Randomized benchmarking

Estimate average error-rate for a set of operations: Apply random sequences of Clifford operations, then measure the average sequence fidelity.

Learn from noisy quantum experiments

“A sequence of models for the observable fidelity decay. as a function of a perturbative expansion of the errors.

“Full characterization of any quantum process is possible though quantum process tomography.

But QPT sufferers from two shortcomings:

assumptions that the set of measurements and state preparations admit much lower errors than the process which is being characterized;

the number of experiments required grows exponentially with the number of qubits.”

“scalable methods for partial characterization of the noise affecting a quantum process.”

“RB steps:

1. Generate a sequence of m + 1 quantum operations.

the first m operations chosen uniformly at random from some group G ⊆ U (d). the final operation (m + 1) chosen so that the net sequence (if realized without errors) is the identity operation. Let G corresponds to the Clifford group on n-qubits (d = 2n)."

1. For each sequence the survival probability Tr[Eψ Sim (ρψ)] is measured. Here ρψ is initial state taking into account preparation errors. And Eψ is the POVM element that takes into account measurement errors. In the ideal noise-free case ρψ = Eψ = |ψ⟩⟨ψ|”

2. Average over random realizations of the sequence to find the averaged sequence fidelity, …”

3. Fit the results for the averaged sequence fidelity [Eq. (2)] to the model”

References

• tweet;

• Emerson2010;