Description
Quantum harmonic oscillators play a crucial role across quantum computation, simulation, and sensing. Across all of these applications, a common and essential prerequisite is the ability to extract information from the oscillator whether to read out the outcome of a computation, to measure observables of a simulated system, or to obtain a sensing signal. While existing readout methods for oscillators allow full reconstruction of their quantum state via estimation of the Wigner or the characteristic functions, they are resource intensive. Moreover, the full state reconstruction is often overkill as one is only interested in a specific meaningful physical quantity. Here, we propose a method for estimating arbitrary observables that are functions of a quantum harmonic oscillator operator, including position, momentum, and number. Our method uses an ancilla qubit to control the oscillator within the bosonic quantum signal processing framework. By invoking the Fejér–Riesz theorem, we obtain a direct analytical mapping from a target observable to experimentally implementable oscillator–qubit control operations. This yields a fully analytical construction of the required control sequences, which is systematically improvable and supports explicit error and scaling analyses. Notably, our framework encompasses existing readout methods, such as estimation of the Wigner and characteristic functions, as special cases. We illustrate the method with examples involving the estimation of moments of the position operator relevant for measuring physical properties of a simulated system, and the measurement of logical Pauli operators for the square Gottesman-Kitaev-Preskill (GKP) code, the latter of which enables single-shot readout of the GKP logical state.
| I am the presenting author | Yes |
|---|