Compressed sensing quantum process tomography for superconducting quantum gates

TL;DR

This paper demonstrates that compressed sensing quantum process tomography can efficiently characterize superconducting quantum gates with significantly less data than traditional methods, maintaining high accuracy even with underdetermined systems.

Contribution

The study introduces the application of compressed sensing QPT to superconducting qubits, showing it works effectively with reduced data and in underdetermined scenarios, and compares different bases for process matrix sparsity.

Findings

High-fidelity process matrix estimates with less data

Effective underdetermined system handling

Consistent results across different bases

Abstract

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix $\chi$ is approximately sparse, and show that the resulting estimates of the process matrices match each ther with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.