In one embodiment, a two-junction phase qubit includes a superconducting loop and two Josephson junctions separated by a mesoscopic island on one side and a bulk loop on another side. The material forming the superconducting loop is a superconducting material with an order parameter that violates time reversal symmetry. In one embodiment, a two-junction phase qubit includes a loop of superconducting material, the loop having a bulk portion and a mesoscopic island portion. The loop further includes a relatively small gap located in the bulk portion. The loop further includes a first Josephson junction and a second Josephson junction separating the bulk portion from the mesoscopic island portion. The superconducting material on at least one side of the first and second Josephson junctions has an order parameter having a non-zero angular momentum in its pairing symmetry. In one embodiment, a qubit includes a superconducting loop having a bulk loop portion and a mesoscopic island portion. The superconducting loop further includes first and second Josephson junctions separating the bulk loop portion from the mesoscopic island portion. The superconducting loop further includes a third Josephson junction in the bulk loop portion. In one embodiment, the third Josephson junction has a Josephson energy relatively larger than a Josephson energy of the first and second Josephson junctions.