junction is discussed in detail. The vortex potential is formed due to its interaction with an inplane magnetic field and a bias current applied to the junction. The profile of the potential is calculated using a standard perturbation approach. We examine the dependence of the potential properties on the junction shape and its electrical parameters and discuss the requirements for observing quantum effects in this system. We have developed and experimentally tested methods for the preparation and read-out of vortex states of this qubit in the classical regime. 1. Introduction In the past years several types of different superconducting circuits [1–6] based on small Josephson junctions in the phase or charge regime have been shown to achieve parameters which are favorable for quantum computation. In Ref. [7], a qubit based on the motion of a Josephson vortex in a long Josephson junction was proposed. A major difference from the small Josephson junction qubit proposals where the effective potential is created by the Josephson or charging energy, is that in the vortex qubit the potential is formed by the magnetic interaction of the vortex magnetic moment with an external magnetic field, as described in Ref. [8]. In heart-shaped annular junctions two classically stable vortex states can be arranged, corresponding to two minima of the potential. While the external field is always applied in the plane of the long junction, its angle Q and strength h can be varied. The bias current across the junction can be used to tilt the potential. These parameters allow to manipulate and control the potential and to read out the qubit state using a zero-voltage critical current measurement. The scheme of readout and preparation of the state for this type of qubit was already demonstrated in the classical regime as briefly described in Ref. [9]. This paper describes details of the calculations necessary to determine the parameter range for the quantum regime, as well as details on the calculation of the effective potential for the vortex. An explanation of the implementation of the elementary single-bit quantum gates using the two in-plane magnetic field components is given. For the calculation of the potential a single-vortex perturbation theory approach [10] is used. Tunneling rates in the quantum regime are determined by numerical diagonalization of the Hamiltonian and compared to a WKB calculation.