Speaker: Thomas Gorin (Universidad de Guadalajara, Mexico)
Title: Quantum processes with non-unitary gates for solving optimization problems
Date: 20 July 2023., 13:00
Place: Building 2, Media room
Abstarct:
The capacity to solve optimization problems efficiently is fundamental in life. From the evolution and survival of organisms to the solution of
Travelling Salesman type problems in the flow of goods and services. Though it is natural to ask, whether quantum algorithms can outperform classical ones. Traditionally, quantum algorithms are assembled from a few basic quantum gates and protected from decoherence and errors by quantum error correction. But one may envisage building algorithms from imperfect (non-unitary) quantum gates, which may be realizable with current quantum computers.
In this talk, I will discuss a proof of principle that such a strategy might actually work. Starting from the classical zero-temperature Metropolis algorithm for the minimum search in an Ising spin system, we replace random which-path decisions by superpositions of all possible paths. We them show by numerical simulations that the resulting relaxation process has different scaling properties than the original classical one. This remains true even when the decoherence rate is drastically reduced. Finally, we find that the scaling properties also depend on the phases chosen for the superpositions, with the result that the relaxation times may be larger or shorter than the classical one.
