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 article, we consider a specific class of higher-level representations, that is, PUBOs, and devise novel automatic transformation mechanisms into widely used QUBOs that substantially improve efficiency and versatility over the state of the art. In addition, we conduct a comprehensive investigation of industry-relevant problem formulations and their conversion into a quantum-specific representation, identifying significant obstacles in scaling behaviour and demonstrating how these can be circumvented.
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 article, we consider a specific class of higher-level representations, that is, PUBOs, and devise novel automatic transformation mechanisms into widely used QUBOs that substantially improve efficiency and versatility over the state of the art. In addition, we conduct a comprehensive investigation of industry-relevant problem formulations and their conversion into a quantum-specific representation, identifying significant obstacles in scaling behaviour and demonstrating how these can be circumvented.
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.
The rapid advancement of quantum computing has created new opportunities for solving computationally intensive problems across diverse fields such as optimization, physical system simulation, and machine learning. However, practical implementation on Noisy Intermediate-Scale Quantum (NISQ) devices remains challenging due to hardware limitations including noise, decoherence, and restricted qubit connectivity. A fundamental constraint further complicating this effort is that all quantum operations must be unitary, while many real-world problems are naturally expressed in non-unitary forms. This discrepancy necessitates novel techniques for transforming non-unitary mathematical structures into unitary or Hamiltonian representations compatible with quantum hardware.This thesis proposes a unified framework for converting structured, sparse, or otherwise non-unitary classical matrices into unitary forms that can be executed efficiently on NISQ devices. The methodology introduces general transformation strategies such as linear combinations of unitaries, structured embeddings, and resource-aware circuit construction, enabling the deployment of quantum algorithms without incurring prohibitive overhead. Each technique is developed with an emphasis on preserving problem structure, minimizing circuit depth, and ensuring compatibility with IBM’s NISQ hardware. The proposed frameworks are validated through theoretical analysis and quantum simulations, with performance benchmarks based on gate count, circuit fidelity, convergence behavior, and scalability. This work demonstrates how non-unitary formulations arising in various computational contexts can be systematically adapted for quantum execution, advancing the practical utility of NISQ-era devices.
The quantum approximate optimisation algorithm (QAOA) and its variants are at the core of many scenarios that aim at combining the power of quantum computers (QC) and classical high-performance computing (HPC) appliances for combinatorial optimisation. Several obstacles challenge concrete benefits now and in the foreseeable future: Imperfections quickly degrade algorithmic performance below practical utility; over-heads arising from alternating between classical and quantum primitives can counter any advantage; and the choice of parameters or algorithmic variant can substantially influence runtime and result quality. Selecting the appropriate combination is a non-trivial issue, as it not only depends on end-user requirements, but also on details of the hardware and software stack. Appropriate automation can alleviate the burden of choosing optimal combinations for end-users: They should not be required to understand technicalities like detail differences between QAOA variants, required number of QAOA layers, or necessary measurement samples. Yet, they should receive the best possible satisfaction of their non-functional requirements, be it performance or other. We determine factors that influence approximation quality and temporal behaviour of four QAOA variants using comprehensive density-matrix-based numerical simulations targeting three widely studied optimisation problems. Our simulations consider ideal quantum computation, and a continuum of scenarios troubled by realistic imperfections. Our quantitative results, accompanied by a comprehensive reproduction package, show strong performance differences between QAOA variants that can be pinpointed to narrow and specific effects. We identify influential co-variables and relevant non-functional quality goals that, as we argue, mark the rele-vant ingredients for designing appropriate software engineering abstraction mechanisms and automated tool-chains for devising quantum solutions from higher-level problem specifications.
Abstract Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP -hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. The paper starts by drawing parallels between classical and quantum optimisation problems, highlighting their conceptual similarities and differences. Two main paradigms for quantum hardware are then discussed: analogue and gate-based quantum computers. While analog devices such as quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation algorithm and the quantum alternating operator ansatz framework, are discussed in detail. However, it is still unclear whether these techniques will yield quantum advantage, even with advancements in hardware and noise reduction. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.
Early-stage decisions in the pharmaceutical development process carry outsized consequences for eventual clinical success, yet the computational tools underpinning these decisions remain fundamentally constrained. Computer-aided drug design (CADD) has transformed how researchers navigate chemical space and predict ligand–target interactions, but classical implementations rely on mechanical force-field approximations that fail to capture polarisation, charge transfer, and electron correlation effects central to molecular recognition and reactivity. Quantum-mechanical treatments that correctly describe these phenomena scale exponentially with system size on classical hardware, rendering them impractical for drug-relevant biomolecules. Quantum computing offers a physically motivated path beyond this scaling barrier: by exploiting superposition, entanglement, and interference, quantum algorithms can in principle simulate electronic structure with polynomial resource requirements for targeted problem classes. This article provides a theoretical review of how quantum computation integrates throughout the drug discovery pipeline, from target identification to lead optimisation. Its primary contribution is a pipeline-level mapping of quantum methods—including the Variational Quantum Eigensolver (VQE), quantum machine learning, and quantum-enhanced optimisation—to specific drug development stages. The review critically distinguishes near-term NISQ (Noisy Intermediate-Scale Quantum: current devices with 50–1,000 noisy qubits operating without full error correction) capabilities from fault-tolerant quantum computing (FTQC) requirements, quantifies current resource gaps through a worked CYP3A4 case study, and identifies algorithmic limitations (barren plateaus, ansatz expressibility, measurement overhead), hardware scalability, and error correction overhead as the principal barriers to practical deployment.
Quantum computers have emerged as an alternative computer paradigm that will allow to solve some complex problems of large numbers that are not tractable for classical computers, e.g. factorization. Quantum computers also have the ability to simulate quantum mechanics in a real and direct way. The development of quantum computers faces many unique obstacles. In recent years, various quantum computer prototypes have been created by com- panies such as Google and IBM, on which we can run some quantum algorithms. But these prototypes are far from the quantum computers we envision and can function like today?s classical computers. It is said that we are in the time of Noisy Intermediate-Scale Quantum (NISQ) computers. This means that current quantum computers are very noisy and their size is very small compared to classical comput- ers. The challenge with small, noisy quantum devices running quantum algorithms is that due to the hardware limitations they face which must be respected, quantum algorithm needs to be modified before their execution on quantum devices. To solve this problem in quantum computers, a mapping process is needed, which is part of the compilation step that modifies the quantum algorithms to take into account all the limitations of the targeted quantum device. After mapping process, the resulting quantum circuit usually has a higher number of gates and (execution time) latency, decreasing the algorithm?s reliability. Different mapping solutions have been already proposed. Most of them are meant for a specific quan- tum processor and different in methodology, approach and features. In addition, they are usually only compared in terms of added gates (gate overhead) or added circuit execution time (latency overhead). No thorough comparative analysis of the different mapping solutions performance and features has been performed so far. In this thesis, we apply structured Design Space Exploration to the mapping of quantum circuits. By doing so, we will be able to have a deeper understanding of this process, make a thorough comparison of the mapper approaches and even develop optimized solutions for given applications and quantum devices. Moreover, we apply Design Space Exploration to the generation of quantum algorithms used as benchmarks and start to explore profiling them in a structured approach.