SQUAB
A Fast Benchmarking Software
for Surface Quantum Computing Architectures

In this page, we go through an example to illustrate how our software can help to design a quantum architecture and test its robustness. We construct a tiling supporting a quantum architecture and we generate a performance report to evaluate its performance.

• Preliminaries
• Help
• Create a tiling
• Puncture the tiling
• Open some boundaries
• Construct a periodic tiling
• Parameters of the code
• Generate a performance report

Preliminaries

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• Using the instructions given here, start with the following steps:
  
  1. Download and extract the files
  2. Compile with make clean
  3. Execute ./squab in the terminal
  4. Open the file figure.pdf using Skim or another PDF reader
  
  You should now see something like that
  
  
  
  
  
  with at the left the file figure.pdf opened with Skim and at the right the terminal. A list of all the commands is printed. You can now construct your tiling.
  

Help

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• At any time you can use Help and HelpMin to print a list of all the commands.
  >>HelpMin
  
  

Create a tiling

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• Construct a 4-regular tiling of size 5 x 3:
  
  >>Tiling 4 5 3
>>Draw
  
  



• The same command with degree 3 or 6 allows to constuct hexagon and triangle tilings. One can also construct a tiling from scratch starting from a grid of vertices and adding faces of any shape using the commands Grid lx ly and the command AddFace k v1 v2 ... vk that create a face going through the vertices v1 v2 ... vk. In that way, we can construct a small tiling and then obtain a periodic version of it using Translate. When constructing a tiling from a grid CleanV can be used at the end to remove useless vertices.

Puncture the tiling

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• Create a hole by removing face 6:
  
  >>Tiling 4 5 3
>>Hole 6
>>Draw
  
  



• Alternatively, one can create a rectangle hole from vertex v3 to v16 as follows.
  
  >>Tiling 4 5 3
>>HoleRect 3 16
>>Draw
  
  



• See also HoleList to remove a list of faces or HoleRectOpen to create a rectangle hole with open boundaries.

Open some boundaries

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• Open a list of 3 edges on the boundary
  
  >>Tiling 4 5 3
>>HoleRectangle 3 16
>>OpenList 3 6 9 12
>>Draw
  
  



• Open edges are represented by dotted line and their enpoints (open vertices) are white nodes. One can open a single egde using Open e. The command HoleRectOpen creates a rectangle hole with open boundaries. One can also close an open edge or a list of open edges using Close and CloseList.

Construct a periodic tiling

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• Translated the tiling 3 times in the direction (0,3) then twice in the direction (5,0)
  
  >>Tiling 4 5 3
>>HoleRectangle 3 16
>>OpenList 3 6 9 12
>>Translate 3 0 3
>>Translate 2 5 0
>>Draw
  
  

Parameters of the code

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• The command Code is used to print the code's parameters.
  
  >>Tiling 4 5 3
>>HoleRectangle 3 16
>>OpenList 3 6 9 12
>>Translate 3 0 3
>>Translate 2 5 0
>>Code
  
  



• Quantum error-correction with this layout encodes 11 logical qubits and requires 17 physical qubits per logical qubit. More parameters will be obtained using Report

Generate a performance report

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• The function Report runs the simulation and generate a performance report. Below, using Report 0 .3 .01 100000, we simulate the performance of our surface code for against erasure at an erasure rate varying between 0 and .3 with step size .01 and we run up to 100000 trials for each data point.
  
  >>Tiling 4 5 3
>>HoleRectangle 3 16
>>OpenList 3 6 9 12
>>Translate 3 0 3
>>Translate 2 5 0
>>Report 0 .3 .01 100000
  
  
  
  In only 6 lines, one can generate a performance report of a non-trivial planar architecture! This report was generated in 14 seconds.