Mesoscopic d-wave qubits: Can high-Tc cuprates play a role in quantum computing?

Due to nontrivial orbital pairing symmetry, surfaces and interfaces of high-Tc superconductors support states which violate time-reversal $(\Gamma-)$ symmetry. Such naturally degenerate states, useful as working states of a qubit, are standard for atomic or molecular-size qubit prototypes (e.g. based on nuclear spins), but exceptional for mesoscopic qubits. (In particular, they hold promise of a better scalability.) In these lectures I review the physics of $\Gamma$-breaking on surfaces and interfaces of high-$T_c$ superconductors; then describe existing proposals for high-$T_c$ based qubits and the current state of experiments; finally, I discuss the decoherence sources in the system, open questions, and future research directions.