arXiv subjects

Tom Krüger

Publications and source records attributed to Tom Krüger.

6 recordsLinked to original sources

arXiv2026

Generative AI Beyond Tokens: Quantum Resource Consumption of IQP Circuits

Quantum generative modelling casts sampling as a generative task: a parametrised quantum circuit is trained such that sampling reproduces a target probability distribution. Instantaneous Quantum Polynomial-time (IQP) circuits combine structural simplicity with complexity-theoretic evidence for quantum advantage. Yet their practical value depends not only on expressivity, but on how efficiently they consume genuinely quantum resources. We study this question through the lens of magic, or non-stabiliserness, as a resource for quantum generative modelling. We show that established fidelity- and geodesic-based notions of computational progress in a projective Hilbert space are ill-suited to generative models, since operational performance is determined by output probability distributions rather than quantum states themselves. We evaluate magic-consumption directly on the probability simplex, using changes in Jensen-Shannon divergence to quantify progress. Applying this framework to trained random γ-sparse IQP circuits shows signatures of efficient magic use, with the dominant contribution arising from two-qubit gates. As IQP circuits produce remarkably low intermediate magic relative to phase-randomised states with the same sampling distributions, this renders IQP-based quantum generative models as promising candidates for resource-efficient demonstrations of quantum advantage on early fault-tolerant architectures.

quant-ph↗

arXiv2026

Geometric and Resource-Theoretic Characterisation of Non-Stabiliserness in Quantum Algorithms

While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a still incomplete understanding of the sources of quantum computational power. Advancing towards systematic quantum advantage calls for a better understanding of the efficient use of non-classical resources like non-stabiliser states. We present an approach to track non-classical contributions in the form of non-stabiliserness across various algorithms by pairing resource theory of non-stabiliser entropies with the geometry of quantum state evolution, and introduce permutation agnostic distance measures that reveal and quantify non-stabiliser effects previously hidden by a subset of Clifford operations. We find different efficiency in the use of non-stabiliserness for structured and unstructured variational approaches, and show that greater freedom for classical optimisation in quantum-classical methods increases unnecessary non-stabiliser consumption. Our results open new means of analysing the efficient utilisation of quantum resources, and contribute towards the targeted construction of algorithmic quantum advantage.

quant-ph↗

arXiv2025

Out of the Loop: Structural Approximation of Optimisation Landscapes and non-Iterative Quantum Optimisation

The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure required in every iteration is itself known to be \NP-hard. Still, advantage over classical approaches is suspected for certain scenarios, but nature and origin of its computational power are not yet satisfactorily understood. By introducing means of efficiently and accurately approximating the QAOA optimisation landscape from solution space structures, we derive a new algorithmic variant of unit-depth QAOA for two-level Hamiltonians (including all problems in NP): Instead of performing an iterative quantum-classical computation for each input instance, our non-iterative method is based on a quantum circuit that is instance-independent, but problem-specific. It matches or outperforms unit-depth QAOA for key combinatorial problems, despite reduced computational effort. Our approach is based on proving a long-standing conjecture regarding instance-independent structures in QAOA. By ensuring generality, we link existing empirical observations on QAOA parameter clustering to established approaches in theoretical computer science, and provide a sound foundation for understanding the link between structural properties of solution spaces and quantum optimisation.

quant-ph↗

arXiv2023

Effects of Imperfections on Quantum Algorithms: A Software Engineering Perspective

Quantum computers promise considerable speedups over classical approaches, which has raised interest from many disciplines. Since any currently available implementations suffer from noise and imperfections, achieving concrete speedups for meaningful problem sizes remains a major challenge. Yet, imperfections and noise may remain present in quantum computing for a long while. Such limitations play no role in classical software computing, and software engineers are typically not well accustomed to considering such imperfections, albeit they substantially influence core properties of software and systems. In this paper, we show how to model imperfections with an approach tailored to (quantum) software engineers. We intuitively illustrate, using numerical simulations, how imperfections influence core properties of quantum algorithms on NISQ systems, and show possible options for tailoring future NISQ machines to improve system performance in a co-design approach. Our results are obtained from a software framework that we provide in form of an easy-to-use reproduction package. It does not require computer scientists to acquire deep physical knowledge on noise, yet provide tangible and intuitively accessible means of interpreting the influence of noise on common software quality and performance indicators.

cs.ET↗

arXiv2022

Too much information: why CDCL solvers need to forget learned clauses

Conflict-driven clause learning (CDCL) is a remarkably successful paradigm for solving the satisfiability problem of propositional logic. Instead of a simple depth-first backtracking approach, this kind of solver learns the reason behind occurring conflicts in the form of additional clauses. However, despite the enormous success of CDCL solvers, there is still only a limited understanding of what influences the performance of these solvers in what way. Considering different measures, this paper demonstrates, quite surprisingly, that clause learning (without being able to get rid of some clauses) can not only help the solver but can oftentimes deteriorate the solution process dramatically. By conducting extensive empirical analysis, we furthermore find that the runtime distributions of CDCL solvers are multimodal. This multimodality can be seen as a reason for the deterioration phenomenon described above. Simultaneously, it also gives an indication of why clause learning in combination with clause deletion is virtually the de facto standard of SAT solving, in spite of this phenomenon. As a final contribution, we show that Weibull mixture distributions can accurately describe the multimodal distributions. Thus, adding new clauses to a base instance has an inherent effect of making runtimes long-tailed. This insight provides an explanation as to why the technique of forgetting clauses is useful in CDCL solvers apart from the optimization of unit propagation speed.

cs.AI↗

arXiv2020

Quantum Annealing-Based Software Components: An Experimental Case Study with SAT Solving

Quantum computers have the potential of solving problems more efficiently than classical computers. While first commercial prototypes have become available, the performance of such machines in practical application is still subject to exploration. Quantum computers will not entirely replace classical machines, but serve as accelerators for specific problems. This necessitates integrating quantum computational primitives into existing applications. In this paper, we perform a case study on how to augment existing software with quantum computational primitives for the Boolean satisfiability problem (SAT) implemented using a quantum annealer (QA). We discuss relevant quality measures for quantum components, and show that mathematically equivalent, but structurally different ways of transforming SAT to a QA can lead to substantial differences regarding these qualities. We argue that engineers need to be aware that (and which) details, although they may be less relevant in traditional software engineering, require considerable attention in quantum computing.

cs.ET↗