Circuit quantum electrodynamics embeds Josephson junction qubits within superconducting cavities, and has emerged as a leading approach to quantum computing and quantum simulation.Despite the many permutations of circuit geometry that have been explored, Josephson connectivities have so far been planar, making them effectively low-dimensional. Here we show that a non-planar qubit — a 3×3 crossbar Josephson array — gives rise to flux-tunable ℤ3 combinatorial gauge symmetry (CGS), potentially enabling spin-liquid behavior when networked into a lattice. The observed excitation spectrum shows excellent agreement with predictions from a neural network trained to generate variational quantum states, demonstrating that we have predictive power over our high-dimensional quantum system. Fine-structure splittings near the CGS point are compatible with weak tunneling or symmetry breaking due to experimental imperfections. We additionally use the superconducting cavity to externally induce symmetry breaking, observing a restoration of symmetry at the CGS point where ground states differ only by a ℤ3 phase. This work initiates a general program exploring lattice gauge theories using the toolbox of circuit quantum electrodynamics. More broadly, introducing non-planar Josephson connectivities opens a vast space for experimental and theoretical exploration of structures in almost any imaginable dimensionality and geometry.
We introduce a method for breaking Lorentz reciprocity based upon the non-commutation of frequency conversion and delay. The method requires no magnetic materials or resonant physics,allowing for the design of scalable and broadband non-reciprocal circuits. With this approach, two types of gyrators — universal building blocks for linear, non-reciprocal circuits — are constructed. Using one of these gyrators, we create a circulator with > 15 dB of isolation across the 5 — 9 GHz band. Our designs may be readily extended to any platform with suitable frequency conversion elements, including semiconducting devices for telecommunication or an on-chip superconducting implementation for quantum information processing.
An electro-optomechanical device capable of microwave-to-optics conversion has recently been demonstrated, with the vision of enabling optical networks of superconducting qubits. Herewe present an improved converter design that uses a three-dimensional (3D) microwave cavity for coupling between the microwave transmission line and an integrated LC resonator on the converter chip. The new design simplifies the optical assembly and decouples it from the microwave part of the setup. Experimental demonstrations show that the modular device assembly allows us to flexibly tune the microwave coupling to the converter chip while maintaining small loss. We also find that electromechanical experiments are not impacted by the additional microwave cavity. Our design is compatible with a high-finesse optical cavity and will improve optical performance.