Cat-qubit operations preserving error structure

A universal quantum computer will require error correction to perform in a fault-tolerant way, imposing substantial engineering challenges. Fortunately, many devices are subject to errors with structure that can be exploited to ease the burden of fault tolerance. Stabilized cat qubits in superconducting circuits push this principle to the extreme, with recent work identifying dramatic reduction of fault-tolerance requirements on this platform. Essential to this reduction is the ability to perform operations on the qubits that preserve the error structure, made possible by the infinite-dimensional Hilbert space in which the cats live. We present additional operations fulfilling this requirement and discuss their potential for near- and long-term applications.