Simultaneous readout of two charge qubits

TL;DR

This paper analyzes a system of two charge qubits coupled to a single-electron transistor, comparing measurement methods and discussing quantum efficiency and dephasing effects in qubit readout.

Contribution

It introduces a detailed analysis of simultaneous readout of two charge qubits via a SET, including full counting statistics and efficiency comparison of different measurement techniques.

Findings

Quantum efficiency of current measurement can be unity.

Real-time charge detection achieves quantum efficiency of one.

Full quantum efficiency possible by measuring average charge and current.

Abstract

We consider a system of two solid state charge qubits, coupled to a single read-out device, consisting of a single-electron transistor (SET). The conductance of each tunnel junction is influenced by its neighboring qubit, and thus the current through the transistor is determined by the qubits' state. The full counting statistics of the electrons passing the transistor is calculated, and we discuss qubit dephasing, as well as the quantum efficiency of the readout. The current measurement is then compared to readout using real-time detection of the SET island's charge state. For the latter method we show that the quantum efficiency is always unity. Comparing the two methods a simple geometrical interpretation of the quantum efficiency of the current measurement appears. Finally, we note that full quantum efficiency in some cases can be achieved measuring the average charge of the SET island, in addition to the average current.