arXiv subjects

Vihaan Dheer

Publications and source records attributed to Vihaan Dheer.

2 recordsLinked to original sources

arXiv2023

An Infinitary Model of Diagrammatic Calculus in Unbiased Monoidal Categories

Properties of morphisms represented by so-called 'string diagrams' of monoidal categories (and their braided and symmetric derivatives), mainly their resistance in value to isotopic deformation, have made the usage of graphical calculi commonplace in category theory ever since the correspondence between diagrams and tensor categories was rigorously established by Joyal and Street in 1991. However, we find it important to make certain additions to the existing theory of monoidal categories and their diagrams, with the goal of extending to so-called 'infinitary monoidal categories'. Most crucially, we employ a structure inherently resistant to isotopic deformation, thus replacing topological details with categorical ones. In the process, we coherently introduce infinitary tensor product and transfinite composition into the diagrammatic formalism.

math.CT↗

arXiv2021

The Optimization of Flux Trajectories for the Adiabatic Controlled-Z Gate on Split-Tunable Transmons

In a system of two tunable-frequency qubits, it is well-known that adiabatic tuning into strong coupling-interaction regions between the qubit subspace and the rest of the Hilbert space can be used to generate an effective controlled Z rotation. We address the problem of determining a preferable adiabatic trajectory along which to tune the qubit frequency, and apply this to the flux-tunable transmon model. The especially minimally anharmonic nature of these quantum processors makes them good candidates for qubit control using non-computational states, as long as higher-level leakage is properly addressed. While the statement of this method has occurred multiple times in literature, there has been little discussion of which trajectories may be used. We present a generalized method for optimizing parameterized families of possible flux trajectories and provide examples of use on five test families of one and two parameters.

quant-ph↗