With the general theorem of SQPT, we shall develop a scheme to detemine an arbitrary matrix element of
chi, which is expanded with the Choi operators, in a scalbe way.
As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as
T1 and
T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multiqubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique naturally builds on standard process tomography and
T1/T2 measurement protocols, characterizes and accounts for state-preparation and measurement errors, and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.
Direct characterization of quantum dynamics (DCQD) introduced by Mohseni and Lidar [Phys. Rev. Lett. 97, 170501 (2006)] offers an effective way for estimation of quantum dynamical systems. Employing single-photon two-qubit states, we experimentally implement DCQD of one-qubit dynamics. The requirement of two-body interactions is thus eliminated such that the algorithm can be realized more conveniently. Both DCQD and standard quantum process tomography (SQPT) measurements are performed for several processes. The data from both methods show good agreement. Although the average process fidelities of the data obtained via DCQD are a little lower than that of SQPT, the number of experimental configurations is quadratically reduced evidencing the quadratic advantage of DCQD scheme. Partial information of the quantum dynamics can also be directly extracted via DCQD with fewer measurements.