Quantum Computation Beyond the Circuit Model

TL;DR

This thesis explores alternative models of quantum computation beyond the circuit model, presenting new methods for fault tolerance, complexity classification, and interaction simulation, along with future research directions.

Contribution

It introduces novel approaches to fault tolerance, complexity analysis, and interaction simulation in various quantum computation models, expanding beyond the traditional circuit framework.

Findings

Improved fault tolerance in adiabatic quantum computers using error detecting codes

Proved certain problems are complete for the one clean qubit complexity class

Generalized perturbative gadgets for simulating k-body interactions with 2-body interactions

Abstract

The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Lastly, I discuss general principles regarding quantum computation that I learned in the course of my research, and using these principles I propose directions for future research.