TY - CHAP A1 - Schmidbauer, Lukas A1 - Wintersperger, Karen A1 - Lobe, Elisabeth A1 - Mauerer, Wolfgang T1 - Polynomial Reduction Methods and their Impact on QAOA Circuits T2 - IEEE International Conference on Quantum Software (QSW), 7-13 July 2024, Shenzhen, China N2 - Abstraction layers are of paramount importance in software architecture, as they shield the higher-level formulation of payload computations from lower-level details. Since quantum computing (QC) introduces many such details that are often unaccustomed to computer scientists, an obvious desideratum is to devise appropriate abstraction layers for QC. For discrete optimisation, one such abstraction is to cast problems in quadratic unconstrained binary optimisation (QUBO) form, which is amenable to a variety of quantum approaches. However, different mathematically equivalent forms can lead to different behaviour on quantum hardware, ranging from ease of mapping onto qubits to performance scalability. In this work, we show how using higher-order problem formulations (that provide better expressivity in modelling optimisation tasks than plain QUBO formulations) and their automatic transformation into QUBO form can be used to leverage such differences to prioritise between different desired non-functional properties for quantum optimisation. Based on a practically relevant use-case and a graph-theoretic analysis, we evaluate how different transformation approaches influence widely used quantum performance metrics (circuit depth, gates count, gate distribution, qubit scaling), and also consider the classical computational efforts required to perform the transformations, as they influence possibilities for achieving future quantum advantage. Furthermore, we establish more general properties and invariants of the transformation methods. Our quantitative study shows that the approach allows us to satisfy different trade-offs, and suggests various possibilities for the future construction of general-purpose abstractions and automatic generation of useful quantum circuits from high-level problem descriptions. KW - HW-SW co design KW - NISQ systems KW - noisy quantum computing KW - quantum software engineering Y1 - 2024 U6 - https://doi.org/10.1109/QSW62656.2024.00018 SP - 35 EP - 45 ER - TY - GEN A1 - Schmidbauer, Lukas A1 - Lobe, Elisabeth A1 - Schäfer, Ina A1 - Mauerer, Wolfgang T1 - It's Quick to be Square: Fast Quadratisation for Quantum Toolchains [Data set] N2 - Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an order as determined by the structure of the objective function and the properties of target hardware. When the structure of the problem representation is not aligned with structure and boundary conditions of the executing hardware, various overheads to degrade the computation may arise, possibly negating any possible quantum advantage. Therefore, automatic transformations of problem representations play an important role in quantum computing when descriptions (semi-)targeted at humans must be cast into forms that can be executed on quantum computers. Mathematically equivalent formulations are known to result in substantially different non-functional properties depending on hardware, algorithm and detail properties of the problem. Given the current state of noisy-intermediate scale quantum hardware (NISQ), these effects are considerably more pronounced than in classical computing. Likewise, efficiency of the transformation itself is relevant because possible quantum advantage may easily be eradicated by the overhead of transforming between representations. In this paper we consider a specific class of higher-level representations (polynomial unconstrained binary optimisation problems), and devise novel automatic transformation mechanisms into widely used quadratic unconstrained binary optimisation problems that substantially improve efficiency and versatility over the state of the art. We also identify what influence factors of lower-level details can be abstracted away in the transformation process, and which details must be made available to higher-level abstractions. Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.14245588 N1 - Paper: 10.48550/arXiv.2411.19934 Software: https://github.com/lfd/Fast_Quadratisation ER - TY - INPR A1 - Schmidbauer, Lukas A1 - Lobe, Elisabeth A1 - Schäfer, Ina A1 - Mauerer, Wolfgang T1 - It's Quick to be Square: Fast Quadratisation for Quantum Toolchains N2 - Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an order as determined by the structure of the objective function and the properties of target hardware. When the structure of the problem representation is not aligned with structure and boundary conditions of the executing hardware, various overheads degrading the computation may arise, possibly negating any possible quantum advantage. Therefore, automatic transformations of problem representations play an important role in quantum computing when descriptions (semi-)targeted at humans must be cast into forms that can be executed on quantum computers. Mathematically equivalent formulations are known to result in substantially different non-functional properties depending on hardware, algorithm and detail properties of the problem. Given the current state of noisy intermediate-scale quantum (NISQ) hardware, these effects are considerably more pronounced than in classical computing. Likewise, efficiency of the transformation itself is relevant because possible quantum advantage may easily be eradicated by the overhead of transforming between representations. In this paper, we consider a specific class of higher-level representations, i.e. polynomial unconstrained binary optimisation problems, and devise novel automatic transformation mechanisms into widely used quadratic unconstrained binary optimisation problems that substantially improve efficiency and versatility over the state of the art. We also identify what influence factors of lower-level details can be abstracted away in the transformation process, and which details must be made available to higher-level abstractions. Y1 - 2024 N1 - Der Aufsatz wurde peer-reviewed veröffentlicht und ist ebenfalls in diesem Repositorium verzeichnet unter: https://opus4.kobv.de/opus4-oth-regensburg/frontdoor/index/index/docId/9006 ER -