Local Geometric Phase and Quantum State Tomography in a Superconducting Qubit

TL;DR

This paper presents a novel quantum state tomography method for superconducting qubits that accounts for local geometric phases induced by Aharonov-Bohm flux, enabling unambiguous density matrix reconstruction.

Contribution

It introduces a measurement scheme incorporating local geometric phases and Faraday's law, allowing accurate quantum state reconstruction in superconducting qubits.

Findings

Reconstruction of the full density matrix without gauge ambiguity.

Demonstration of the quantum Faraday effect's role in qubit dynamics.

Effective measurement of charge and local currents for state tomography.

Abstract

We investigate quantum state reconstruction of a superconducting qubit threaded by an Aharonov-Bohm flux, with particular attention to the local geometric phase. A state reconstruction scheme is introduced with a proper account of the local geometric phase generated by Faraday's law of induction. Our scheme is based on measurement of three complementary quantities, that is, the extra charge and two local currents. Incorporating time-reversal symmetry and the Faraday's law, we show that the full density matrix can be reconstructed without ambiguity in the choice of gauge. This procedure clearly demonstrates that the quantum Faraday effect plays an essential role in the dynamics of a quantum system that involves Aharonov-Bohm flux.