Superconducting qubits - measurement, entanglement, and noise

Doctoral thesis, 2009

In the early 1980’s, it was suggested that a computer obeying the laws of quantum mechanics would be able to solve problems beyond the capabilities of a classical computer. The novel ways in which such a quantum computer works relies on the quantum properties of the quantum bits (qubits) used to store the information. Any candidate for a quantum computer must thus be able to sustain these properties and offer means to manipulate and read-out the information. One such candidate are quantum mechanical, superconducting circuits, where the logical bit is encoded in the energy eigenstates of the system. In circuit quantum electrodynamics, such a qubit is coupled to a microwave cavity allowing the qubit to be coherently controlled and read-out by probing the cavity. In this thesis, we theoretically investigate the destructive effects of noise which couple to the system as one tries to measure and control the qubits. We study the so called quantum capacitance read-out scheme, where the state of the qubit is mapped onto an equivalent capacitance of the circuit. It is shown that this is quantum limited, in the sense that the state of the qubit can be determined while simultaneously adding a minimum amount of noise to the system. Apart from the added noise, a measurement on a qubit will perturb it, causing the state to collapse to one of the measurement eigenstates. Such a state collapse can be utilized to generate entanglement between qubits by measuring on the cavity. We show that high-fidelity entangled states can be produced in this way and discuss the potential of the measurement to violate a bound given by local hidden variable theories. The possibility to prolong the life-time of the quantum state by active error correction is also investigated and we discuss limits on gate operation times to benefit from such a code, given realistic values for the error probabilities. This work was supported by the European Commission through IST-015708 EuroSQIP integrated pro ject, and by the Swedish Research Council.