thesis.bib

@inreference{sdq_at_kit_latex_nodate,
	title = {{LaTeX} - {SDQ}-Wiki-Artikel},
	url = {https://sdq.kastel.kit.edu/wiki/LaTeX},
	author = {{SDQ at KIT}},
}

@misc{parrish_jacobi_2019,
	title = {A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization},
	doi = {10.48550/arXiv.1904.03206},
	author = {Parrish, Robert M. and Iosue, Joseph T. and Ozaeta, Asier and {McMahon}, Peter L.},
	date = {2019},
	keywords = {interesting},
}

@article{nakanishi_sequential_2020,
	title = {Sequential minimal optimization for quantum-classical hybrid algorithms},
	volume = {2},
	doi = {10.1103/PhysRevResearch.2.043158},
	pages = {043158},
	number = {4},
	journaltitle = {Phys. Rev. Res.},
	author = {Nakanishi, Ken M. and Fujii, Keisuke and Todo, Synge},
	date = {2020-10},
	note = {Publisher: American Physical Society},
}

@article{ostaszewski_structure_2021,
	title = {Structure optimization for parameterized quantum circuits},
	volume = {5},
	issn = {2521-327X},
	doi = {10.22331/q-2021-01-28-391},
	pages = {391},
	journaltitle = {Quantum},
	author = {Ostaszewski, Mateusz and Grant, Edward and Benedetti, Marcello},
	date = {2021-01},
	note = {Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften},
}

@article{ciliberto_quantum_2018,
	title = {Quantum machine learning: a classical perspective},
	volume = {474},
	doi = {10.1098/rspa.2017.0551},
	abstract = {Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning ({ML}) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical {ML} algorithms. Here we review the literature in quantum {ML} and discuss perspectives for a mixed readership of classical {ML} and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in {ML} are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed.},
	number = {2209},
	journaltitle = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
	author = {Ciliberto, Carlo and Herbster, Mark and Ialongo, Alessandro Davide and Pontil, Massimiliano and Rocchetto, Andrea and Severini, Simone and Wossnig, Leonard},
	date = {2018},
}

@inreference{informatik_studiengang-service_bachelorarbeit_nodate,
	title = {Bachelorarbeit (generell) - {FAQ}-Wiki-Artikel},
	url = {https://www.informatik.kit.edu/faq-wiki/doku.php?id=bachelorarbeit_allg},
	author = {{Informatik Studiengang-Service}},
	urldate = {2023-07-10},
}

@legislation{kit-senat_satzung_nodate,
	title = {Satzung zur Sicherung guter wissenschaftlicher Praxis am Karlsruher Institut für Technologie ({KIT})},
	pages = {228--249},
	author = {{KIT-Senat}},
}

@misc{kingma_adam_2017,
	title = {Adam: A Method for Stochastic Optimization},
	doi = {10.48550/arXiv.1412.6980},
	author = {Kingma, Diederik P. and Ba, Jimmy},
	date = {2017},
}

@article{stokes_quantum_2020,
	title = {Quantum Natural Gradient},
	volume = {4},
	issn = {2521-327X},
	doi = {10.22331/q-2020-05-25-269},
	pages = {269},
	journaltitle = {Quantum},
	author = {Stokes, James and Izaac, Josh and Killoran, Nathan and Carleo, Giuseppe},
	date = {2020-05},
	note = {Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften},
}

@article{sim_expressibility_2019,
	title = {Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum-Classical Algorithms},
	volume = {2},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qute.201900070},
	doi = {https://doi.org/10.1002/qute.201900070},
	abstract = {Abstract Parameterized quantum circuits ({PQCs}) play an essential role in the performance of many variational quantum algorithms. One challenge in implementing such algorithms is choosing an effective circuit that well represents the solution space while maintaining a low circuit depth and parameter count. To characterize and identify expressible, yet compact, circuits, several descriptors are proposed, including expressibility and entangling capability, that are statistically estimated from classical simulations. These descriptors are computed for different circuit structures, varying the qubit connectivity and selection of gates. From these simulations, circuit fragments that perform well with respect to the descriptors are identified. In particular, a substantial improvement in performance of two-qubit gates in a ring or all-to-all connected arrangement, compared to that of those on a line, is observed. Furthermore, improvement in both descriptors is achieved by sequences of controlled X-rotation gates compared to sequences of controlled Z-rotation gates. In addition, it is investigated how expressibility “saturates” with increased circuit depth, finding that the rate and saturated value appear to be distinguishing features of a {PQC}. While the correlation between each descriptor and algorithm performance remains to be investigated, methods and results from this study can be useful for algorithm development and design of experiments.},
	number = {12},
	journaltitle = {Advanced Quantum Technologies},
	author = {Sim, Sukin and Johnson, Peter D. and Aspuru-Guzik, Alán},
	date = {2019},
	keywords = {quantum algorithms, quantum circuits, quantum computation},
}

@book{bishop_pattern_2006,
	location = {New York, {NY}},
	title = {Pattern recognition and machine learning},
	isbn = {978-0-387-31073-2},
	url = {https://link.springer.com/book/9780387310732},
	series = {Information science and statistics},
	publisher = {Springer},
	author = {Bishop, Christopher M.},
	date = {2006},
	keywords = {Maschinelles Lernen, Mustererkennung, Mustererkennung / Maschinelles Lernen, Pattern perception / Machine learning / Pattern recognition / Artificial intelligence / Machine learning},
}

@article{kerenidis_quantum_2020,
	title = {Quantum gradient descent for linear systems and least squares},
	volume = {101},
	url = {https://doi.org/10.1103%2Fphysreva.101.022316},
	doi = {10.1103/physreva.101.022316},
	number = {2},
	journaltitle = {Physical Review A},
	author = {Kerenidis, Iordanis and Prakash, Anupam},
	date = {2020-02},
	note = {Publisher: American Physical Society ({APS})},
}

@article{shor_polynomial-time_1997,
	title = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer},
	volume = {26},
	doi = {10.1137/S0097539795293172},
	abstract = {A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.},
	pages = {1484--1509},
	number = {5},
	journaltitle = {{SIAM} Journal on Computing},
	author = {Shor, Peter W.},
	date = {1997},
	note = {\_eprint: https://doi.org/10.1137/S0097539795293172},
}

@book{hidary_quantum_2021,
	location = {Cham, Switzerland},
	edition = {Second edition},
	title = {Quantum Computing: An Applied Approach},
	isbn = {978-3-030-83273-5},
	url = {https://doi.org/10.1007/978-3-030-83274-2},
	publisher = {Springer},
	author = {Hidary, Jack D.},
	date = {2021},
	keywords = {Quantencomputer / Qubit},
}

@book{nielsen_quantum_2007,
	location = {Cambridge},
	edition = {9},
	title = {Quantum computation and quantum information},
	isbn = {978-0-521-63503-5},
	url = {https://www.cambridge.org/9780521635035},
	publisher = {Cambridge Univ. Press},
	author = {Nielsen, Michael A. and Chuang, Isaac L.},
	date = {2007},
	keywords = {Quantencomputer, Quantencomputer / Informationstheorie, Quantencomputer / Paralleler Algorithmus, Quantum computers},
}

@article{deutsch_quantum_1985,
	title = {Quantum theory, the Church–Turing principle and the universal quantum computer},
	volume = {400},
	doi = {10.1098/rspa.1985.0070},
	abstract = {It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the 'universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it. The intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than Everett’s. Some of the numerous connections between the quantum theory of computation and the rest of physics are explored. Quantum complexity theory allows a physically more reasonable definition of the ‘complexity’ or ‘knowledge’ in a physical system than does classical complexity theory.},
	pages = {97--117},
	number = {1818},
	journaltitle = {Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
	author = {Deutsch, David and Penrose, Roger},
	date = {1985},
}

@article{wecker_progress_2015,
	title = {Progress towards practical quantum variational algorithms},
	volume = {92},
	doi = {10.1103/PhysRevA.92.042303},
	pages = {042303},
	number = {4},
	journaltitle = {Phys. Rev. A},
	author = {Wecker, Dave and Hastings, Matthew B. and Troyer, Matthias},
	date = {2015-10},
	note = {Publisher: American Physical Society},
}

@misc{wendenius_gradient-free_2023,
	title = {Gradient-free Optimization of Parameterized Quantum Circuits},
	abstract = {Currently, parameterized quantum circuits are commonly trained by classical optimizers and by applying the parameter-shift rule to determine gradients. In this way, the pipeline and the workflow established in classical machine learning are directly transferred to quantum computing. In our work, we present an approach to train parameterized quantum circuits by taking advantage of quantum-specific properties. Specifically, we exploit that the influence of a parameterized rotational gate on the expectation value of a quantum circuit can be represented by a sine wave. By determining this sine wave with a minimum number of circuit evaluations, we are able to directly set the parameters to their optimal value in the current circuit configuration. Iterating this process over all learnable parameters allows for a rapid decrease in training loss. We briefly present the theoretical background of our approach, investigate practical implications, and perform experiments on several circuits used
in the literature. Our results show that we can consistently outperform established and widely used optimizers.},
	author = {Wendenius, Christof and Kuehn, Eileen and Fischer, Max and Strobl, Melvin and Streit, Achim},
	date = {2023},
	file = {Wendenius et al. - 2023 - Gradient-free Optimization of Parameterized Quantu.pdf:/home/max/Zotero/storage/UBYVC2ZM/Wendenius et al. - 2023 - Gradient-free Optimization of Parameterized Quantu.pdf:application/pdf},
}

@article{schuld_evaluating_2019,
	title = {Evaluating analytic gradients on quantum hardware},
	volume = {99},
	doi = {10.1103/physreva.99.032331},
	number = {3},
	journaltitle = {Physical Review A},
	author = {Schuld, Maria and Bergholm, Ville and Gogolin, Christian and Izaac, Josh and Killoran, Nathan},
	date = {2019-03},
	note = {Publisher: American Physical Society ({APS})},
}

@article{mitarai_quantum_2018,
	title = {Quantum circuit learning},
	volume = {98},
	doi = {10.1103/physreva.98.032309},
	number = {3},
	journaltitle = {Physical Review A},
	author = {Mitarai, K. and Negoro, M. and Kitagawa, M. and Fujii, K.},
	date = {2018-09},
	note = {Publisher: American Physical Society ({APS})},
}

@misc{watanabe_optimizing_2023,
	title = {Optimizing Parameterized Quantum Circuits with Free-Axis Selection},
	author = {Watanabe, Hiroshi C. and Raymond, Rudy and Ohnishi, Yu-ya and Kaminishi, Eriko and Sugawara, Michihiko},
	date = {2023},
}

@misc{wada_sequential_2023,
	title = {Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits},
	author = {Wada, Kaito and Raymond, Rudy and Sato, Yuki and Watanabe, Hiroshi C.},
	date = {2023},
}

@article{wierichs_general_2022,
	title = {General parameter-shift rules for quantum gradients},
	volume = {6},
	doi = {10.22331/q-2022-03-30-677},
	pages = {677},
	journaltitle = {Quantum},
	author = {Wierichs, David and Izaac, Josh and Wang, Cody and Lin, Cedric Yen-Yu},
	date = {2022-03},
	note = {Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},
	keywords = {interesting},
}

@misc{bergholm_pennylane_2018,
	title = {{PennyLane}: Automatic differentiation of hybrid quantum-classical computations},
	doi = {10.48550/arXiv.1811.04968},
	author = {Bergholm, Ville and Izaac, Josh and Schuld, Maria and Gogolin, Christian and Ahmed, Shahnawaz and Ajith, Vishnu and Alam, M. Sohaib and Alonso-Linaje, Guillermo and {AkashNarayanan}, B. and Asadi, Ali and Arrazola, Juan Miguel and Azad, Utkarsh and Banning, Sam and Blank, Carsten and Bromley, Thomas R. and Cordier, Benjamin A. and Ceroni, Jack and Delgado, Alain and Matteo, Olivia Di and Dusko, Amintor and Garg, Tanya and Guala, Diego and Hayes, Anthony and Hill, Ryan and Ijaz, Aroosa and Isacsson, Theodor and Ittah, David and Jahangiri, Soran and Jain, Prateek and Jiang, Edward and Khandelwal, Ankit and Kottmann, Korbinian and Lang, Robert A. and Lee, Christina and Loke, Thomas and Lowe, Angus and {McKiernan}, Keri and Meyer, Johannes Jakob and Montañez-Barrera, J. A. and Moyard, Romain and Niu, Zeyue and O'Riordan, Lee James and Oud, Steven and Panigrahi, Ashish and Park, Chae-Yeun and Polatajko, Daniel and Quesada, Nicolás and Roberts, Chase and Sá, Nahum and Schoch, Isidor and Shi, Borun and Shu, Shuli and Sim, Sukin and Singh, Arshpreet and Strandberg, Ingrid and Soni, Jay and Száva, Antal and Thabet, Slimane and Vargas-Hernández, Rodrigo A. and Vincent, Trevor and Vitucci, Nicola and Weber, Maurice and Wierichs, David and Wiersema, Roeland and Willmann, Moritz and Wong, Vincent and Zhang, Shaoming and Killoran, Nathan},
	date = {2018},
}

@misc{vidal_calculus_2018,
	title = {Calculus on parameterized quantum circuits},
	author = {Vidal, Javier Gil and Theis, Dirk Oliver},
	date = {2018},
}

@article{schuld_effect_2021,
	title = {Effect of data encoding on the expressive power of variational quantum-machine-learning models},
	volume = {103},
	url = {https://doi.org/10.1103%2Fphysreva.103.032430},
	doi = {10.1103/physreva.103.032430},
	number = {3},
	journaltitle = {Physical Review A},
	author = {Schuld, Maria and Sweke, Ryan and Meyer, Johannes Jakob},
	date = {2021-03},
	note = {Publisher: American Physical Society ({APS})},
}

@misc{vidal_input_2020,
	title = {Input Redundancy for Parameterized Quantum Circuits},
	author = {Vidal, Javier Gil and Theis, Dirk Oliver},
	date = {2020},
	note = {\_eprint: 1901.11434},
}

@book{bronstejn_taschenbuch_2016,
	location = {Haan-Gruiten},
	edition = {10., überarbeitete Auflage},
	title = {Taschenbuch der Mathematik},
	isbn = {978-3-8085-5790-7},
	url = {https://d-nb.info/1081907711},
	series = {Edition Harri Deutsch},
	publisher = {Verlag Europa-Lehrmittel - Nourney, Vollmer {GmbH} \& Co. {KG}},
	author = {Bronštejn, Il'ja N.},
	editor = {Semendjaev, Konstantin A. and Musiol, Gerhard and Mühlig, Heiner},
	date = {2016},
	keywords = {Mathematics / Mathematics, Mathematik},
}

@online{unitary_fund_team_results_2022,
	title = {Results Are in for the 2022 Quantum Open Source Software Survey!},
	url = {https://unitary.fund/posts/2022_survey_results/},
	titleaddon = {Unitary Fund Blog},
	author = {{Unitary Fund Team}},
	urldate = {2023-11-26},
	date = {2022-11-07},
}

@article{duchi_adaptive_2011,
	title = {Adaptive Subgradient Methods for Online Learning and Stochastic Optimization},
	volume = {12},
	issn = {1532-4435},
	abstract = {We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.},
	pages = {2121--2159},
	journaltitle = {J. Mach. Learn. Res.},
	author = {Duchi, John and Hazan, Elad and Singer, Yoram},
	date = {2011-07},
}

@article{preskill_quantum_2018,
	title = {Quantum Computing in the {NISQ} era and beyond},
	volume = {2},
	issn = {2521-327X},
	doi = {10.22331/q-2018-08-06-79},
	pages = {79},
	journaltitle = {Quantum},
	author = {Preskill, John},
	date = {2018-08},
	note = {Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},
}

@article{cerezo_variational_2021,
	title = {Variational quantum algorithms},
	volume = {3},
	issn = {2522-5820},
	doi = {10.1038/s42254-021-00348-9},
	abstract = {Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers, owing to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will probably not be available in the near future. Current quantum devices have serious constraints, including limited numbers of qubits and noise processes that limit circuit depth. Variational quantum algorithms ({VQAs}), which use a classical optimizer to train a parameterized quantum circuit, have emerged as a leading strategy to address these constraints. {VQAs} have now been proposed for essentially all applications that researchers have envisaged for quantum computers, and they appear to be the best hope for obtaining quantum advantage. Nevertheless, challenges remain, including the trainability, accuracy and efficiency of {VQAs}. Here we overview the field of {VQAs}, discuss strategies to overcome their challenges and highlight the exciting prospects for using them to obtain quantum advantage.},
	pages = {625--644},
	number = {9},
	journaltitle = {Nature Reviews Physics},
	shortjournal = {Nature Reviews Physics},
	author = {Cerezo, M. and Arrasmith, Andrew and Babbush, Ryan and Benjamin, Simon C. and Endo, Suguru and Fujii, Keisuke and {McClean}, Jarrod R. and Mitarai, Kosuke and Yuan, Xiao and Cincio, Lukasz and Coles, Patrick J.},
	date = {2021-09-01},
}

@article{spall_multivariate_1992,
	title = {Multivariate stochastic approximation using a simultaneous perturbation gradient approximation},
	volume = {37},
	doi = {10.1109/9.119632},
	pages = {332--341},
	number = {3},
	journaltitle = {{IEEE} Transactions on Automatic Control},
	author = {Spall, J.C.},
	date = {1992},
}

@article{benedetti_parameterized_2019,
	title = {Parameterized quantum circuits as machine learning models},
	volume = {4},
	issn = {2058-9565},
	doi = {10.1088/2058-9565/ab4eb5},
	pages = {043001},
	number = {4},
	journaltitle = {Quantum Science and Technology},
	author = {Benedetti, Marcello and Lloyd, Erika and Sack, Stefan and Fiorentini, Mattia},
	date = {2019-11},
	note = {Publisher: {IOP} Publishing},
}

@software{schweikart_schweikartcrotosolve_2023,
	title = {schweikart/crotosolve},
	url = {https://doi.org/10.5281/zenodo.10413938},
	version = {v0.1.0},
	publisher = {Zenodo},
	author = {Schweikart, Max},
	date = {2023-12},
}

@article{jordan_machine_2015,
	title = {Machine learning: Trends, perspectives, and prospects},
	volume = {349},
	doi = {10.1126/science.aaa8415},
	abstract = {Machine learning addresses the question of how to build computers that improve automatically through experience. It is one of today’s most rapidly growing technical fields, lying at the intersection of computer science and statistics, and at the core of artificial intelligence and data science. Recent progress in machine learning has been driven both by the development of new learning algorithms and theory and by the ongoing explosion in the availability of online data and low-cost computation. The adoption of data-intensive machine-learning methods can be found throughout science, technology and commerce, leading to more evidence-based decision-making across many walks of life, including health care, manufacturing, education, financial modeling, policing, and marketing.},
	pages = {255--260},
	number = {6245},
	journaltitle = {Science},
	author = {Jordan, M. I. and Mitchell, T. M.},
	date = {2015},
}

@article{nelder_simplex_1965,
	title = {A Simplex Method for Function Minimization},
	volume = {7},
	issn = {0010-4620},
	doi = {10.1093/comjnl/7.4.308},
	abstract = {A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n + 1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.},
	pages = {308--313},
	number = {4},
	journaltitle = {The Computer Journal},
	author = {Nelder, J. A. and Mead, R.},
	date = {1965-01},
}