Supervised learning of time-independent Hamiltonians for gate design

Author:

Innocenti LucaORCID,Banchi LeonardoORCID,Ferraro AlessandroORCID,Bose SougatoORCID,Paternostro MauroORCID

Abstract

Abstract We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the time-independent gate generator, thus translating the task into an inverse eigenvalue problem. We illustrate our methodology by identifying suitable time-independent generators implementing Toffoli and Fredkin gates without the need for ancillae or effective evolutions. We show how the same conditions can be used to solve the problem numerically, via supervised learning techniques. In turn, this allows us to solve problems that are not amenable, in general, to direct analytical solution, providing at the same time a high degree of flexibility over the types of gate-design problems that can be approached. As a significant example, we find generators for the Toffoli gate using only diagonal pairwise interactions, which are easier to implement in some experimental architectures. To showcase the flexibility of the supervised learning approach, we give an example of a non-trivial four-qubit gate that is implementable using only diagonal, pairwise interactions.

Funder

Fondazione Angelo della Riccia

Engineering and Physical Sciences Research Council

MIUR - Rita Levi Montalcini

H2020 Future and Emerging Technologies

FP7 Ideas: European Research Council

Science Foundation Ireland - Department for Economy

Leverhulme Trust

Royal Society Wolfson Fellowship

Publisher

IOP Publishing

Subject

General Physics and Astronomy

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