In this talk, I will present some of my past and current works on quantum algorithms. The first part of the talk will be on quantum algorithms for far-future quantum computers with large-scale and perfectly functioning components. The second part will be on employing machine-learning methods for analysing the average-case complexity of algorithms and our vision for applying them to current and near-future noisy quantum computers.
Specifically, in the first part, I will talk about simulating quantum field theories on a quantum computer and an optimal approach for extracting information encoded in a quantum state. Along the way, I will describe how representing quantum fields in multiple scales using wavelets enables more efficient preparation of certain states of a quantum field and dealing with non-linearities in a system. In the second part, I will discuss empirical hardness models, their various applications, and our vision to bring them to the quantum domain. These models allow us to characterize the difficulty of solving a given family of problems using the best available algorithms. These algorithms typically have exponentially varying performances and no attractive theoretical guarantees but work astonishingly well in practice.
This video was produced by the Fields Institute, as part of their Quantum Information Seminar series.
