Modeling Quantum Devices and the Reconstruction of Physics in Practical Systems

Modeling quantum devices is to find a model according to quantum theory that can explain the result of experiments in a quantum device. We find that usually we cannot correctly identify the model describing the actual physics of the device, regardless of the experimental effort, given a limited set of operations. According to sufficient conditions that we find, correctly reconstructing the model requires either a particular set of pure states and projective measurements or a set of evolution operators that can generate all unitary operators.

Figure 1

(a) In quantum device modeling, we guess a model that is consistent with the quantum theory and the statistics of data from the experiment. However, such a model may not reflect actual physics in the system. (b) If there is only one model consistent with the corresponding probability distribution, then the model can always be correctly identified. Here, we assume that the statistical fluctuation is negligible provided sufficient data; i.e., we ignore the error in the estimation of the probability distribution. (c) If there is more than one model consistent with the corresponding probability distribution, the model $[{\mathfrak{m}}^{\prime }]$ reconstructed from the distribution may be different from the genuine model of the system $[\mathfrak{m}]$ that causes the experimental result.