Towards a Quantum Programming Language by Peter Selinger. We will mostly focus on Chapter 1-3 for background. [pdf]
Lecture notes on the lambda calculus by Peter Selinger. Chapter 1,2,3,6. [pdf]
Matrix Theory and Linear Algebra by Peter Selinger. Reference for matrics and linear algebra, with interesting applications of linear algbra. [pdf]
Linear Algebra Done Right by Seldon Axler. Slightly more in-depth reference for matrics and linear algebra. [pdf]
Category Theory by Steve Awodey. Standard reference. Available freely online via University's library.
A survey of graphical languages for monoidal categories by Peter Selinger. Standard reference for graphical languages. [pdf]
Quantum computation and quantum information by Michael A. Nielsen and Isaac L. Chuang. Reference. I suggest checking out Chapter 4 for background.
Towards a Quantum Programming Language by Peter Selinger. [pdf]
A lambda calculus for quantum computation with classical control by Peter Selinger and Benoît Valiron. [pdf]
Quantum Weakest Preconditions by Ellie D'Hondt and Prakash Panangaden. [pdf]
The measurement calculus by Vincent Danos, Elham Kashefi, Prakash Panangaden. [pdf]
Quipper: a scalable quantum programming language by Alexander S Green, Peter LeFanu Lumsdaine, Neil J Ross, Peter Selinger, Benoît Valiron. [pdf]
A categorical model for a quantum circuit description language by Francisco Rios, Peter Selinger. [pdf]
QWIRE: A Core Language for Quantum Circuits by Jennifer Paykin, Robert Rand, and Steve Zdancewic. [pdf]
The Heisenberg Representation of Quantum Computers by Daniel Gottesman, [pdf]
Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond by Maarten Van den Nest. [pdf]
Methodology for quantum logic gate constructions by Xinlan Zhou, Debbie W. Leung, Isaac L. Chuang. [pdf]
Quantum circuits of T-depth one by Peter Selinger. [pdf]
Generators and relations for n-qubit Clifford operators by Peter Selinger. [pdf]
Exact synthesis of multi-qubit Clifford+T circuits by Brett Giles, Peter Selinger. [pdf]
A new quantum ripple-carry addition circuit by Steven A. Cuccaro, Thomas G. Draper, Samuel A. Kutin, David Petrie Moulton [pdf]
Elementary gates for quantum computation by A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, H. Weinfurter [pdf]
The phase/state duality in reversible circuit design by Matthew Amy, Neil J. Ross. [pdf]
A categorical semantics of quantum protocols by Samson Abramsky and Bob Coecke. [pdf]
Dagger compact closed categories and completely positive maps by Peter Selinger. [pdf]
Interacting Quantum Observables: Categorical Algebra and Diagrammatics by Bob Coecke, Ross Duncan. [pdf]
The ZX-calculus is complete for stabilizer quantum mechanics by Miriam Backens. [pdf]
The ZX-calculus is incomplete for quantum mechanics by Christian Schröder de Witt, Vladimir Zamdzhiev. [pdf]
Completeness of the ZX-Calculus by Emmanuel Jeandel, Simon Perdrix and Renaud Vilmart. [pdf]
One-way Quantum Computation - a tutorial introduction by Dan E. Browne and Hans J. Briegel. [pdf]