compute the minimum distance of QLDPC using Mixed Integer Programming

[Fe-r-oz]

This PR implements the Mixed Integer programming (MIP) approach to compute the minimum distance of QLDPC using GNU's Linear Programming Kit. This method is used by Panteleev and Kalachev and by Bravyi et. al.. The latter reference mentioned that this MIP approach was originally developed in 2011 and used in this reference

This PR allows the users to compute the minimum distance with ease and also provide the necessary documentation along with the relevant modern usecases. The tests have been conducted in #435

ILP/MILP methods: https://quantumcomputing.stackexchange.com/questions/37289/compute-the-exact-minimum-distance-of-a-qecc-with-integer-linear-programming-met

P.S. Mixed Integer Programming (MIP) or mixed integer linear program refer to same thing in the literature, in this context.

Edit:

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.
• We recently started enforcing formatting checks. If formatting issues are reported in the new code you have written, please correct them.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 83.42%. Comparing base (6065fab) to head (e40b4b3).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #439      +/-   ##
==========================================
+ Coverage   82.82%   83.42%   +0.60%     
==========================================
  Files          70       73       +3     
  Lines        4651     4808     +157     
==========================================
+ Hits         3852     4011     +159     
+ Misses        799      797       -2     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[Fe-r-oz]

Please help review this PR, thank you :)

Thanks to GNU for open-souring GLPK. I have tested all the instances of 2bga codes using distance and added other tests for correctness. Many more tests are in #435. Referring to #353 as it's related a issue. This PR aims to provide the first reasonable step. This MIP method is used by Panteleev and Kalachev and by Bravyi et. al.. This MILP method that Bravyi used was also asked on stack exchange. The end goal is to be able to compute minimum distance of QECC/QLDPC codes with n being $10^3$ or $10^4$: QDistRnd or MaxSAT solvers or upcoming algorithms appear to be helpful for that. There is a lot more work to be done in this direction. I will be happy if this PR is one of my PRs you are most excited about, along with in-place Ted's Pauli measurement algorithm PR. :)

Possible Future TODOs include:

• More performance optimizations if possible
• comparison with distance solvers from stim.
  • It uses Microsoft's z3 SAT solver. This method formulate task the problem into maxSAT problem. Julia does have the z3.jlbinding! stim also uses pysat for maxSAT problem.
  • stim also uses pysat to convert distance-finding problem into a maxSAT problem
• comparison with QDistRnd Package from GAP: we can use Oscar to directly use QDistRnd package. User would have to provide the matrix is MTX format.
• integrate latest solvers: Grassl, Eric and others are working towards it and have some papers in this new directions
• implement minimum distance solvers in pure Julia
• Benchmark Lifted product codes Lifted and lifted product codes via Hecke's GroupAlgebra #356
• Benchmark 2BGA codes with finitely presented groups and with Direct product of General Groups, e.g. direct product of two finite groups using Oscar add QuantumCliffordOscarExt to provide convenient API for finitely presented groups via specific group presentation #400
• Benchmark Haah's cubic code using abelian group ℤ₃ˣ³ via Hecke's Group Algebra #388,
• Benchmark Coprime Bivariate Bicycle code via Hecke's Group Algebra #378
• Benchmark Multivariate Bicycle code via Hecke's Group Algebra #381
• Benchmark Implementing Bivariate Bicycle Codes using 2BGA as the parent via Hecke's Group Algebra #399
• Benchmark add tests and examples of Cₘ × C₂ 2BGA codes #392
• Benchmark Honeycomb color code via Hecke's Group Algebra #436
• Benchmark more tests of bivariate bicycle codes #441
• Benchmark Haah's cubic code via LP construction method #442
• Benchmark color codes with varying distances according to formula
• Test MIP minimum distance solver for color codes with varying distances according to formula: Color codes support 1 #361
• Cross-check the minimum distance of La-Cross codes in [[2n², 2k², d]] and [[(n - k)² + n², k², d]] La-cross code using Hecke's univariate polynomial ring #471

[Krastanov]

This is really interesting and deserving of a bounty.

Regrettably there are a few merge conflicts related to the doc fixes in an earlier PR. Could you fix those?

I also probably would suggest looking into a slightly different API, or at least some easier way to support independent solvers. But that can be discussed after the first round of review.

[Krastanov]

I pushed a few minor changes:

• making sure the docs build correctly and list the new content
• a different more idiomatic way to give hints about what needs to be imported
• other mixed cleanup

Could you:

• check the changes in my last commit and make sure I have not broken anything
• fix the existing latex in the docstring you have added (if you render the docs and open the ECC_API page, you will see that your docstring is not formatted correctly (the latex in it is not formatted))
• add a docstring to the struct where I have left a bunch of TODOs. You can used DocStringExtensions to simplify that by putting a docstring for each struct field (QuantumSavory.ProtocolZoo uses that a lot)

To build the docs locally you can do

cd QuantumClifford.jl
julia --project=docs -e '
            using Pkg
            Pkg.develop(PackageSpec(path=pwd()))
            Pkg.instantiate()';
julia --project=docs -i docs/make.jl
# and then the docs are in the build folder

If you do that you will see that currently there are a few issues:

The admonitions are note rendered correctly:

The latex is not rendered (just one example, make sure to correct all of the latex in your pr):

There is a missing citation:

This is a great addition! We should push it out soon and make sure the bounty for it is claimed.

[Fe-r-oz]

Thank you very much for the amazing improvements and suggestions on the documentation build!! Nothing appears to be broken by the changes.

Regarding LaTeX rendering: I tried building the documentation locally, but since I don’t yet have VSCode installed, I didn’t get the HTML link of documentation after processing the commands. For LaTeX, I used @doc raw""" to avoid escaping \ or $, which hopefully seems to work well.

A few other fixes to the aforementioned issues: resolved the formatting error with !!! note, added the missing citation and followed the QuantumSavory.ProtocolZoo format for the MIPDistanceAlgorithm docstring.

The CI documentation error is unrelated to this PR—it occurs because linkcheck sometimes fails when testing tutorial Jupyter notebook link. Please help review this PR, Thank you!!

[Krastanov]

Regarding LaTeX rendering: I tried building the documentation locally, but since I don’t yet have VSCode installed, I didn’t get the HTML link of documentation after processing the commands

Not immediately important, but just posting for future reference: VS Code should not be related or necessary for the doc building. You probably did not get the index.html and others because your doc build failed. If that is the case, it will report why it failed. You can just add exceptions to those failures in the config in main.jl, e.g. warnonly = [:some_other_reason, ...] and checklinks=false.

[Krastanov]

Thanks! This looks great. One last comment left below.

After you address that comment, please go ahead and officially claim the bounty, no need to wait for review. It would be convenient for me if you make the claim promptly, as otherwise some of the processing can be significantly delayed.

[Krastanov]

Probably last comment on this:

These two configuration options are not "orthogonal". Can we simplify them a bit. For instance, it looks like we can just completely drop all_logical_qubits as logical_qubit === nothing can already unambiguously mean "all logical qubits".

[Fe-r-oz]

Absolutely agree!! Thank you very much!!

[Fe-r-oz]

VS Code should not be related or necessary for the doc building.

Thank you for your amazing suggestions!! That's awesome news!!

Thank you very much for helpful suggestion!! Incorporated the code review suggestion and added remaining distance test for the remaining GB codes in (test_ecc_generalized_bicycle_codes.jl) so that the entire testset there does not take more than extra 1 minute. When I test all the GB codes there, it takes total 2 minutes to run the entire set of codes so I left one of them out so extra time < 1 min. Testing individually, it takes ≤ 60s to test distance of each of these GB codes though, within default time limit of solver. Please let me know if there’s anything else that needs to be done!! Thank you!!

[Fe-r-oz]

Hi Stefan, Please help review this PR when you have a moment! Once it’s pushed, I’m excited to start working on the satisfiability formulation of minimum distance problem as we discussed in the meeting! Really appreciate your very helpful suggestions in shaping this work! Thank you! 😀

[Fe-r-oz]

I have added AbstractDistanceAlg to the QECCore because the abstract ECC interfaces are now imported from there.

All the tests related to this PR pass. The failing CI JET =true/false tests fail on master CI so they are not related to this PR.

This PR is ready for review! Thank you!

[Fe-r-oz]

Hi, @Krastanov, just a friendly bump on this PR! Thank you!

[Krastanov]

Thank you, this is great!

[Fe-r-oz]

Thank you! 😃