Catalytic Embedding: A Framework for Improved Expressibility and Approximation Assistant
Speaker
Sam Mendelson
Naval Surface Warefare Center – Dahlgren
Monday, February 13, 2023, from 12:30–1:30 pm
3301 Exploratory Hall, Fairfax Campus, George Mason University
Zoom: https://go.gmu.edu/qcseminar
Abstract
Given a finite or countably infinite gate set G, the set of unitary operators implementable over G is necessarily a subset of U(C). To implement unitary operators lying outside G, approximation by a sequence of gates in G is typically used, usually as the result of appropriate approximate synthesis algorithms. We introduce a method for increasing the expressability of gate set via the framework of catalytic embeddings. In this framework, approximations are relegated to a fixed number of reusable resource states called catalysts. In the limit of increasing gate count and target precision, when possible, catalytic embedding always produces shorter circuits, due to this fixed number of approximations. This generalizes a technique previously used to implement the Quantum Fourier Transform over Clifford+T with O(n) gate approximations.
In this talk, we will discuss different classes of catalytic embeddings and their structural properties.
We give a constructive method for a class of catalytic embeddings and reduce the problem to finding a normal matrix with a given characteristic polynomial. Finally, we will discuss both practical and theoretical applications of these embedding techniques.