Add support for Leakage Randomized Benchmarking (LRB) on two qubits

[deanpoulos]

Changes

• Added support for the leakage randomized benchmarking (LRB) protocol when f-state discrimination data is present
• Refactored analysis, plotting, fitting and fidelity calculations into sub-modules
• Refactored directory structure so that two_qubit_rb is accessed directly under qualang_tools.characterization
• Updated README

Leakage Randomized Benchmarking

Overview

Implemented the Leakage Randomized Benchmarking protocol, which uses a double-exponential fit when f-state discrimination data is present. When it is not present, the regular 2Q RB protocol is used.

Method

In the presence of state data outside of the computational state (that is, data about states that are not |00>, |01>, |10>, |11>), you can discriminate between decay in the |00> recovery probability due to leakage and gate errors. When such data is present:

1. Calculate the combined probability that the state was |00>, |01>, |10> or |11> $P_\mathbb{1}(m)$
2. Fit a single-exponential $A + B\lambda^m$ to $P_\mathbb{1}(m)$ and extract the decay due to leakage
3. Fit a double-exponential $A + B\lambda_1^m + C\lambda_2^m$ to the $P_{|00\rangle}(m)$ recovery probability, but fix $\lambda_1 \equiv \lambda$ from the leakage fit
4. Extract the average gateset Clifford fidelity $F = \frac{1}{4}[3\lambda_2 +1 - L_1$] where $L_1 = (1-A)(1-\lambda)$, the leakage rate, is extracted from the fit in step 2

Results

Fidelity results

to be measured

Example with high leakage rate

Using res.plot_two_qubit_state_distribution()

References

Wood, C.J. and Gambetta, J.M., 2018. Quantification and characterization of leakage errors. Physical Review A, 97(3), p.032306.

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