Lecture 14: Open quantum systems: quantum process formulation

So far in this course you’ve mainly seen what ideal quantum operations looks like. For example, a state transformation is a unitary map |ψ〉 → U |ψ〉, and a projective measurement is the following map: |ψ〉 → Pi|ψ〉 √pi . But in reality when we perform a quantum operation (e.g., rotation, measurement, coupling) there will inevitably be errors due to noise in the experimental apparatus. Some examples of errors that are commonly encountered in quantum information processing are: 1. Uncertainty in the implemented rotation angle. 2. Control pulses with electronic noise. 3. Noise from nearby “junk”, which are usually uncontrollable degrees of freedom that couple to qubits. In this lecture and the next four we will discuss how to model these nonidealities and how to deal with them and do quantum information tasks reliably in their presence.