2
$\begingroup$

I have a solution to the Peres-Mermin magic squares game (Wikipedia quantum pseudo-telepathy)

I simulate the six measurements using projective (non-unitary) measurement operators like in Nielson and Chuang's equation 2.94. I apply each of the $M_m$ to the state vector to generate a move by a player. The move, $\pm 1$, is the eignevalue.

Anyway, I want to port my solutin to qiskit so that I can run it on a real quantum computer. However, I am faced with a conceptual or mathematical difficulty. My measurement projection operators are not unitary but, I believe, in qiskit you simulate a measurement in a basis other than the computational basis using a unitary matrix. My matrices are not unitary.

How do you go from a projective measurement operator to a unitary transformation that reproduces the measurment?

$\endgroup$

1 Answer 1

1
$\begingroup$

The unitary operator for a measurement that has outcomes $|a0\rangle$, $|a1\rangle$, $|b0\rangle$ and $|b1\rangle$, is constructed as the transformation that maps these eigenstates to the computatitonal basis: $$ |00\rangle\langle a0|+|01\rangle\langle a1|+|10\rangle\langle b0|+|11\rangle\langle b1| $$ That enables me to compute state vectors, in Qiskit, that match my calculations. However, the measurement counts still aren't right - they correspond to illegal moves in the game :-(

To recover the state after the mesurement, you apply the inverse transformation (adjoint).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.