd number $>1$ (for Color Code, we only support $d\leq 5$). However, larger $d$ may result in significantly longer running times.

You can also use the following script, which can automatically run all experiments in Table 1.

bash run_table1.sh

The experiments are run in row-major order and results are recorded in the file Table1_results.txt. Due to the time cost, the row for Rotated Surface Code with $d=7$ is deferred to the end and the time-out setting is skipped.

Larger Code Distance

If you set $d$ to a larger value, e.g. run julia example/RotatedSurfaceCode.jl meas 7, you may encounter the following error,

NERRS should be >= 13
ERROR: LoadError: AssertionError: false

Then, you need to provide the required number ($13$ in this case) as the third parameter, that is, run julia example/RotatedSurfaceCode.jl meas 7 13.

Build outside Docker

To use our tool outside Docker, you need to have the following software installed on your system:

• Julia 1.10.5. Due to frequent API changes, we can only support up to Julia 1.10 LTS.
• Bitwuzla SMT solver 0.7.0

More detailed instructions can be found in the file Dockerfile.

Copyright

This project is based on QuantumSE.jl, originally developed by Fang Wang and licensed under the MIT License.

Modifications and extensions © 2025 Kean Chen.