You can place it in two categories that we could call learning about the quantum world using classic machines and using quantum machines. People now have quantum computers with hundreds of quantum bits or quubits, and completing that characterizes the condition of a quantum computer with Hungs of Qubits is beyond our ability because the complete description grows exponentially with the number of Qubits.
If we go to make to make progress, we need to have a way to translate the quantum information into classic information that we can understand. So part of our work – and this was with two brilliant partners, Robert Huang, a student and Richard Kueng, a postdoc – was a way of translating this very complex quantum system into a brief classic description.
What we showed is that there is a way of performing a relatively modest number of experiments that give you a description of the quantum system from which you can predict a lot of properties – much more properties than the number of measurements you had to make. We call this description a “classic shade”.
Let’s say there is a three -dimensional object and we try to understand its geometry. We can take snapshots of it from different directions that project it on two dimensions. This is like only on steroids because the quantum system lives in some incredibly large dimension, and we project it down to a little bit of information. What we showed is that you don’t need so many of these snapshots to predict a lot of what a physicist would typically be interested in.
We would like to use the data we get from quantum experiments and generalize to predict what looks good when we look at related quantum system or when we look at the quantum system in a different way. And you know AI is everywhere these days and many people are considering using machine learning to understand the quantum system. But it is mostly very heuristic: People try different things and they hope it gives them the opportunity to generalize and make good predictions.
What we wanted to do is provide strict performance guarantees that you don’t need so many of these snapshots to generalize with a small error. And we are able to prove it in some sets.
When it comes to learning with quantum machines, let’s do something else. Let’s grab some quantum data – maybe we produce them on a quantum calculation, or we have a Sensing network that has collected some photons somewhere – and store it in a quantum memory. We just measure it and put it in a classic memory; We store it in a quantum memory and then we make a quantum calculation of this data. And at the end of the calculation we get a classic answer, because at the end of a quantum calculation you always do it.
What we were able to show is that for some speeds of the quantum system that you may want to know it is much more effective to treat with a quantum computer than a classic computer.