I’m implementing an arbitrary single-qubit gate in Q# , using pauli decompositon. The goal is to match the behavior of a specified unitary matrix acting on a single qubit. Here’s the code I’ve written so far:
operation Task1 (q : Qubit, matrix : Complex[][]) : Unit is Adj + Ctl {
let u00 = matrix[0][0];
let u01 = matrix[0][1];
let u10 = matrix[1][0];
let u11 = matrix[1][1];
let det_arg = ArgComplex(MinusC(TimesC(u00, u11), TimesC(u01, u10)));
let phase = 0.5 * det_arg;
let theta = 2.0 * ArcTan2(AbsComplex(u10), AbsComplex(u00));
let ang1 = ArgComplex(u11);
let ang2 = ArgComplex(u10);
let phi = ang1 + ang2 - det_arg;
let lam = ang1 - ang2;
R1(phase, q);
Rz(lam, q);
Ry(theta, q);
Rz(phi, q);
}
When running this operation through the testing harness, my output matches the expected values for u01 and u11, but u00 and u10 don't match. I'm not sure what’s causing this discrepancy and would appreciate guidance on where I might be going wrong.
Is there an issue in the way I’m calculating the parameters (phase, theta, phi, lam) for the rotation gates to reconstruct the unitary matrix?