Describe the bug
Given some observable that has non-commuting elements e.g. "IX" + "IZ", the variances that is used to compute the standard error is incorrect
Then define your observable (SparsePauliOp)
observable = SparsePauliOp(["IX", "IZ"])
Check answer to find that it is not the expected result. Since we cannot get the variance directly from the device, we compute the variance from the standard error. In the source code, the standard error is computed from the variance that is measured, so this is just reversing that step.
res = estimator.run([(qc, observable)])
var = (res.result()[0].data.stds/res.result()[0].metadata["target_precision"]) ** 2 ## 1.2167353630065918
Expected behavior
var should be around 0.43
Suggested solutions
Account for covariance when calculating variances of non-commuting observables.
Additional Information
You can verify that the variance is wrong by computing the variance manually.
Using Var(A+B) = E((A+B)^2) - (E(A+B))^2
var = estimator.run([(qc, observable.dot(observable))]).result()[0].data.evs - estimator.run([(qc, observable)]).result()[0].data.evs ** 2
Describe the bug Given some observable that has non-commuting elements e.g. "IX" + "IZ", the variances that is used to compute the standard error is incorrect
Steps to reproduce Define some circuit e.g.
Then define your observable (SparsePauliOp)
observable = SparsePauliOp(["IX", "IZ"])Check answer to find that it is not the expected result. Since we cannot get the variance directly from the device, we compute the variance from the standard error. In the source code, the standard error is computed from the variance that is measured, so this is just reversing that step.
Expected behavior var should be around 0.43
Suggested solutions Account for covariance when calculating variances of non-commuting observables.
Additional Information You can verify that the variance is wrong by computing the variance manually. Using Var(A+B) = E((A+B)^2) - (E(A+B))^2
var = estimator.run([(qc, observable.dot(observable))]).result()[0].data.evs - estimator.run([(qc, observable)]).result()[0].data.evs ** 2