Quantum Filtering and Control in Example: Unstable Qubits

V. P. Belavkin

A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

Prateek Tandon, Stanley Lam, Ben Shih +3 more

Yu Zeng, Yuxing He, Hongxiang Shen +1 more

This paper discusses a class of filters utilized in a low-power superconductor rapid single-flux-quantum (rapid SFQ, RSFQ) microwave pulse generator for controlling quantum bits (qubits). Here, the filter plays an important role to convert SFQ pulse trains (generated by RSFQ digital gates) and output a microwave control pulse. Characteristic of the output pulse can be adjusted by the in-band and roll-off performances of the filter, which is analyzed through numerical examples. Moreover, a novel in-line topology lumped network is proposed for the filter implementation, which can satisfy complex terminal cases at source (connecting an RSFQ digital block) and load (connecting a qubit). For the validation, we carry out a fourth-order bandpass filter using multilayer niobium (Nb) then-film technology, then incorporate it into an RSFQ control-pulse generator, and finally confirm correct functionality by both simulation and measurement.

Hongting Song, Shuangshuang Fu, Zairong Xi

Seth Lloyd

Pierre Rouchon, Jason F. Ralph

We discuss an efficient numerical scheme for the recursive filtering of diffusive quantum stochastic master equations. We show that the resultant quantum trajectory is robust and may be used for feedback based on inefficient measurements. The proposed numerical scheme is amenable to approximation, which can be used to further reduce the computational burden associated with calculating quantum trajectories and may allow real-time quantum filtering. We provide a two-qubit example where feedback control of entanglement may be within the scope of current experimental systems.