Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering

Abstract

Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another. Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network. The standard criteria of QST are based on the fidelity between the prepared and received states. However, a non-vanishing fidelity is obtained even when the received quantum states are described using the classical model, called the local-hidden state (LHS) model. With the above definition of the classical QST process, in this work, we quantify the non-classicality of a QST process by measuring the spatio-temporal steerability. We show that the spatio-temporal steerability is preserved when the perfect QST process is successful. Otherwise, it decreases under imperfect QST processes. Therefore, the failure of the LHS model implies not only the achievement of spatio-temporal steering but also QST non-classicality. We then apply the spatio-temporal steerability measurement technique to benchmark quantum devices including the IBM quantum experience and QuTech quantum inspire under QST tasks. The experimental results show that the spatio-temporal steerability decreases as the circuit depth increases, and the reduction agrees with the noise model, which refers to the accumulation of errors during the QST process. Moreover, we show that the no-signaling in time condition could be violated because of the intrinsic non-Markovian effect of the devices.