Quantum feedback or quantum feedback control is a class of methods to prepare and manipulate a quantum system in which that system's

quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...

or trajectory is used to evolve the system towards some desired outcome. Just as in the classical case,

feedback Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...

occurs when outputs from the system are used as inputs that control the dynamics (e.g. by controlling the

Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...

of the system). The feedback signal is typically filtered or processed in a classical way, which is often described as measurement based feedback. However, quantum feedback also allows the possibility of maintaining the quantum coherence of the output as the signal is processed (via unitary evolution), which has no classical analogue. General Feedback Loop

Measurement based feedback

In the closed loop quantum control, the feedback may be entirely dynamical (that is, the plant and controller form a single dynamical system and the controller with the two influencing each other through direct interaction). This is named Coherent Control. Alternatively, the feedback may be entirely information theoretic insofar as the controller gains information about the plant due to measurement of the plant. This is measurement-based control.

Coherent feedback

Unlike measurement based feedback, where the quantum state is measured (causing it to collapse) and control is conditioned on the classical measurement outcome, coherent feedback maintains the full quantum state and implements deterministic, non-destructive operations on the state, using fully quantum devices. One example is a mirror, reflecting photons (the quantum states) back to the emitter.

Notes

References

* H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, 2009). * * * * * * * * {{refend Quantum mechanics