Oscillator noise spectroscopy via displaced Schrödinger-cat states

We present a technique for the characterization of noise in oscillator-mediated entangling operations applicable to a range of gate implementations in both trapped ion and superconducting circuit architectures. A major source of error in this class of entangling gates is residual coupling between the system of qubits and the intermediate oscillator modes, often caused by noise on the mode frequencies. In order to characterize this leading source of gate error, we use discrete phase modulation of the field driving the gate to construct sequences of oscillator-phase-space displacements with a band-limited sensitivity to oscillator frequency noise. By displacing the motion of a single trapped ¹⁷¹Yb⁺ ion, we characterize the sensitivity of these sequences to engineered noise, verifying analytic predictions in the filter function formalism for the observed signal strength. We also perform sensing of intrinsic noise, leveraging tools for spectrum reconstruction based on a singular value decomposition approach developed at Q-CTRL.