Accelerate PBC layer commutation with symplectic bases

[jk20342]

Context:

PBCLayer checked a candidate against every operation already in the layer
this repeated Pauli normalization and became quadratic for large commuting layers

Description of the Change:

• store Pauli operators as packed X and Z bit vectors
• maintain a lazy row echelon basis over GF(2)
• test commutation with XOR and popcount against independent basis rows
• invalidate the basis when an operation is removed
• add an MLIR regression test for dependent commuting operators

Benefits:

• preserves layer membership and operation order
• bounds basis rank by the number of qubits
• avoids basis construction for disjoint only layers
• reached 26.7x speedup for 16000 dependent terms on 64 qubits

Possible Drawbacks:

None off the top of my head

Related GitHub Issues:

None

[zsb-xqc]

Thanks @jk20342, this looks like an efficient representation for the PBC layer, leading to a significant speedup. We will review shortly and get back to you.