Preparation and manipulation of a fault-tolerant superconducting qubit

We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors introduced by the interaction with the environment and during manipulations. We show how to prepare the fault-tolerant state and manipulate the system. The discussed operations suffice to perform quantum computation on the encoded state, syndrome extraction, and quantum error correction. We also comment on the physical sources of errors and possible imperfections while manipulating the system.

Figure 1

The simplest flux qubits (Ref. 21) can be used to encode a qubit in their continuous variables. (a) The rf-SQUID, a simple loop with a Josephson junction, and (b) rf-SQUID with tunable Josephson coupling.

Figure 2

A possible method of the inductive meter-qubit coupling. In this geometry (when the qubit is placed inside the meter), the coupling is strong, and $\lambda \approx 1$. For simplicity, the qubit is shown without the smaller, dc-SQUID loop.

Figure 3

Inductive coupling of two qubits is realized with the Josephson energy tuned to zero. It is thus the coupling of two $LC$ oscillators. In the rotating frame of reference, this coupling provides equivalent of quantum-optical beam splitter (see the text for explanation).