Foundational Abstractions for Quantum Programming

Abstract

Bringing the promise of quantum computation into reality requires not only building a quantum computer but also correctly programming it to run a quantum algorithm. To obtain asymptotic advantage over classical algorithms for applications including simulation, search, and optimization, quantum algorithms rely on the ability of data in quantum superposition to exhibit phenomena such as interference and entanglement. In turn, an implementation of the algorithm as a program must correctly orchestrate these phenomena in the states of qubits. Otherwise, it would yield incorrect outputs or lose quantum computational advantage.

Given a quantum algorithm, what are the challenges and costs of realizing it as a program that can run on a physical quantum computer? In this thesis, I answer this question by showing how the basic abstractions of programming upon which many quantum algorithms rely – such as data structures and control flow – can fail to work correctly or efficiently on a quantum computer. I then demonstrate how we can leverage insights from research in programming languages to re-invent the software stack – including abstractions, libraries, and compilers – to meet the demands of quantum algorithms. This approach holds out a promise of expressive and efficient tools to program a quantum computer and thereby practically realize its computational advantage.