Superconducting circuits are an exemplary platform for digital computing as well as quantum information science, and it is a pleasure to be showing an unusual niche of superconducting circuits to you. Although superconducting qubits have recently achieved improved coherence and well-deserved popularity, superconducting digital logic built using single-flux-quanta (SFQs) as bits, can beat CMOS technology in gate speed and energy efficiency. However, most bit switching in SFQ logic is thermodynamically irreversible. Here we discuss reversibility as an ingredient to make SFQ logic more energy efficient and scalable. There exist multiple adiabatic-powered SFQ logic families, and one of them can realize a reversible gate. In our logic, named Reversible Fluxon Logic (RFL), we have found a way to use bit states that are the opposite polarities of the same SFQ, which is unique. Additionally, we use the momentum of our moving bits to “autonomously power” the gates, which is also fairly unique. Most of our results are numerical and analytical, but we also have collected some encouraging data. We start our introduction to RFL with SFQ of long-Josephson junctions (LJJs) which are sine-Gordon solitons. This allows ballistic motion of SFQ which is already unusual. Moreover, to switch bit states using RFL gates, we build a resonance into the gate structure. These gates contain circuit interfaces between LJJs, and allow a bit flip with 97% energy efficiency. Useful reversible gates should use conditional bit flips, and we have found one class of such gates called ballistic shift registers. Fortunately, these gates are asynchronous and reversible such that they don't have to be carefully timed. We are developing our logic around physical limitations and one is the imperfect reversibility of our gates. Since ballistic gates are unpowered other than from the momentum of input bits, they have a practical limitation because bits slow slightly after each gate operation. To compensate, we have developed a device we call the Booster, named after the boost Lorentz transformation in relativistic mechanics. To achieve the boost of two different fluxon polarities, we repurpose an Aharonov-Casher Ring. The Booster does not allow the famous Aharonov-Casher effect for a couple of reasons that we will discuss. However, the Booster accelerates both bit states equally, which is useful. This should allow scaling of RFL logic; it also allows an energy efficiency comparison to a standard SFQ logic type.
