Prediction and retrodiction for a continuously monitored superconducting qubit.

Area of Science:

• Quantum Information Science
• Superconducting Quantum Computing
• Cavity Quantum Electrodynamics

Background:

• Superconducting transmon qubits are key components in quantum computers.
• Monitoring qubit states is crucial for quantum computation and error correction.
• Cavity-mediated measurements offer a non-destructive way to probe quantum systems.

Purpose of the Study:

• To develop and experimentally validate a method for predicting and retrodicting quantum state measurements.
• To utilize density matrices conditioned on past and future measurement data for enhanced quantum state reconstruction.
• To demonstrate the application of these matrices in analyzing both weak and strong qubit measurements.

Main Methods:

• Monitoring the quantum state of a superconducting transmon qubit within a 3D cavity using microwave field transmission.
• Incorporating measurement record information into a time-dependent density matrix (ρt) conditioned on past probe results.
• Developing an auxiliary matrix (Et) conditioned on future probe results for retrodiction.
• Extracting these matrices directly from experimental data.

Main Results:

• Successfully obtained experimental density matrices (ρt and Et) from measurement data.
• Demonstrated the ability of these matrices to accurately predict the outcomes of future qubit measurements.
• Showcased the effectiveness of the auxiliary matrix in retrodicting past qubit measurement outcomes.
• Illustrated the application for both weak and strong measurement regimes.

Conclusions:

• The developed method provides a robust framework for quantum state reconstruction in superconducting qubits.
• Experimental validation confirms the utility of past and future-conditioned density matrices for precise state monitoring.
• This technique enhances the understanding and control of quantum systems, paving the way for improved quantum computing.