Quantum state tomography for Kerr parametric oscillators

TL;DR

This paper presents a practical method for quantum state tomography of Kerr parametric oscillators using reflection measurements, enabling accurate qubit state readout in circuit QED systems.

Contribution

The authors develop a reflection measurement-based tomography scheme for KPOs, establishing a one-to-one correspondence between reflection coefficient and qubit density matrix elements.

Findings

Reflection coefficient correlates with density matrix diagonal elements.

Proper probe frequency and single-photon drive enable accurate state reconstruction.

The scheme allows for qubit state readout and tomography using reflection measurement.

Abstract

Kerr parametric oscillators (KPOs) implemented in the circuit QED architecture can operate as qubits. Their applications to quantum annealing and universal quantum computation have been studied intensely. For these applications, the readout of the state of KPOs is of practical importance. We develop a scheme of state tomography for KPOs with reflection measurement. Although it is known that the reflection coefficient depends on the state of the KPO, it is unclear whether tomography of a qubit encoded into a KPO can be performed in a practical way mitigating decoherence during the measurement, and how accurate it is. We show 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 introduced. Thus, our scheme offers a novel way to readout the qubit along an axis of the Bloch sphere, and therefore the reflection measurement and single-qubit gates can constitute state tomography.