@article(AbramskyCoecke08, author = {Samson Abramsky and Bob Coecke}, year = {2008}, title = {Categorical Quantum Mechanics}, journal = {\href{https://arxiv.org/abs/0808.1023}{\tt arXiv:0808.1023 [quant-ph]}}, ) @article(BackensEtAl20, author = {Miriam Backens and {Miller-Bakewell}, Hector and {de Felice}, Giovanni and Leo Lobski and {van de Wetering}, John}, year = {2020}, title = {There and Back Again: {{A}} Circuit Extraction Tale}, journal = {\href{https://arxiv.org/abs/2003.01664}{\tt arXiv:2003.01664 [quant-ph]}}, ) @article(BenedettiEtAl19, author = {Marcello Benedetti and Erika Lloyd and Stefan Sack}, year = {2019}, title = {Parameterized Quantum Circuits as Machine Learning Models}, journal = {\href{https://arxiv.org/abs/1906.07682}{\tt arXiv:1906.07682 [quant-ph]}}, ) @article(BluteEtAl06, author = {R.~F. Blute and J.~R.~B. Cockett and R.~A.~G. Seely}, year = {2006}, title = {Differential Categories}, journal = {Mathematical Structures in Computer Science}, volume = {16}, number = {06}, pages = {1049}, doi = {10.1017/S0960129506005676}, ) @article(ChancellorEtAl18, author = {Nicholas Chancellor and Aleks Kissinger and Joschka Roffe and Stefan Zohren and Dominic Horsman}, year = {2018}, title = {Graphical {{Structures}} for {{Design}} and {{Verification}} of {{Quantum Error Correction}}}, journal = {\href{https://arxiv.org/abs/1611.08012}{\tt arXiv:1611.08012 [quant-ph]}}, ) @book(Clifford73, author = {William~Kingdon Clifford}, year = {1873}, title = {A Preliminary Sketch of Biquaternions}, ) @article(CockettEtAl19, author = {Robin Cockett and Geoffrey Cruttwell and Jonathan Gallagher and Jean-Simon~Pacaud Lemay and Benjamin MacAdam and Gordon Plotkin and Dorette Pronk}, year = {2019}, title = {Reverse Derivative Categories}, journal = {\href{https://arxiv.org/abs/1910.07065}{\tt arXiv:1910.07065 [cs, math]}}, ) @article(CoeckeEtAl20, author = {Bob Coecke and {de Felice}, Giovanni and Konstantinos Meichanetzidis and Alexis Toumi}, year = {2020}, title = {Foundations for {{Near}}-{{Term Quantum Natural Language Processing}}}, journal = {ArXiv e-prints}, ) @inproceedings(CoeckeDuncan08, author = {Bob Coecke and Ross Duncan}, year = {2008}, title = {Interacting {{Quantum Observables}}}, editor = {Luca Aceto and Damg{\r a}rd, Ivan and Leslie~Ann Goldberg and Magn{\'u}s~M. Halld{\'o}rsson and Anna Ing{\'o}lfsd{\'o}ttir and Igor Walukiewicz}, booktitle = {Automata, {{Languages}} and {{Programming}}}, series = {Lecture {{Notes}} in {{Computer Science}}}, publisher = {{Springer Berlin Heidelberg}}, pages = {298--310}, doi = {10.1016/0022-4049(80)90101-2}, ) @book(CoeckeKissinger17, author = {Bob Coecke and Aleks Kissinger}, year = {2017}, title = {Picturing {{Quantum Processes}}: {{A First Course}} in {{Quantum Theory}} and {{Diagrammatic Reasoning}}}, publisher = {{Cambridge University Press}}, address = {{Cambridge}}, doi = {10.1017/9781316219317}, ) @article(CowtanEtAl20a, author = {Alexander Cowtan and Silas Dilkes and Ross Duncan and Will Simmons and Seyon Sivarajah}, year = {2020}, title = {Phase {{Gadget Synthesis}} for {{Shallow Circuits}}}, journal = {Electronic Proceedings in Theoretical Computer Science}, volume = {318}, pages = {213--228}, doi = {10.4204/EPTCS.318.13}, ) @article(CowtanEtAl20, author = {Alexander Cowtan and Will Simmons and Ross Duncan}, year = {2020}, title = {A {{Generic Compilation Strategy}} for the {{Unitary Coupled Cluster Ansatz}}}, journal = {\href{https://arxiv.org/abs/2007.10515}{\tt arXiv:2007.10515 [quant-ph]}}, ) @article(CruttwellEtAl21, author = {G.~S.~H. Cruttwell and Bruno Gavranovi{\'c} and Neil Ghani and Paul Wilson and Fabio Zanasi}, year = {2021}, title = {Categorical {{Foundations}} of {{Gradient}}-{{Based Learning}}}, journal = {\href{https://arxiv.org/abs/2103.01931}{\tt arXiv:2103.01931 [cs, math]}}, ) @article(DeBeaudrapEtAl20, author = {{de Beaudrap}, Niel and Xiaoning Bian and Quanlong Wang}, year = {2020}, title = {Fast and Effective Techniques for {{T}}-Count Reduction via Spider Nest Identities}, journal = {\href{https://arxiv.org/abs/2004.05164}{\tt arXiv:2004.05164 [quant-ph]}}, ) @inproceedings(DeFeliceEtAl20, author = {{de Felice}, Giovanni and Alexis Toumi and Bob Coecke}, year = {2020}, title = {{{DisCoPy}}: {{Monoidal Categories}} in {{Python}}}, booktitle = {Proceedings of the 3rd Annual International Applied Category Theory Conference, {{ACT}}}, volume = {333}, publisher = {{EPTCS}}, doi = {10.4204/EPTCS.333.13}, ) @article(DeGriendDuncan20, author = {{de Griend}, Arianne Meijer-van and Ross Duncan}, year = {2020}, title = {Architecture-Aware Synthesis of Phase Polynomials for {{NISQ}} Devices}, journal = {\href{https://arxiv.org/abs/2004.06052}{\tt arXiv:2004.06052 [quant-ph]}}, ) @article(DuncanEtAl20, author = {Ross Duncan and Aleks Kissinger and Simon Perdrix and {van de Wetering}, John}, year = {2020}, title = {Graph-Theoretic {{Simplification}} of {{Quantum Circuits}} with the {{ZX}}-Calculus}, journal = {Quantum}, volume = {4}, pages = {279}, doi = {10.22331/q-2020-06-04-279}, ) @inproceedings(DuncanPerdrix10, author = {Ross Duncan and Simon Perdrix}, year = {2010}, title = {Rewriting Measurement-Based Quantum Computations with Generalised Flow}, booktitle = {International Colloquium on Automata, Languages, and Programming}, organization = {{Springer}}, pages = {285--296}, doi = {10.1007/s10472-009-9141-x}, ) @article(GidneyFowler19, author = {Craig Gidney and Austin~G. Fowler}, year = {2019}, title = {Flexible Layout of Surface Code Computations Using {{AutoCCZ}} States}, journal = {\href{https://arxiv.org/abs/1905.08916}{\tt arXiv:1905.08916 [quant-ph]}}, ) @inproceedings(HadzihasanovicEtAl18, author = {Amar Hadzihasanovic and Kang~Feng Ng and Quanlong Wang}, year = {2018}, title = {Two {{Complete Axiomatisations}} of {{Pure}}-State {{Qubit Quantum Computing}}}, booktitle = {Proceedings of the 33rd {{Annual ACM}}/{{IEEE Symposium}} on {{Logic}} in {{Computer Science}}}, series = {{{LICS}} '18}, publisher = {{ACM}}, address = {{New York, NY, USA}}, pages = {502--511}, doi = {10.1145/3209108.3209128}, ) @article(HavlicekEtAl19, author = {Vojtech Havlicek and Antonio~D. C{\'o}rcoles and Kristan Temme and Aram~W. Harrow and Abhinav Kandala and Jerry~M. Chow and Jay~M. Gambetta}, year = {2019}, title = {Supervised Learning with Quantum Enhanced Feature Spaces}, journal = {Nature}, volume = {567}, number = {7747}, pages = {209--212}, doi = {10.1038/s41586-019-0980-2}, ) @article(HaydonSobocinski20, author = {Nathan Haydon and Pawel Sobocinski}, year = {2020}, title = {Compositional {{Diagrammatic First}}-{{Order Logic}}}, pages = {16}, ) @article(Hoffmann16, author = {Philipp H.~W. Hoffmann}, year = {2016}, title = {A {{Hitchhiker}}'s {{Guide}} to {{Automatic Differentiation}}}, journal = {Numerical Algorithms}, volume = {72}, number = {3}, pages = {775--811}, doi = {10.1007/s11075-015-0067-6}, ) @inproceedings(JeandelEtAl18a, author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart}, year = {2018}, title = {A {{Complete Axiomatisation}} of the {{ZX}}-{{Calculus}} for {{Clifford}}+{{T Quantum Mechanics}}}, booktitle = {Proceedings of the 33rd {{Annual ACM}}/{{IEEE Symposium}} on {{Logic}} in {{Computer Science}}}, series = {{{LICS}} '18}, publisher = {{ACM}}, address = {{New York, NY, USA}}, pages = {559--568}, doi = {10.1145/3209108.3209131}, ) @article(JoyalStreet88, author = {Andr{\'e} Joyal and Ross Street}, year = {1988}, title = {Planar Diagrams and Tensor Algebra}, journal = {Unpublished manuscript, available from Ross Street's website}, ) @article(JoyalStreet91, author = {Andr{\'e} Joyal and Ross Street}, year = {1991}, title = {The Geometry of Tensor Calculus, {{I}}}, journal = {Advances in Mathematics}, volume = {88}, number = {1}, pages = {55--112}, doi = {10.1016/0001-8708(91)90003-P}, ) @article(KimEtAl20, author = {Joon-Hwi Kim and Maverick S.~H. Oh and Keun-Young Kim}, year = {2020}, title = {Boosting {{Vector Calculus}} with the {{Graphical Notation}}}, journal = {\href{https://arxiv.org/abs/1911.00892}{\tt arXiv:1911.00892 [hep-th, physics:physics]}}, ) @article(KissingerVanDeWetering19, author = {Aleks Kissinger and {van de Wetering}, John}, year = {2019}, title = {{{PyZX}}: {{Large Scale Automated Diagrammatic Reasoning}}}, journal = {\href{https://arxiv.org/abs/1904.04735}{arXiv:1904.04735 [quant-ph]}}, ) @article(KissingerVanDeWetering20, author = {Aleks Kissinger and {van de Wetering}, John}, year = {2020}, title = {Reducing {{T}}-Count with the {{ZX}}-Calculus}, journal = {Physical Review A}, volume = {102}, number = {2}, pages = {022406}, doi = {10.1103/PhysRevA.102.022406}, ) @inproceedings(MeichanetzidisEtAl20a, author = {Konstantinos Meichanetzidis and Stefano Gogioso and De~Felice, Giovanni and Nicol{\`o} Chiappori and Alexis Toumi and Bob Coecke}, year = {2020}, title = {Quantum {{Natural Language Processing}} on {{Near}}-{{Term Quantum Computers}}}, booktitle = {Quantum {{Physics}} and {{Logic}} ({{QPL}})}, ) @inproceedings(Mellies06, author = {Paul-Andr{\'e} Melli{\`e}s}, year = {2006}, title = {Functorial {{Boxes}} in {{String Diagrams}}}, editor = {Zolt{\'a}n {\'E}sik}, booktitle = {Computer {{Science Logic}}}, series = {Lecture {{Notes}} in {{Computer Science}}}, publisher = {{Springer Berlin Heidelberg}}, pages = {1--30}, doi = {10.1023/A:1024247613677}, ) @article(MeurerEtAl17, author = {Aaron Meurer and Christopher~P. Smith and Mateusz Paprocki and {\v C}ert{\'i}k, Ond{\v r}ej and Sergey~B. Kirpichev and Matthew Rocklin and AMiT Kumar and Sergiu Ivanov and Jason~K. Moore and Sartaj Singh and Thilina Rathnayake and Sean Vig and Brian~E. Granger and Richard~P. Muller and Francesco Bonazzi and Harsh Gupta and Shivam Vats and Fredrik Johansson and Fabian Pedregosa and Matthew~J. Curry and Andy~R. Terrel and Rou{\v c}ka, {\v S}t{\v e}p{\'a}n and Ashutosh Saboo and Isuru Fernando and Sumith Kulal and Robert Cimrman and Anthony Scopatz}, year = {2017}, title = {{{SymPy}}: Symbolic Computing in {{Python}}}, journal = {PeerJ Computer Science}, volume = {3}, pages = {e103}, doi = {10.7717/peerj-cs.103}, ) @article(Penrose71, author = {Roger Penrose}, year = {1971}, title = {{Applications of Negative Dimensional Tensors}}, journal = {Scribd}, ) @book(PenroseRindler84, author = {Roger Penrose and Wolfgang Rindler}, year = {1984}, title = {Spinors and {{Space}}-{{Time}}: {{Volume}} 1: {{Two}}-{{Spinor Calculus}} and {{Relativistic Fields}}}, series = {Cambridge {{Monographs}} on {{Mathematical Physics}}}, volume = {1}, publisher = {{Cambridge University Press}}, address = {{Cambridge}}, doi = {10.1017/CBO9780511564048}, ) @article(SchuldEtAl19, author = {Maria Schuld and Ville Bergholm and Christian Gogolin and Josh Izaac and Nathan Killoran}, year = {2019}, title = {Evaluating Analytic Gradients on Quantum Hardware}, journal = {Physical Review A}, volume = {99}, number = {3}, pages = {032331}, doi = {10.1103/PhysRevA.99.032331}, ) @article(SivarajahEtAl20, author = {Seyon Sivarajah and Silas Dilkes and Alexander Cowtan and Will Simmons and Alec Edgington and Ross Duncan}, year = {2020}, title = {Tket : {{A Retargetable Compiler}} for {{NISQ Devices}}}, journal = {\href{https://arxiv.org/abs/2003.10611}{\tt arXiv:2003.10611 [quant-ph]}}, ) @article(Stone32, author = {M.~H. Stone}, year = {1932}, title = {On One-Parameter Unitary Groups in Hilbert Space}, journal = {Annals of Mathematics}, volume = {33}, number = {3}, pages = {643--648}, doi = {10.2307/1968538}, ) @article(VanDerWaltEtAl11, author = {{van der Walt}, Stefan and S.~Chris Colbert and Gael Varoquaux}, year = {2011}, title = {The {{NumPy Array}}: {{A Structure}} for {{Efficient Numerical Computation}}}, journal = {Computing in Science Engineering}, volume = {13}, number = {2}, pages = {22--30}, doi = {10.1109/MCSE.2011.37}, ) @article(Wang20, author = {Quanlong Wang}, year = {2020}, title = {Completeness of Algebraic {{ZX}}-Calculus over Arbitrary Commutative Rings and Semirings}, journal = {\href{https://arxiv.org/abs/1912.01003}{\tt arXiv:1912.01003 [quant-ph]}}, ) @article(Yeung20, author = {Richie Yeung}, year = {2020}, title = {Diagrammatic {{Design}} and {{Study}} of {{Ansatze}} for {{Quantum Machine Learning}}}, journal = {\href{https://arxiv.org/abs/2011.11073}{\tt arXiv:2011.11073 [quant-ph]}}, ) @article(ZhaoGao21, author = {Chen Zhao and Xiao-Shan Gao}, year = {2021}, title = {Analyzing the Barren Plateau Phenomenon in Training Quantum Neural Network with the {{ZX}}-Calculus}, journal = {\href{https://arxiv.org/abs/2102.01828}{\tt arXiv:2102.01828 [quant-ph]}}, )