Read-out of superconducting qubits - a quantum measurement process

Abstract: In this work we consider measurements on quantum systems emphasizing on read-out of superconducting qubits. The qubit is always coupled to an environment, containing a macroscopic number of degrees of freedom. This perturbs the qubit and destroys the phase coherence of the quantum state. One tries to minimize this destructive effect by encoding the quantum information in quantum states which do not couple strongly to the dominant noise sources. It is therefore necessary to design read-out methods that can distinguish these states. We focus primarily on the single Cooper-pair box (SCB) charge qubit, whose properties are based on the Josephson effect and Coulumb blockade in superconducting electrical circuits. By encoding the information in the qubit energy eigenstates, it is possible to protect it from the most dangerous decoherence source - charge fluctuations in the environment. We investigate the measurement setup, where the SCB is coupled to a lumped element LCoscillator whose resonance frequency is orders of magnitude smaller than the qubit energy splitting. In this regime the SCB will act as an effective positive or negative capacitance, depending on the quantum state. This quantum capacitance then shifts the oscillator resonance frequency, which can be detected in a homodyne phase measurement. We have found that reading out a charge qubit by measuring its quantum capacitance in this manner is quantum limited, independently of the oscillator quality factor Q. Moreover, we have found that the low-Q oscillator is advantageous for the measurement in two ways: first, such an oscillator better protects the qubit from thermal dephasing, and, second, it allows to increase the speed of the read-out, making it possible to distinguish the qubit states in a single shot measurement.