Add conversion pattern for qecl.qec ops to convert-qecl-to-qecp pass

[joeycarter]

Context: The convert-qecl-to-qecp dialect-conversion pass requires a rewrite pattern for qecl.qec operations.

Description of the Change: This pass adds the QecCycleOpConversion rewrite pattern to the convert-qecl-to-qecp dialect-conversion pass. This pattern replaces qecl.qec ops with a call to a subroutine that performs a single cycle of quantum error correction. The QEC protocol used here is the "textbook" protocol for a CSS code, which applies separate X and Z stabilizers to obtain the respective error-syndrome measurement (ESM) results in order to apply Z and X corrections, respectively. The decoding of the ESM is abstracted by the qecp.decode_esm_css op, which will eventually be lowered to a runtime library call to perform the actually decoding (not yet implemented).

This PR also adds a handful of utility functions to help with the conversion pattern, such as the function qecp.tanner_graph_lib.dense_tanner_graph_to_csc(), which converts a dense parity-check matrix to the equivalent matrix in compressed sparse column (CSC) form.

Example:

Before:

builtin.module @test_module {
  func.func @test_program() {
    %0 = "test.op"() : () -> !qecl.codeblock<1>
    %1 = qecl.qec %0 : !qecl.codeblock<1>
    func.return
  }
}

After (using Steane code):

builtin.module @test_module {
  %0 = arith.constant dense<[0, 0, 1, 0, 1, 2, 0, 2, 1, 1, 2, 2]> : tensor<12xi32>
  %1 = arith.constant dense<[0, 1, 3, 6, 8, 9, 11, 12]> : tensor<8xi32>
  %2 = qecp.assemble_tanner %0, %1 : tensor<12xi32>, tensor<8xi32> -> !qecp.tanner_graph<12, 8, i32>
  %3 = arith.constant dense<[0, 0, 1, 0, 1, 2, 0, 2, 1, 1, 2, 2]> : tensor<12xi32>
  %4 = arith.constant dense<[0, 1, 3, 6, 8, 9, 11, 12]> : tensor<8xi32>
  %5 = qecp.assemble_tanner %3, %4 : tensor<12xi32>, tensor<8xi32> -> !qecp.tanner_graph<12, 8, i32>
  func.func @test_program() {
    %6 = "test.op"() : () -> !qecp.codeblock<1 x 7>
    %7 = func.call @qec_cycle_Steane(%6) : (!qecp.codeblock<1 x 7>) -> !qecp.codeblock<1 x 7>
    func.return
  }
  func.func private @qec_cycle_Steane(%6: !qecp.codeblock<1 x 7>) -> !qecp.codeblock<1 x 7> {
    %7 = qecp.alloc_aux : !qecp.qubit<aux>
    %8 = qecp.alloc_aux : !qecp.qubit<aux>
    %9 = qecp.alloc_aux : !qecp.qubit<aux>
    %10 = qecp.hadamard %7 : !qecp.qubit<aux>
    %11 = qecp.hadamard %8 : !qecp.qubit<aux>
    %12 = qecp.hadamard %9 : !qecp.qubit<aux>
    %13 = qecp.extract %6[0] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %14 = qecp.extract %6[1] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %15 = qecp.extract %6[2] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %16 = qecp.extract %6[3] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %17 = qecp.extract %6[4] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %18 = qecp.extract %6[5] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %19 = qecp.extract %6[6] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %20, %21 = qecp.cnot %10, %13 : !qecp.qubit<aux>, !qecp.qubit<data>
    %22, %23 = qecp.cnot %20, %14 : !qecp.qubit<aux>, !qecp.qubit<data>
    %24, %25 = qecp.cnot %22, %15 : !qecp.qubit<aux>, !qecp.qubit<data>
    %26, %27 = qecp.cnot %24, %16 : !qecp.qubit<aux>, !qecp.qubit<data>
    %28, %29 = qecp.cnot %11, %23 : !qecp.qubit<aux>, !qecp.qubit<data>
    %30, %31 = qecp.cnot %28, %25 : !qecp.qubit<aux>, !qecp.qubit<data>
    %32, %33 = qecp.cnot %30, %17 : !qecp.qubit<aux>, !qecp.qubit<data>
    %34, %35 = qecp.cnot %32, %18 : !qecp.qubit<aux>, !qecp.qubit<data>
    %36, %37 = qecp.cnot %12, %31 : !qecp.qubit<aux>, !qecp.qubit<data>
    %38, %39 = qecp.cnot %36, %27 : !qecp.qubit<aux>, !qecp.qubit<data>
    %40, %41 = qecp.cnot %38, %35 : !qecp.qubit<aux>, !qecp.qubit<data>
    %42, %43 = qecp.cnot %40, %19 : !qecp.qubit<aux>, !qecp.qubit<data>
    %44 = qecp.insert %6[0], %21 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %45 = qecp.insert %44[1], %29 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %46 = qecp.insert %45[2], %37 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %47 = qecp.insert %46[3], %39 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %48 = qecp.insert %47[4], %33 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %49 = qecp.insert %48[5], %41 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %50 = qecp.insert %49[6], %43 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %51 = qecp.hadamard %26 : !qecp.qubit<aux>
    %52 = qecp.hadamard %34 : !qecp.qubit<aux>
    %53 = qecp.hadamard %42 : !qecp.qubit<aux>
    %54, %55 = qecp.measure %51 : i1, !qecp.qubit<aux>
    %56, %57 = qecp.measure %52 : i1, !qecp.qubit<aux>
    %58, %59 = qecp.measure %53 : i1, !qecp.qubit<aux>
    qecp.dealloc_aux %55 : !qecp.qubit<aux>
    qecp.dealloc_aux %57 : !qecp.qubit<aux>
    qecp.dealloc_aux %59 : !qecp.qubit<aux>
    %60 = tensor.from_elements %54, %56, %58 : tensor<3xi1>
    %61 = qecp.decode_esm_css(%60 : tensor<3xi1>) %2 : !qecp.tanner_graph<12, 8, i32> -> tensor<1xindex>
    %62 = arith.constant 0 : index
    %63 = arith.constant 1 : index
    %64 = arith.constant 1 : index
    %65 = scf.for %66 = %62 to %63 step %64 iter_args(%67 = %50) -> (!qecp.codeblock<1 x 7>) {
      %68 = tensor.extract %61[%66] : tensor<1xindex>
      %69 = arith.index_cast %68 : index to i64
      %70 = arith.constant -1 : i64
      %71 = arith.cmpi ne, %69, %70 : i64
      %72 = scf.if %71 -> (!qecp.codeblock<1 x 7>) {
        %73 = qecp.extract %67[%68] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
        %74 = qecp.z %73 : !qecp.qubit<data>
        %75 = qecp.insert %50[%68], %74 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
        scf.yield %75 : !qecp.codeblock<1 x 7>
      } else {
        scf.yield %67 : !qecp.codeblock<1 x 7>
      }
      scf.yield %72 : !qecp.codeblock<1 x 7>
    }
    %76 = qecp.alloc_aux : !qecp.qubit<aux>
    %77 = qecp.alloc_aux : !qecp.qubit<aux>
    %78 = qecp.alloc_aux : !qecp.qubit<aux>
    %79 = qecp.extract %72[0] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %80 = qecp.extract %72[1] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %81 = qecp.extract %72[2] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %82 = qecp.extract %72[3] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %83 = qecp.extract %72[4] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %84 = qecp.extract %72[5] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %85 = qecp.extract %72[6] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
    %86, %87 = qecp.cnot %79, %76 : !qecp.qubit<data>, !qecp.qubit<aux>
    %88, %89 = qecp.cnot %80, %87 : !qecp.qubit<data>, !qecp.qubit<aux>
    %90, %91 = qecp.cnot %81, %89 : !qecp.qubit<data>, !qecp.qubit<aux>
    %92, %93 = qecp.cnot %82, %91 : !qecp.qubit<data>, !qecp.qubit<aux>
    %94, %95 = qecp.cnot %88, %77 : !qecp.qubit<data>, !qecp.qubit<aux>
    %96, %97 = qecp.cnot %90, %95 : !qecp.qubit<data>, !qecp.qubit<aux>
    %98, %99 = qecp.cnot %83, %97 : !qecp.qubit<data>, !qecp.qubit<aux>
    %100, %101 = qecp.cnot %84, %99 : !qecp.qubit<data>, !qecp.qubit<aux>
    %102, %103 = qecp.cnot %96, %78 : !qecp.qubit<data>, !qecp.qubit<aux>
    %104, %105 = qecp.cnot %92, %103 : !qecp.qubit<data>, !qecp.qubit<aux>
    %106, %107 = qecp.cnot %100, %105 : !qecp.qubit<data>, !qecp.qubit<aux>
    %108, %109 = qecp.cnot %85, %107 : !qecp.qubit<data>, !qecp.qubit<aux>
    %110 = qecp.insert %72[0], %86 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %111 = qecp.insert %110[1], %94 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %112 = qecp.insert %111[2], %102 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %113 = qecp.insert %112[3], %104 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %114 = qecp.insert %113[4], %98 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %115 = qecp.insert %114[5], %106 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %116 = qecp.insert %115[6], %108 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
    %117, %118 = qecp.measure %93 : i1, !qecp.qubit<aux>
    %119, %120 = qecp.measure %101 : i1, !qecp.qubit<aux>
    %121, %122 = qecp.measure %109 : i1, !qecp.qubit<aux>
    qecp.dealloc_aux %118 : !qecp.qubit<aux>
    qecp.dealloc_aux %120 : !qecp.qubit<aux>
    qecp.dealloc_aux %122 : !qecp.qubit<aux>
    %123 = tensor.from_elements %117, %119, %121 : tensor<3xi1>
    %124 = qecp.decode_esm_css(%123 : tensor<3xi1>) %5 : !qecp.tanner_graph<12, 8, i32> -> tensor<1xindex>
    %125 = arith.constant 0 : index
    %126 = arith.constant 1 : index
    %127 = arith.constant 1 : index
    %128 = scf.for %129 = %125 to %126 step %127 iter_args(%130 = %116) -> (!qecp.codeblock<1 x 7>) {
      %131 = tensor.extract %124[%129] : tensor<1xindex>
      %132 = arith.index_cast %131 : index to i64
      %133 = arith.constant -1 : i64
      %134 = arith.cmpi ne, %132, %133 : i64
      %135 = scf.if %134 -> (!qecp.codeblock<1 x 7>) {
        %136 = qecp.extract %130[%131] : !qecp.codeblock<1 x 7> -> !qecp.qubit<data>
        %137 = qecp.x %136 : !qecp.qubit<data>
        %138 = qecp.insert %116[%131], %137 : !qecp.codeblock<1 x 7>, !qecp.qubit<data>
        scf.yield %138 : !qecp.codeblock<1 x 7>
      } else {
        scf.yield %130 : !qecp.codeblock<1 x 7>
      }
      scf.yield %135 : !qecp.codeblock<1 x 7>
    }
    func.return %135 : !qecp.codeblock<1 x 7>
  }
}

[sc-115303]

[codecov]

Codecov Report

❌ Patch coverage is 92.07921% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.01%. Comparing base (d21ea60) to head (3f6755d).

Files with missing lines	Patch %	Lines
..._interface/transforms/qecp/convert_qecl_to_qecp.py	91.30%	4 Missing and 4 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2754      +/-   ##
==========================================
+ Coverage   96.99%   97.01%   +0.02%     
==========================================
  Files         165      166       +1     
  Lines       18503    18599      +96     
  Branches     1783     1788       +5     
==========================================
+ Hits        17947    18044      +97     
+ Misses        399      397       -2     
- Partials      157      158       +1     

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[joeycarter]

I think this is wrong, self.qec_code.x_tanner is the parity check matrix, and dense_tanner_graph_to_csc just converts the dense matrix to a CSC matrix. But in fact what we want is the adjacency matrix of the Tanner graph in CSC format. Let me fix this...