Measured responses to quantum Bayesianism

Christopher G. Timpson

Peiyue Wang, Lupei Qin, Xin-Qi Li

Compared with the quantum trajectory equation (QTE), the quantum Bayesian approach has the advantage of being more efficient to infer a quantum state under monitoring, based on the integrated output of measurements. For weak measurement of qubits in circuit quantum electrodynamics (cQED), properly accounting for the measurement backaction effects within the Bayesian framework is an important problem of current interest. Elegant work towards this task was carried out by Korotkov in 'bad-cavity' and weak-response limits (Korotkov 2011 Quantum Bayesian approach to circuit QED measurement (arXiv: 1111.4016 )). In the present work, based on insights from the cavity-field states (dynamics) and the help of an effective QTE, we generalize the results of Korotkov to more general system parameters. The obtained Bayesian rule is in full agreement with Korotkovʼs result in limiting cases and as well holds satisfactory accuracy in non-limiting cases in comparison with the QTE simulations. We expect the proposed Bayesian rule to be useful for future cQED measurement and control experiments.

Jon Frost, Carlos Madeira, Harald Uhlig

F. Cosco, Nicola Lo Gullo

The authors have developed a scheme to measure the states of qubits with improved efficiency and accuracy. Their method leverages Bayesian inference, creating a probability distribution for each qubit state based on the response of the measurement device. The approach is able to embed the effects of different sources of noise which affect current quantum computers, thus improving results of quantum computation.

Hans Christian von Baeyer

Christopher Ferrie, Christopher Granade, Gerardo A. Paz-Silva +1 more

As commonly understood, the noise spectroscopy problem—characterizing the statistical properties of a noise process affecting a quantum system by measuring its response—is mathematically ill-posed, in the sense that no unique noise process leads to a set of responses unless extra assumptions are taken into account. Ad-hoc solutions assume an implicit structure, which is often never determined. Thus, it is unclear when the method will succeed or whether one should trust the solution obtained. Here, we propose to treat the problem from the point of view of statistical estimation theory. We develop a Bayesian solution to the problem which allows one to easily incorporate assumptions which render the problem solvable. We compare several numerical techniques for noise spectroscopy and find the Bayesian approach to be superior in many respects.