Tomographic Characterization with Error Amplification for Cyclic Quantum Gates

Further improvement of elementary quantum operations' accuracy is an important task towards realizing practical fault-tolerant quantum computation, especially from the perspective of quantum error correction. As errors of quantum gates becomes smaller, it becomes harder to precisely characterize the errors. Error amplification (EA) is a technique to amplify effects of such small errors, and it is used in several characterization protocols categorized into randomized benchmarking or quantum tomography. Although EA plays an important role in the protocols, it suffers from its complicated structures originated from co-existence of Hamiltonian errors and decoherence, non-commutativity between different gates in an EA circuit or between errors and ideal action of a gate, and a problem of tomographic data-fitting becomes highly nonlinear, which can make the data-fitting unstable and heavy. In order to avoid such difficulties, we introduce a linear approximation approach for analyzing EAs' action. A key assumption is that ideal counterparts of gates in an EA circuit are cyclic, which makes the analysis simpler. We explain the theoretical framework of the approach. We also explain our numerical results on small systems. These results indicate that the approach of the linear approximation works well even regardless of its simplicity.