arXiv subjects

Marvin Schwiering

Publications and source records attributed to Marvin Schwiering.

4 recordsLinked to original sources

arXiv2026

One for All: Universal Quantum Conic Programming Framework for Hard-Constrained Combinatorial Optimization Problems

We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimisation problems, generalising the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many favourable properties of the original proposal such as preventing barren plateaus and NP-hard parameter optimisation. By collecting the entire classical feasibility structure in a single constraint, we enlarge QCP's scope to arbitrary hard-constrained problems. Yet, we prove that the additional restriction is mild enough to still allow for an efficient parameter optimisation via the formulation of a generalised eigenvalue problem (GEP) of adaptable dimension. Our rigorous proof further fills some apparent gaps in prior derivations of GEPs from parameter optimisation problems. We further detail a measurement protocol for formulating the classical parameter optimisation that does not require us to implement any problem-specific objective Hamiltonian or a quantum feasibility oracle. Lastly, we prove that, even under the influence of noise, QCP's parameterised ansatz class always captures the optimum attainable within its generated subcone. All of our results hold true for arbitrarily-constrained combinatorial optimisation problems.

quant-ph↗

arXiv2026

Exhaustive and feasible parametrisation with applications to the travelling salesperson problem

This paper introduces the concept of exhaustively parametrised, feasibility-respecting quantum circuits for constrained combinatorial optimisation problems. Such circuits can reach, given the right parameter values, every feasible solution with certainty -- including the optimum -- with a fixed number of parameters, while avoiding infeasible solutions altogether. This is in sharp contrast to conventional quantum alternating operator ansatz schemes, which are merely guaranteed to reach the optimum asymptotically. We introduce an abstract pipeline for constructing exhaustively parametrised, feasibility-respecting circuits from a transitive group action on a problem's feasible set. Our constructions rely on the simple combination of the group action with group representation and the novel notion of generating sequences: group elements in fixed order, possibly with repetitions, that generate the entire group. That is, we trace expressivity of parametrised quantum circuits back to the most fundamental concepts of group theory. We apply this pipeline to two concrete examples for the travelling salesperson problem, thus showing that exhaustively parametrised, feasibility-respecting circuits are not an empty definition. Furthermore, we provide numerical proof-of-principles on instances with up to nine cities, comparing the suitability of our constructions for parameter optimisation purposes against established mixers.

quant-ph↗

arXiv2026

A 3D lattice defect and efficient computations in topological MBQC

We describe an efficient, fully fault-tolerant implementation of Measurement-Based Quantum Computation (MBQC) in the 3D cluster state. The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and (ii) the use of the Rudolph-Grover rebit encoding. Concretely, (i) allows for a topological implementation of the Hadamard gate, while (ii) does the same for the phase gate. Furthermore, we develop general ideas towards circuit compaction and algorithmic circuit verification, which we implement for the Reed-Muller code used for magic state distillation. Our performance analysis highlights the overall improvements provided by the new methods.

quant-ph↗

arXiv2025

Quantum Fisher-Yates shuffle: Unifying methods for generating uniform superpositions of permutations

Uniform superpositions over permutations play a central role in quantum error correction, cryptography, and combinatorial optimisation. We introduce a simple yet powerful quantisation of the classical Fisher-Yates shuffle, yielding a suite of efficient quantum algorithms for preparing such superpositions on composite registers. Our method replaces classical randomness with coherent control, enabling five variants that differ in their output structure and entanglement with ancillary systems. We demonstrate that this construction achieves the best known combination of asymptotic resources among all existing approaches, requiring only $\mathcal{O}(n \log(n))$ qubits and $\mathcal{O}(n^{2} \log(n))$ gates and circuit depth. These results position the quantum Fisher-Yates shuffle as a strong candidate for optimality within this class of algorithms. Our work unifies several prior constructions under a single, transparent framework and opens up new directions for quantum state preparation using classical combinatorial insights. Our implementation in Qiskit is available as open-source code, supporting reproducibility and future exploration of quantum permutation-based algorithms.

quant-ph↗