Merge branch 'master' into bounds

.github/workflows/benchmark-comment.yml

@@ -26,7 +26,7 @@ jobs:
       - uses: actions/checkout@v4
 
       # restore records from the artifacts
-      - uses: dawidd6/action-download-artifact@v6
+      - uses: dawidd6/action-download-artifact@v7
         with:
           workflow: benchmark.yml
           name: performance-tracking

.github/workflows/ci-julia-nightly.yml

@@ -44,7 +44,7 @@ jobs:
           JULIA_NUM_THREADS: ${{ matrix.threads }}
           JET_TEST: ${{ matrix.jet }}
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}

.github/workflows/ci.yml

@@ -56,7 +56,7 @@ jobs:
         env:
           JULIA_NUM_THREADS: ${{ matrix.threads }}
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v4
+      - uses: codecov/codecov-action@v5
         with:
           file: lcov.info
           token: ${{ secrets.CODECOV_TOKEN }}

CHANGELOG.md

@@ -5,6 +5,15 @@
 
 # News
 
+## v0.9.16 - 2024-12-29
+
+- 100× faster unbiased `random_pauli`.
+- Enhancements to `GF(2)` Linear Algebra: unexported, experimental `gf2_row_echelon_with_pivots!`, `gf2_nullspace`, `gf2_rowspace_basis`.
+
+## v0.9.15 - 2024-12-22
+
+- `pftrajectories` now supports fast multiqubit measurements with `PauliMeasurement` in addition to the already supported single qubit measurements `sMX/Z/Y` and workarounds like `naive_syndrome_circuit`.
+
 ## v0.9.14 - 2024-11-03
 
 - **(fix)** `affectedqubits()` on `sMX`, `sMY`, and `sMR*`
@@ -75,7 +84,7 @@
 - Gate errors are now conveniently supported by the various ECC benchmark setups in the `ECC` module.
 - Significant improvements to the low-level circuit compiler (the sumtype compactifier), leading to faster Pauli frame simulation of noisy circuits.
 - Bump `QuantumOpticsBase.jl` package extension compat bound.
-- **(fix)** Remove printing of spurious debug info from the PyBP decoder. 
+- **(fix)** Remove printing of spurious debug info from the PyBP decoder.
 - **(fix)** Failed compactification of gates now only raises a warning instead of throwing an error. Defaults to slower non-compactified gates.
 
 ## v0.9.3 - 2024-04-10
@@ -93,7 +102,7 @@
 - Implemented `iscss` function to identify whether a given code is known to be a CSS (Calderbank-Shor-Steane) code.
 - Added the classical Reed-Muller code in the ECC module.
 - Added the surface code to the ECC module.
- 
+
 ## v0.9.0 - 2024-03-19
 
 - **(breaking)** The defaults in `random_pauli` are now `realphase=true` and `nophase=true`.

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumClifford"
 uuid = "0525e862-1e90-11e9-3e4d-1b39d7109de1"
 authors = ["Stefan Krastanov <[email protected]> and QuantumSavory community members"]
-version = "0.9.14"
+version = "0.9.16"
 
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
@@ -48,15 +48,15 @@ Combinatorics = "1.0"
 DataStructures = "0.18"
 DocStringExtensions = "0.9"
 Graphs = "1.9"
-Hecke = "0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34"
+Hecke = "0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35"
 HostCPUFeatures = "0.1.6"
 ILog2 = "0.2.3, 1, 2"
 InteractiveUtils = "1.9"
 LDPCDecoders = "0.3.1"
 LinearAlgebra = "1.9"
 MacroTools = "0.5.9"
-Makie = "0.20, 0.21"
-Nemo = "0.42.1, 0.43, 0.44, 0.45, 0.46, 0.47"
+Makie = "0.20, 0.21, 0.22"
+Nemo = "0.42.1, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48"
 Plots = "1.38.0"
 PrecompileTools = "1.2"
 PyQDecoders = "0.2.1"

README.md

@@ -41,21 +41,21 @@ To install it use:
 ```
 
 Works efficiently with
-[pure](https://quantumsavory.github.io/QuantumClifford.jl/dev/manual/#Stabilizers-1) and
-[mixed stabilizer](https://quantumsavory.github.io/QuantumClifford.jl/dev/mixed/#Mixed-Stabilizer-States-1)
+[pure](https://qc.quantumsavory.org/dev/stab-algebra-manual/#Stabilizers) and
+[mixed stabilizer](https://qc.quantumsavory.org/dev/mixed/#Mixed-Stabilizer-States)
 states of thousands of qubits
 as well as
-[sparse or dense Clifford operations](https://quantumsavory.github.io/QuantumClifford.jl/dev/manual/#Clifford-Operators-1)
+[sparse or dense Clifford operations](https://qc.quantumsavory.org/dev/stab-algebra-manual/#Clifford-Operators)
 acting upon them.
 
-Implements [Pauli frames](https://quantumsavory.github.io/QuantumClifford.jl/dev/ecc_example_sim/) for fast sampling.
+Implements [Pauli frames](https://qc.quantumsavory.org/dev/ecc_example_sim/) for fast sampling.
 
 Provides
-[canonicalization](https://quantumsavory.github.io/QuantumClifford.jl/dev/manual/#Canonicalization-of-Stabilizers-1),
-[projection](https://quantumsavory.github.io/QuantumClifford.jl/dev/manual/#Projective-Measurements-1), and
-[generation](https://quantumsavory.github.io/QuantumClifford.jl/dev/manual/#Generating-a-Pauli-Operator-with-Stabilizer-Generators-1) operations,
+[canonicalization](https://qc.quantumsavory.org/dev/stab-algebra-manual/#Canonicalization-of-Stabilizers),
+[projection](http://qc.quantumsavory.org/dev/stab-algebra-manual/#Projective-Measurements), and
+[generation](https://qc.quantumsavory.org/dev/stab-algebra-manual/#Generating-a-Pauli-Operator-with-Stabilizer-Generators) operations,
 as well as
-[partial traces](https://quantumsavory.github.io/QuantumClifford.jl/dev/manual/#Partial-Traces-1).
+[partial traces](https://qc.quantumsavory.org/dev/stab-algebra-manual/#Partial-Traces).
 
 ```jldoctest
 julia> P"X" * P"Z"

docs/src/references.bib

@@ -419,13 +419,13 @@ @article{RevModPhys.87.307
 }
 
 @misc{goodenough2024bipartiteentanglementnoisystabilizer,
-  title={Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes}, 
+  title={Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes},
   author={Kenneth Goodenough and Aqil Sajjad and Eneet Kaur and Saikat Guha and Don Towsley},
   year={2024},
   eprint={2406.02427},
   archivePrefix={arXiv},
   primaryClass={quant-ph},
-  url={https://arxiv.org/abs/2406.02427}, 
+  url={https://arxiv.org/abs/2406.02427},
 }
 
 @article{panteleev2021degenerate,
@@ -532,7 +532,7 @@ @article{wang2024coprime
 }
 
 @misc{voss2024multivariatebicyclecodes,
-  title={Multivariate Bicycle Codes}, 
+  title={Multivariate Bicycle Codes},
   author={Lukas Voss and Sim Jian Xian and Tobias Haug and Kishor Bharti},
   year={2024},
   eprint={2406.19151},
@@ -562,6 +562,29 @@ @article{haah2011local
   year={2011},
 }
 
+@article{golay1949notes,
+  title={Notes on digital coding},
+  author={Golay, Marcel JE},
+  journal={Proc. IEEE},
+  volume={37},
+  pages={657},
+  year={1949}
+}
+
+@book{huffman2010fundamentals,
+  title={Fundamentals of error-correcting codes},
+  author={Huffman, W Cary and Pless, Vera},
+  year={2010},
+  publisher={Cambridge university press}
+}
+
+@article{bhatia2018mceliece,
+  title={McEliece cryptosystem based on extended Golay code},
+  author={Bhatia, Amandeep Singh and Kumar, Ajay},
+  journal={arXiv preprint arXiv:1811.06246},
+  year={2018}
+}
+
 @article{hamming1950error,
   title={Error detecting and error correcting codes},
   author={Hamming, Richard W},
@@ -572,10 +595,3 @@ @article{hamming1950error
   year={1950},
   publisher={Nokia Bell Labs}
 }
-
-@book{huffman2010fundamentals,
-  title={Fundamentals of error-correcting codes},
-  author={Huffman, W Cary and Pless, Vera},
-  year={2010},
-  publisher={Cambridge university press}
-}

docs/src/references.md

@@ -56,6 +56,9 @@ For classical code construction routines:
 - [bose1960class](@cite)
 - [bose1960further](@cite)
 - [error2024lin](@cite)
+- [golay1949notes](@cite)
+- [huffman2010fundamentals](@cite)
+- [bhatia2018mceliece](@cite)
 - [hamming1950error](@cite)
 - [huffman2010fundamentals](@cite)
 

ext/QuantumCliffordHeckeExt/lifted_product.jl

@@ -28,7 +28,7 @@ During the construction, we do arithmetic operations to get the group algebra el
 Here `x` is the generator of the group algebra, i.e., offset-1 cyclic permutation, and `GA(1)` is the unit element.
 
 ```jldoctest
-julia> import Hecke: group_algebra, GF, abelian_group, gens; import LinearAlgebra: diagind;
+julia> import Hecke: group_algebra, GF, abelian_group, gens; import LinearAlgebra: diagind; using QuantumClifford.ECC;
 
 julia> l = 63; GA = group_algebra(GF(2), abelian_group(l)); x = gens(GA)[];
 
@@ -52,10 +52,12 @@ julia> code_n(c1), code_k(c1)
 (882, 24)
 ```
 
-A [[175, 19, d ≤ 0]] code from Eq. (18) in Appendix A of [raveendran2022finite](@cite),
+A [[175, 19, d ≤ 10]] code from Eq. (18) in Appendix A of [raveendran2022finite](@cite),
 following the 4th constructor.
 
 ```jldoctest
+julia> import Hecke; using QuantumClifford.ECC;
+
 julia> base_matrix = [0 0 0 0; 0 1 2 5; 0 6 3 1]; l = 7;
 
 julia> c2 = LPCode(base_matrix, l .- base_matrix', l);
@@ -162,15 +164,15 @@ Here is an example of a [[56, 28, 2]] 2BGA code from Table 2 of [lin2024quantum]
 with direct product of `C₄ x C₂`.
 
 ```jldoctest
-julia> import Hecke: group_algebra, GF, abelian_group, gens
+julia> import Hecke: group_algebra, GF, abelian_group, gens; using QuantumClifford.ECC;
 
 julia> GA = group_algebra(GF(2), abelian_group([14,2]));
 
 julia> x, s = gens(GA);
 
-julia> A = 1 + x^7
+julia> A = 1 + x^7;
 
-julia> B = 1 + x^7 + s + x^8 + s*x^7 + x
+julia> B = 1 + x^7 + s + x^8 + s*x^7 + x;
 
 julia> c = two_block_group_algebra_codes(A,B);
 
@@ -189,7 +191,7 @@ The ECC Zoo has an [entry for this family](https://errorcorrectionzoo.org/c/qcga
 A [[756, 16, ≤ 34]] code from Table 3 of [bravyi2024high](@cite):
 
 ```jldoctest
-julia> import Hecke: group_algebra, GF, abelian_group, gens
+julia> import Hecke: group_algebra, GF, abelian_group, gens; using QuantumClifford.ECC;
 
 julia> l=21; m=18;
 
@@ -215,10 +217,14 @@ where `𝐺ᵣ = ℤ/l₁ × ℤ/l₂ × ... × ℤ/lᵣ`.
 A [[48, 4, 6]] Weight-6 TB-QLDPC code from Appendix A Table 2 of [voss2024multivariatebicyclecodes](@cite).
 
 ```jldoctest
-julia> import Hecke: group_algebra, GF, abelian_group, gens; # hide
+julia> import Hecke: group_algebra, GF, abelian_group, gens; using QuantumClifford.ECC;
 
 julia> l=4; m=6;
 
+julia> GA = group_algebra(GF(2), abelian_group([l, m]));
+
+julia> x, y = gens(GA);
+
 julia> z = x*y;
 
 julia> A = x^3 + y^5;
@@ -238,10 +244,10 @@ where `𝑙` and `𝑚` are coprime, and can be expressed as univariate polynomi
 with generator `𝜋 = 𝑥𝑦`. They can be viewed as a special case of Lifted Product construction
 based on abelian group `ℤₗ x ℤₘ` where `ℤⱼ` cyclic group of order `j`.
 
-[108, 12, 6]] coprime-bivariate bicycle (BB) code from Table 2 of [wang2024coprime](@cite).
+[[108, 12, 6]] coprime-bivariate bicycle (BB) code from Table 2 of [wang2024coprime](@cite).
 
 ```jldoctest
-julia> import Hecke: group_algebra, GF, abelian_group, gens;
+julia> import Hecke: group_algebra, GF, abelian_group, gens; using QuantumClifford.ECC;
 
 julia> l=2; m=27;
 
@@ -252,6 +258,10 @@ julia> 𝜋 = gens(GA)[1];
 julia> A = 𝜋^2 + 𝜋^5  + 𝜋^44;
 
 julia> B = 𝜋^8 + 𝜋^14 + 𝜋^47;
+
+julia> c = two_block_group_algebra_codes(A, B);
+
+julia> code_n(c), code_k(c)
 (108, 12)
 ```
 
@@ -271,6 +281,8 @@ See also: [`two_block_group_algebra_codes`](@ref), [`bicycle_codes`](@ref).
 A [[254, 28, 14 ≤ d ≤ 20]] code from (A1) in Appendix B of [panteleev2021degenerate](@cite).
 
 ```jldoctest
+julia> import Hecke; using QuantumClifford.ECC
+
 julia> c = generalized_bicycle_codes([0, 15, 20, 28, 66], [0, 58, 59, 100, 121], 127);
 
 julia> code_n(c), code_k(c)
@@ -281,6 +293,8 @@ An [[70, 8, 10]] *abelian* 2BGA code from Table 1 of [lin2024quantum](@cite), wi
 order `l = 35`, illustrates that *abelian* 2BGA codes can be viewed as GB codes.
 
 ```jldoctest
+julia> import Hecke; using QuantumClifford.ECC
+
 julia> l = 35;
 
 julia> c1 = generalized_bicycle_codes([0, 15, 16, 18], [0, 1, 24, 27], l);
@@ -317,6 +331,8 @@ code with the group `G = ℤ₃ˣ³` corresponds to a cubic code.
 The ECC Zoo has an [entry for this family](https://errorcorrectionzoo.org/c/haah_cubic).
 
 ```jldoctest
+julia> import Hecke; using QuantumClifford.ECC;
+
 julia> c = haah_cubic_codes([0, 15, 20, 28, 66], [0, 58, 59, 100, 121], 6);
 
 julia> code_n(c), code_k(c)

src/QuantumClifford.jl

@@ -1168,6 +1168,69 @@ function gf2_H_to_G(H)
     G[:,invperm(sindx)]
 end
 
+"""Performs in-place Gaussian elimination on a binary matrix and returns
+its *row echelon form*,*rank*, the *transformation matrix*, and the *pivot
+columns*. The transformation matrix that converts the original matrix into
+the row echelon form. The `full` parameter controls the extent of elimination:
+if `true`, only rows below the pivot are affected; if `false`, both above and
+below the pivot are eliminated."""
+function gf2_row_echelon_with_pivots!(M::AbstractMatrix{Int}; full=false)
+    r, c = size(M)
+    N = Matrix{Int}(LinearAlgebra.I, r, r)
+    p = 1
+    pivots = Int[]
+    for col in 1:c
+        @inbounds for row in p:r
+            if M[row, col] == 1
+                if row != p
+                    M[[row, p], :] .= M[[p, row], :]
+                    N[[row, p], :] .= N[[p, row], :]
+                end
+                break
+            end
+        end
+        if M[p, col] == 1
+            if !full
+                elim_range = p+1:r
+            else
+                elim_range = 1:r
+            end
+            @simd for j in elim_range
+                @inbounds if j != p && M[j, col] == 1
+                    M[j, :] .= (M[j, :] .+ M[p, :]) .% 2
+                    N[j, :] .= (N[j, :] .+ N[p, :]) .% 2
+                end
+            end
+            p += 1
+            push!(pivots, col)
+        end
+        if p > r
+            break
+        end
+    end
+    rank = p - 1
+    return M, rank, N, pivots
+end
+
+"""The nullspace of a binary matrix."""
+function gf2_nullspace(H::AbstractMatrix{Int})
+    m = size(H',1)
+    _, matrix_rank, transformation_matrix, _ = gf2_row_echelon_with_pivots!(copy(H)')
+    if m == matrix_rank
+        # By the rank-nullity theorem, if rank(M) = m, then nullity(M) = 0
+        return zeros(Bool, 1, m)
+    end
+    # Extract the nullspace from the transformation matrix
+    return transformation_matrix[matrix_rank+1:end, :]
+end
+
+"""The basis for the row space of the binary matrix."""
+function gf2_rowspace_basis(H::AbstractMatrix{Int})
+    pivots = gf2_row_echelon_with_pivots!(copy(H)')[4]
+    # Extract the rows corresponding to the pivot columns
+    H[pivots,:]
+end
+
 ##############################
 # Error classes
 ##############################

src/ecc/ECC.jl

@@ -388,6 +388,7 @@ include("codes/quantumreedmuller.jl")
 include("codes/classical/reedmuller.jl")
 include("codes/classical/recursivereedmuller.jl")
 include("codes/classical/bch.jl")
+include("codes/classical/golay.jl")
 include("codes/classical/hamming.jl")
 
 # qLDPC