Practical Characterization of Quantum Devices without Tomography

Quantum tomography is the main method used to assess the quality of quantum information processing devices. However, the amount of resources needed for quantum tomography is exponential in the device size. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.

Figure 1

(a) Wigner function representation of a harmonic oscillator in the superposition $|\psi ⟩=|\alpha ⟩+|-\alpha ⟩$ for $\alpha =3$, (b) ${10}^3$ samples of points in the complex plane drawn according to the relevance density of $|\psi ⟩$, (c) Wigner function representation of a harmonic oscillator in the incoherent mixture of $|\alpha ⟩$ and $|-\alpha ⟩$, corresponding to the preparation of $\widehat{\sigma }$, (d) absolute error in successive estimates of the fidelity $F(\widehat{\rho },\widehat{\sigma })$ for 5 different runs with ${10}^3$ samples each.