Amazingly when electrons are placed near the surface of superfluid helium they bind to the surface forming Rydberg like bound state, in which the electron is suspended about 8nm above the surface. Because they are far above the surface (about 100 atomic radii), they have pristine properties, including the highest known 2d electron gas mobility, and extremely weak predicted spin-orbit coupling. This makes them ideal candidates to serve as spin qubits, and as a rich system to study in general as a microscopic cavity QED system. Further the superfluid substrate itself is fascinating with extremely high Q's predicted at millikelvin temperatures. We are attempting to trap and detect individual electrons and couple them to a superconducting cavity. This will enable us to study the electrons' motional coherence and hopefully measure their spin coherence for the first time.
Superconducting qubits have made tremendous progress in the last decade, starting from barely measurable coherence measured in picoseconds, to coherence times approaching 1 ms. The rapid progress on individual and few qubits, has encouraged research into scaling superconducting quantum processors to larger numbers of qubits. Rather than scale the system by simply microfabricating many copies of a qubit, we are attempting to use multi-mode resonators as quantum memories to store larger numbers of qubits. It is straight forward to create high quality factor resonators with 10's of modes (bits) with their quantum state being controlled by a single Josephson junction circuit. We believe that this multi-plexed approach combined with brute force scaling can realize a medium sized quantum processor in the near term.
When a charged particle encircles magnetic flux, it acquires an Aharonov-Bohm phase. Often cited as an odd consequence of quantum mechanics, this aspect of the magnetic field should perhaps be seen as its central feature. Photons themselves linear electromagnetic fields do not typically experience such a phase shift. However it is possible to build a meta-material in which photons acquire phase when encircling an area, resulting in dynamics mathematically equivalent to that of a charged particle in a magnetic field. We have designed a circuit-based topological insulator in which a series of LC circuits are connected in such a way that they form two copies of a "spin-hall" system, each of which behaves as an independent particle in a magnetic field. Operating at room temperature this shows that the topological nature of such materials is classical in nature and realizable in a wide variety of systems. We are currently moving towards realizing superconducting topological circuit materials, in which it will be possible to introduce single photon interactions to realize a host of exotic quantum phases. This work is done in tight collaboration with Jon Simon's group here at UofC.
All superconducting qubits studied thus far can be described by an LCJ circuit, consisting of an inductor (L), capacitor (C), and Josephson junction (J). The circuits have remarkable properties and have enabled dramatic progress both in quantum computing and in the study of quantum electrodynamics more generally. The coherence of these circuits is generally described by two times: T1 which is the energy relaxation lifetime, and T2 which is the dephasing time of a superposition state. Progress thus far has been accomplished by designing circuits in which quantum noise makes the states indistinguishable to dephasing processes (enabling long T2) but which tend to make circuits more susceptible to relaxation. Despite this T1 lifetimes have increased by improved engineering of the microwave environment and materials. A complimentary approach to increasing lifetimes is to ensure that the quantum overlap of the states is exponentially small, in which case the excited state can become metastable as in a particle in a deep double well. However, traditional implementations of this approach tend to lead to large sensitivity to dephasing. The zero-pi cicuit which we are developing is a larger circuit with 3 degrees of freedom rather than a single one, and allows one to have disjoint logical states which are exponentially protected from relaxation and charge noise, while being 1st order protected against flux noise. Realizing and operating such a circuit promises to be an exciting challenge!
Typical error correction protocols are based on performing a set of quantum gates followed by feedback with an error correcting pulse. This is much like early versions of motional cooling for atoms and electrons where the velocity was measured and an electric or magnetic field was varied in response to create and effective friction towards the ground state. While feasible in principle, this approach towards motional cooling has largely been supplanted by laser cooling in which the feedback is done effectively through an internal resonance of the atom. Laser-cooling a quantum bit is somewhat more challenging because one must cool a manifold of levels (|0>, |1>, or any superposition) without introducing any errors. Nevertheless the principle is the same. One must create a Hamiltonian which differentiates the desired manifold from the error manifold, and then have a process which acts preferentially when there are errors. In laser cooling this is done by performing a joint process of phonon absorption and exciting an internal dipole level, whereas the dipole level can emit without re-emitting the phonon. The spontaneous emission is what forces the process towards the desired state. In our case we engineer a process which simultaneously corrects a single quantum error such as a bit/phase flip and excites a resonator with a fast decay time. When the resonator spontaneously emits the error has been dissipated. Once the appropriate terms have been engineered no pulsing or external feedback is required, just as in laser cooling.