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Olli Hirviniemi

Publications and source records attributed to Olli Hirviniemi.

6 recordsLinked to original sources
arXiv2026

Random Quantum Circuits as Seeds for Continuous Generative Models

We introduce a random circuit family and show they are robust against current classical simulation techniques, specifically tensor network contraction and Pauli propagation. We also show that local variables do not concentrate, ensuring enough variance to be able to produce a diverse set of data points. We therefore argue that using these circuits as a "random seed" for a larger classical generative model is a way to make large-scale quantum-classical hybrid models amenable towards NISQ devices.

quant-ph↗
arXiv2026

A scalable quantum-enhanced greedy algorithm for maximum independent set problems

We investigate a hybrid quantum-classical algorithm for solving the Maximum Independent Set (MIS) problem on regular graphs, combining the Quantum Approximate Optimization Algorithm (QAOA) with a minimal degree classical greedy algorithm. The method leverages pre-computed QAOA angles, derived from depth-$p$ QAOA circuits on regular trees, to compute local expectation values and inform sequential greedy decisions that progressively build an independent set. This hybrid approach maintains shallow quantum circuit and avoids instance-specific parameter training, making it well-suited for implementation on current quantum hardware: we have implemented the algorithm on a 20 qubit IQM superconducting device to find independent sets in graphs with thousands of nodes. We perform tensor network simulations to evaluate the performance of the algorithm beyond the reach of current quantum hardware and compare to established classical heuristics. Our results show that even at low depth ($p=4$), the quantum-enhanced greedy method significantly outperforms purely classical greedy baselines as well as more sophisticated approximation algorithms. The modular structure of the algorithm and relatively low quantum resource requirements make it a compelling candidate for scalable, hybrid optimization in the NISQ era and beyond.

quant-ph↗
arXiv2021

Stretching and Rotation of Planar Quasiconformal Mappings on a Line

In this article, we examine stretching and rotation of planar quasiconformal mappings on a line. We show that for almost every point on the line, the set of complex stretching exponents (describing stretching and rotation jointly) is contained in the disk $ \overline{B}(1/(1-k^4),k^2/(1-k^4))$. This yields a quadratic improvement over the known optimal estimate for general sets of Hausdorff dimension $1$. Our proof is based on holomorphic motions and estimates for dimensions of quasicircles. We also give a lower bound for the dimension of the image of a $1$-dimensional subset of a line under a quasiconformal mapping.

math.CV↗
arXiv2021

On mappings of finite distortion that are quasiconformal in the unit disk

We study quasiconformal mappings of the unit disk that have planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the inverse map, which somewhat surprisingly is almost as good as for global quasiconformal maps. Furthermore, we give examples which improve the known bounds for the three point property of generalized quasidisks. Finally, we establish optimal regularity of such maps when the image of the unit disk has cusp type singularities.

math.CV↗
arXiv2021

Localized Regularity of Planar Maps of Finite Distortion

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion. Analogues of such results were known earlier in the case of quasiconformal mappings. Moreover, we study regularity for maps whose distortion has higher exponential integrability.

math.CV↗