arXiv subjects

Ruben Pariente Bassa

Publications and source records attributed to Ruben Pariente Bassa.

3 recordsLinked to original sources

arXiv2026

Iterative quantum algorithms for the minimum vertex cover problem based on continuous-time quantum walks

We introduce a constraint-preserving hybrid quantum-classical greedy framework for the minimum vertex cover problem, which extends directly to maximum independent set by bitwise complementation. The framework uses projected Pauli-X terms whose sum preserves the feasible subspace and acts within it exactly as the adjacency matrix of a layered graph of feasible covers. This graph is connected, so every feasible cover is linked to the configuration containing all vertices by a sequence of allowed single-vertex flips. Starting from this configuration, the corresponding continuous-time quantum walk propagates amplitude into layers containing progressively smaller covers. We rank vertices using either their marginal cover probabilities or the expected cover size obtained after fixing each candidate vertex in the cover, and use these rankings to guide recursive greedy reductions. Across several random-graph families, with walk times fixed using independent calibration ensembles, the quantum-informed algorithms achieve lower mean approximation ratios and solve a larger fraction of instances optimally than their corresponding classical greedy baselines. The conditioned-energy strategy performs best on the tested instances and retains algorithmic performance close to the exact continuous-time limit under low-depth Trotterisation. For bounded-degree graphs, each Trotter layer has circuit depth independent of system size, and the framework requires neither penalty terms nor variational training.

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arXiv2024

LX-mixers for QAOA: Optimal mixers restricted to subspaces and the stabilizer formalism

We present a novel formalism to both understand and construct mixers that preserve a given subspace. The method connects and utilizes the stabilizer formalism that is used in error correcting codes. This can be useful in the setting when the quantum approximate optimization algorithm (QAOA), a popular meta-heuristic for solving combinatorial optimization problems, is applied in the setting where the constraints of the problem lead to a feasible subspace that is large but easy to specify. The proposed method gives a systematic way to construct mixers that are resource efficient in the number of controlled not gates and can be understood as a generalization of the well-known X and XY mixers and a relaxation of the Grover mixer: Given a basis of any subspace, a resource efficient mixer can be constructed that preserves the subspace. The numerical examples provided show a dramatic reduction of CX gates when compared to previous results. We call our approach logical X-Mixer or logical X QAOA ($\textbf{LX-QAOA}$), since it can be understood as dividing the subspace into code spaces of stabilizers S and consecutively applying logical rotational X gates associated with these code spaces. Overall, we hope that this new perspective can lead to further insight into the development of quantum algorithms.

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arXiv2024

Quantum reservoir computing using the stabilizer formalism for encoding classical data

Utilizing a quantum system for reservoir computing has recently received a lot of attention. Key challenges are related to how on can optimally en- and decode classical information, as well as what constitutes a good reservoir. Our main contribution is a generalization of the standard way to robustly en- and decode time series into subspaces defined by the cosets of a given stabilizer. A key observation is the necessity to perform the decoding step, which in turn ensures a consistent way of encoding. This provides a systematic way to encode classical information in a robust way. We provide a numerical analysis on a discrete time series given by two standard maps, namely the logistic and the Hénon map. Our numerical findings indicate that the system's performance is increasing with the length of the training data.

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