Quantum Control
From Qwiki
The term quantum control may refer to many very different types of control with quantum systems.
Quantum Feedback Control
One class, referred to as quantum feedback control or real-time quantum control involves the measurement of a quantum system by an interaction with an ancilla quantum system which is later destructively measured resulting in a classical measurement record. That measurement record is then processed and fed back to Hamiltonian parameters affecting the same system within its own coherence time. For optimal performance, the measurement record should be mapped onto the conditional quantum state via the stochastic master equation. The problem is then to find the mapping of the state (or measurement record) onto the Hamiltonian actuation variables, i.e. the control law, that achieves some pre-defined task during the lifetime of the original sample.
- A. C. Doherty and H. M. Wiseman, Optimal Quantum Feedback Control for Linear Systems, in preparation, 2005.
Adaptive Measurement
Aside from actuating Hamiltonian parameters of the system with feedback, the observer may also possess the ability to adaptively change the measurement itself according to the measurement record. This could be be done by adjusting the pre-interaction ancilla states (e.g., probe power) adaptively. But the measurement could also be changed, such that the post-interaction ancilla states were destructively measured in an adaptively changing basis. The latter leads to different unravellings of the dynamics. By the nature of the measurement, the ensemble average behavior of the system will be the same for any chosen unravelling or adaptive measurement scheme. Of course, the same will not be true for the average trajectory behavior of the system under different Hamiltonian control laws.
- H. M. Wiseman and A. C. Doherty, Optimal Unravellings for Feedback Control in Linear Quantum Systems, quant-ph/0408099, accepted by Phys. Rev. Lett., 2004.
Coherent Control
Additionally, there exist completely different types of control with quantum systems bearing little resemblance to the measurement techniques discussed here. For instance, one can imagine doing a type of feedback experiment where, instead of destructively measuring the ancilla system, it is returned to interact with the system of interest again, and possibly repeatedly. For the case of the usual optical ancilla system, this has been referred to as all-optical feedback to distinguish it from the electrical measurement signal alternatively produced. In certain cases this kind of coherent control can achieve state preparation goals with minimal processing overhead and delay. In the formalism presented here, one could describe such a process completely at the Langevin equation level.
- H. M. Wiseman and G. J. Milburn, All-optical versus electro-optical quantum-limited feedback, Phys. Rev. A, 49, 4110, 1994.
- Seth Lloyd, Coherent quantum feedback, Phys. Rev. A, 62, 022108, 2000.
Learning Control
Finally, the term 'quantum control' is also used in the literature to refer to yet another scenario, with not one system, but an ensemble of identically prepared systems. Here a system is driven with a pulse, then the result is measured. Subsequently, another system is prepared, another pulse is used to drive it, the result is again measured, and so on. In between trials, the pulse shape is changed based on the previous measurements in some algorithmic (possibly genetic) way to optimize the effect of the pulse. This pulse shaping procedure is a type of learning control and, unlike in the examples above, no feedback occurs during the lifetime of an individual system.
- Herschel Rabitz and Regina de Vivie-Riedle and Marcus Motzkus and Karl Kompa, Whither the Future of Controlling Quantum Phenomena?, Science, 288, 824, 2000.
