Superconducting quantum circuits, such as the transmon, have multiple quantum states beyond the computational subspace. These states can be populated during quantum logic operations;residual population in such states is known as leakage. While control methods can eliminate this error in ideal systems, leakage will arise from transient population in the presence of dephasing. This dephasing-induced leakage effect is analyzed, both analytically and numerically, for common single and two-qubit operations used in transmon-based approaches to quantum information processing.
We propose a tunable nonlinear interaction for the implementation of quantum logic operations on pairs of superconducting resonators, where the two-resonator interaction is mediatedby a transmon quantum bit (qubit). This interaction is characterized by a high on-to-off coupling ratio and allows for fast qubit-type and d-level system (qudit)-type operations for quantum information processing with multiphoton cavity states. We present analytical and numerical calculations showing that these operations can be performed with practically unit fidelity in absence of any dissipative phenomena, whereas physical two-photon two-resonator operations can be realized with a fidelity of 99.9% in presence of qubit and resonator decoherence. The resonator-qubit-resonator system proposed in this Letter can be implemented using available planar or three-dimensional microwave technology.
An all-resonant method is proposed to control the quantum state of
superconducting resonators. This approach uses a tunable artificial atom
linearly coupled to resonators, and allowsfor efficient routes to Fock state
synthesis, qudit logic operations, and synthesis of NOON states. This resonant
approach is theoretically analyzed, and found to perform signficantly better
than existing proposals using the same technology.