Quantum state tomography for Kerr parametric oscillators with reflection measurement*

Kerr parametric oscillators (KPOs) implemented in the circuit QED architecture can work as qubits. The readout of KPOs is required in their applications to quantum annealing and universal quantum computation. In this presentation, we show a scheme of state tomography for KPOs with reflection measurement. A previous paper showed that the reflection coefficient depends on the state of the KPO [1]. However, it is nontrivial if tomography of a qubit encoded into a KPO can be performed in a practical way mitigating the decoherence during the measurement, and how accurate it is. We present that the reflection coefficient has a one-to-one correspondence with a diagonal element of the density matrix of the qubit when a probe frequency is properly chosen, and an additional single-photon-drive is utilized. Our scheme offers a novel method to readout the qubit along an axis of the Bloch sphere, and therefore single-qubit gates followed by the reflection measurement can constitute state tomography [2]. 

[1] S. Masuda, et al., NJP 23, 093023 (2021).

[2] Y. Suzuki, et al., Phys. Rev. Applied 20, 034031 (2023).