A learning theory for quantum photonic processors and beyond
This provides efficient learnability guarantees for optical quantum technologies, including photonic processors, which is incremental but important for practical quantum computing applications.
The paper tackles the problem of learning quantum states, measurements, and channels generated by continuous-variable quantum circuits, showing that these circuits can be learned with a sample complexity that scales polynomially with the number of modes and does not scale with circuit depth.
We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes state-of-the-art photonic processors capable of showing quantum advantage. We define classes of functions that map classical variables, encoded into the CV circuit parameters, to outcome probabilities evaluated on those circuits. We then establish efficient learnability guarantees for such classes, by computing bounds on their pseudo-dimension or covering numbers, showing that CV quantum circuits can be learned with a sample complexity that scales polynomially with the circuit's size, i.e., the number of modes. Our results show that CV circuits can be trained efficiently using a number of training samples that, unlike their finite-dimensional counterpart, does not scale with the circuit depth.