private int i1, i2; // Indices of non-trivial submatrix.
public TwoLevelUnitary(Complex[,] mx, int i1, int i2)
{
Debug.Assert(MatrixUtils.IsMatrixUnitary(mx), "Matrix is not unitary");
this.mx = mx;
this.i1 = i1;
this.i2 = i2;
}
// Decomposes unitary matrix into product of 2-level unitary matrices.
// Every resulting 2-level matrix is represnted by 2x2 non-trivial submatrix and indices
// of this submatrix. Indices are guaranteed to be sorted and to differ in exactly one
// bit.
private IQArray <(IQArray <IQArray <Quantum.Math.Complex> >, long, long)> Decompose(
IQArray <IQArray <Quantum.Math.Complex> > unitary)
{
Complex[,] a = MatrixUtils.MatrixFromQs(unitary);
return(new QArray <(IQArray <IQArray <Quantum.Math.Complex> >, long, long)>(
TwoLevelDecomposeGray(a).Select(matrix => matrix.ToQsharp())
));
}
// Returns list of two-level unitary matrices, which multiply to A.
// Every matrix has indices differing in exactly 1 bit.
private static IEnumerable <TwoLevelUnitary> TwoLevelDecomposeGray(Complex[,] A)
{
int n = A.GetLength(0);
Debug.Assert(A.GetLength(1) == n, "Matrix is not square.");
Debug.Assert(MatrixUtils.IsMatrixUnitary(A), "Matrix is not unitary.");
int[] perm = GrayCode(n);
A = PermuteMatrix(A, perm);
foreach (TwoLevelUnitary matrix in TwoLevelDecompose(A))
{
matrix.ApplyPermutation(perm);
matrix.OrderIndices();
yield return(matrix);
}
}