+++
title = "Summary and further reading"
weight = 5
layout = "section"
slug = "sec:litt"
+++

This introductory chapter covered some of the basic principles of quantum
computation and, in doing so, hopefully, made a convincing argument as to why we
should expect the programs running on quantum hardware to become more complex in
the future, with the intertwining of classical and quantum
computations---processes we refer to as hybrid quantum-classical programs. Prior
to that, we also presented quantum compilation, an emerging discipline that is
introducing many new problems and ideas to the established corpus of work on
compiler research.

If this quantum taster has intrigued you or you would like to learn the basics
from people who _actually_ know what they are talking about, nothing beats the
reference book for quantum information and quantum computing by Nielsen and
Chuang @Nielsen2016. A fascinating alternative perspective on quantum theory has
also been developed within the programme of categorical quantum mechanics, for
which the illustrious "Dodo book" @Coecke2017 would be the go-to introductory
material[^dodo].

[^dodo]:
    And while we're on the topic of my supervisor's brilliant work, there is
    also a very recent textbook, a sort of spiritual successor to @Coecke2017,
    particularly focused on quantum compilation @Kissinger2024. It is just as
    worth a read and might appeal more to the computer science-y reader.

At the risk of turning this thesis into absolutely shameless Oxford
self-promotion, guess what else was a product of this university's _world-class_
research? The quantum circuit itself! These diagrams came from theoretical
physicists (no surprise here) interested in capturing thought experiments in
quantum information theory @Deutsch1989.

The idea caught on, and soon, software tools were created to facilitate building
such diagrams. The Quantum Computation Language (QCL) was one of the first
@Oemer2000. Quantum software[^actuallyclassical] has since proliferated,
especially as the possibility of actually _performing_ these thought experiments
on quantum hardware became more tangible. The result were software packages for
quantum computing, designed for the automatic transformation and _optimisation_
of quantum computations for execution on real hardware @JavadiAbhari2024
@CirqDevelopers2024 @Steiger_2018 @Sivarajah2020&#x200B;---we called them
quantum compilers.

[^actuallyclassical]:
    That is _classical_ software written to control and optimise quantum
    computations.

A recent development for quantum compilers focuses on scalability and
first-class support for hybrid quantum-classical computations. Quantum circuits
that include some form of classical control have been variously called "dynamic
circuits" (e.g. @Corcoles2021), "adaptive circuits" (e.g. @Smith2024), "circuits
with measurements and feedforward" (e.g. @Graham2023), and "circuits assisted by
local operations and classical communication" (e.g. @Piroli2021).

Besides supporting advances in quantum hardware @Corcoles2021 @Graham2023
@Pino2021, hybrid classical-quantum computations are central to many quantum
computing applications. As put recently by Alam and Clark @Alam2024&#x200B;:

> "[...] dynamic quantum circuits are a crucial milestone on the roadmap to
> fault-tolerant quantum computers."

We have covered a small subset of applications of hybrid quantum-classical
computations. Quantum teleportation is undoubtedly one of the oldest
@Bennett1993. The block-encoding technique that we discussed in
{{% reflink "sec:hybrid" %}} is the foundation of several algorithms, including
the Quantum Singular Value Decomposition (QSVT) @Gilyen2019 and the Linear
Combination of Unitaries (LCU) @Chakraborty2024 @Sze2025. Measurement-based
quantum computing (MBQC) was introduced in @Raussendorf_2001 and is forming the
base for some photonic quantum computing architectures @Bartolucci_2023
@Bourassa2021. Hybrid programs have also been shown to be useful for
implementing the Quantum Fourier Transform (QFT) @Baeumer2024 and the Quantum
Phase Estimation (QPE) algorithms @Corcoles2021, two of the most fundamental
computation primitives for quantum algorithms.

On the other hand, repeat until success schemes @Paetznick2014 are widespread in
state preparation routines and will play a key role in fault-tolerant (FT)
quantum computing. Arguably, the most well-known scheme for FT is magic state
distillation @Bravyi2005, a procedure expected to be a core building block of
many FT architectures. State preparation is generally a ubiquitous problem for
FT, as the error-correcting codes that are employed initiate computations
starting from a _logical_ zero state, which may be expensive to prepare on the
qubits of the hardware @Fowler2012.

Finally, quantum error-correcting (QEC) codes themselves must be implemented
using hybrid programs. The quantum error correction (QEC) literature is vast and
can get very technical very quickly, but diving into it promises bountiful
rewards. The field is one of quantum information's fastest-evolving areas of
research. These work-in-progress lecture notes @Gottesman2024 by a coryphaeus of
the field make for excellent introductory material.
