No abstract

We extend the work in 2017 New J. Phys. 19 103015 by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields. This bound is explicitly analyzed for a specific N-level system similar to those used to represent simple models of an atom, or the first excitation sector of a Heisenberg spin chain, both of which are of interest in quantum control for quantum computation. Specifically, it is shown that the resultant bound depends on the dimension of the system, and on the number of controls used to implement a specific target unitary operation. The value of the bound determined numerically, and an estimate of the true minimum gate time are systematically compared for a range of system dimension and number of controls; special attention is drawn to the relationship between these two variables. It is seen that the bound captures the scaling of the minimum time well for the systems studied, and quantitatively is correct in the order of magnitude.

We derive an upper bound for the time needed to implement a generic unitary transformation in a d dimensional quantum system using d control fields. We show that given the ability to control the diagonal elements of the Hamiltonian, which allows for implementing any unitary transformation under the premise of controllability, the time T needed is upper bounded by T ≤ πd 2 (d−1) 2g min where gmin is the smallest coupling constant present in the system. We study the tightness of the bound by numerically investigating randomly generated systems, with specific focus on a system consisting of d energy levels that interact in a tight-binding like manner.

Physicists revolutionized the scientific world when they invented the laser in 1960. During the next two decades, fruitful interplay occurred between theoreticians and experimentalists seeking progress in laser-selective chemistry. In the Early Era, defined as 1960∼1985, scientists gradually realized the immense complexity of the problem of performing tailored manipulations at the molecular scale. However, their efforts opened the doors to a new, broader scientific field of research called quantum control which developed in the Modern Era, defined as 1985 to the present time. This Perspective aims to show that the roots of quantum control may be linked to endeavors to manipulate chemical reactions with lasers and thus reaches as far back as the invention of the laser in 1960. We will emphasize the role of advancing technology, the prescience in the questions raised by researchers, and the role of interdisciplinary research. The Perspective concludes with an assessment of what was achieved in the Early Era.

In this work we design a class of Ansätze to solve MaxCut on a parameterized quantum circuit (PQC). Gaining inspiration from properties of quantum optimal control landscapes, we consider the presence of optimization traps as a measure of complexity for hybrid variational quantum algorithms. In particular, we analytically show that no simple Ansatz, satisfying certain criteria, Declaration I declare that I have not violated the Honor Code during the composition of this work. This paper represents my own work in accordance with University regulations.