Open chriseclectic opened 2 years ago
The efficient method to calculate an inner product between two stabilizer states is described in the last of Sec. Ⅲ https://arxiv.org/abs/quant-ph/0406196.
Does this depend on #7245 and #7269 being merged?
Can this function be extended to compute the state fidelity between twosuperposition
of stabilizer states
too? not only between 2 Stabilizer states..... This is a request from Keio university.
Hello, I am Rishabh, an undergraduate final year computer engineering student. This issue is still open or not? My Interests are:-
What is the expected enhancement?
Currently the
StabilizerState
class is not supported by thestate_fidelity
function which can only handle Statevector and DensityMatrix states.This function should be extended to have an efficient form of computing the state fidelity between two stabilizer states, and a (probably inefficient) version for computing the fidelity between a stabilizer state and a non-stabilizer state (statevector or density matrix).
Possible implementation
I'm not sure if there is a more efficient method but one way you could compute the fidelity between two stabilizer states
|a> = A|0>
,|b> = B|>
for cliffords A, B would be to compute the the all-zero measurement outcome probability for the stabilizer stateB^\dagger A|0>
asp = |<0|B^\dagger A|0>|^2 = F(|a>, |b>)
.For the second case one way would be allowing conversion of a
StabilizerState
toStatevector
. This could be implemented (inefficiently) by running the simulation for the Clifford circuit on theStatevector
class. This would also generally useful functionality to add to theStabilzerState
class.