Abstract

Several proposals exists to encode an error-correctable logical qubit in the large Hilbert space of a harmonic oscillator. While theoretically attractive, manipulating these oscillators is a challenging task due to their linearity. I will describe how we implement high fidelity quantum control over a “Cat-state” qubit encoded in a long-lived superconducting cavity resonator. Nontrivial operations on the oscillator are performed by dispersively coupling it to a transmon qubit and applying time-dependent control fields to the oscillator and the transmon simultaneously. We construct the required pulses numerically using optimal control methods. I will show that we can realize a universal set of gates acting on the logical qubit, with an average gate fidelity of 99%. This shows that linear systems can be efficiently manipulated when coupled to a nonlinearity and that oscillator-encoded states could be a promising resource for quantum error correction protocols.