arXiv subjects

Frédéric Holweck

Publications and source records attributed to Frédéric Holweck.

At least 19 recordsLinked to original sources

arXiv2026

Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction

Variational quantum circuits (VQCs) are parameterized quantum circuits optimized classically. We propose a hybrid variational quantum circuit (HVQC) extending VQCs with a classical affine post-measurement layer, enabling vector-valued regression without the linear overhead of independent scalar circuits. Theoretically, we show that elementary one-and two-qubit circuits can approximate quadratic functions and products via data re-uploading and entanglement, providing the foundations of the full architecture. Experimentally, on two synthetic image reconstruction datasets and the Friedman1 benchmark (40,568 test samples), our HVQC matches Gaussian Process Regression and outperforms XGBoost and Random Forest. An ablation study confirms that both quantum and classical components are essential, and results highlight the central role of the feature map in hybrid quantum-classical models.

cs.LG↗

arXiv2026

Local qubit invariants on quantum computer

We present two general methods to implement quantum circuits for the direct measuring of local unitary invariants on quantum computers. We work these out for important three-qubit invariants, and also demonstrate these on the IBM Quantum Platform for important entanglement measures of three qubits.

quant-ph↗

arXiv2026

A hybrid variational quantum circuit approach for stabilizer states classifiers

Entanglement classification of pure multipartite quantum states is a challenging problem in quantum information theory that can be mathematically stated as orbit classification for some given group action on the ambient Hilbert space. The group action depends on the grained classification one expects, the finer-grained one being the classification up to local unitary transformation (LU). In this article, we show how a variational quantum circuit approach can be used to learn entanglement orbits, and we apply our findings to build a classifier for four-qubit states.

quant-ph↗

arXiv2026

Solving nonlinear differential equations on noisy $156$-qubit quantum computers

In this paper, we report on the resolution of nonlinear differential equations using IBM's quantum platform. More specifically, we demonstrate that the hybrid classical-quantum algorithm H-DES successfully solves a one-dimensional material deformation problem and the inviscid Burgers' equation on IBM's 156-qubit quantum computers. These results constitute a step toward performing physically relevant simulations on present-day Noisy Intermediate-Scale Quantum (NISQ) devices.

quant-ph↗

arXiv2025

H-DES: a Quantum-Classical Hybrid Differential Equation Solver

In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions that are encoded directly in the quantum states generated by different parametrized circuits, and transforms the task of solving the differential equations into an optimization problem. We first describe the principle of the algorithm from a theoretical point of view. We provide a detailed pseudo-code of the algorithm, on which we elaborate preliminary elements for a complexity analysis to highlight some of its scaling properties. We apply our algorithm to a set of examples, running on emulators and real hardware showcasing its applicability across diverse sets of differential equations. We discuss the advantages of our method and potential avenues for further exploration and refinement.

quant-ph↗

arXiv2025

A Quantum Algorithm For Computing Contextuality Bounds

Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements of $N$-qubit spin operators, constraints arise from commutation relations and classical bounds are determined by the $\textit{degree}$ of contextuality, an NP-hard quantity to compute in general, related to the larger class of optimisation problems known as $\texttt{MaxLin2}$. In this work we give a quantum algorithm based on Grover's search algorithm, computing the degree of contextuality in $O(\sqrt{n} \log\log{n})$ in $n$ states, a speedup over classical brute force method. We also study variations of Grover which encode the relevant information in the phases of the basis states, reducing circuit width and depth requirements with indicative complexity of $O(n^{\frac{1}{3}}(\log{n})^{2}\log\log{n})$. Testing on contemporary quantum backends with the IBM quantum experience gives inconclusive outputs due to noise-induced errors, an issue hopefully fixed by future hardware.

quant-ph↗

arXiv2025

Empirical Demonstration of Quantum Contextuality on NISQ Computers

We present definitive violations of non-contextual hidden variable bounds in the latest generation of IBM noisy intermediate-scale quantum computers (NISQ). These violations are based on known tests for contextuality such as the Rio Negro inequality and pseudo-telepathic Mermin games. These are the first violations of the classical Mermin game on IBM NISQ computers, and the largest such violations for the Rio Negro inequality. The use of finite geometries proves instrumental in the development of more effective tests, with larger geometries providing sizeable datasets from which multiple distinct experiments can be compared.

quant-ph↗

arXiv2025

Hexagons govern three-qubit contextuality

Split Cayley hexagons of order two are distinguished finite geometries living in the three-qubit symplectic polar space in two different forms, called classical and skew. Although neither of the two yields observable-based contextual configurations of their own, {\it classically}-embedded copies are found to fully encode contextuality properties of the most prominent three-qubit contextual configurations in the following sense: for each set of unsatisfiable contexts of such a contextual configuration there exists some classically-embedded hexagon sharing with the configuration exactly this set of contexts and nothing else. We demonstrate this fascinating property first on the configuration comprising all 315 contexts of the space and then on doilies, both types of quadrics as well as on complements of skew-embedded hexagons. In connection with the last-mentioned case and elliptic quadrics we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to substantiate our theoretical findings.

quant-ph↗

arXiv2024

Four-Qubit CHSH Games

In this paper, the CHSH quantum game is extended to four players. This is achieved by exploring all possible 4-variable Boolean functions to identify those that yield a game scenario with a quantum advantage using a specific entangled state. Notably, two new four-player quantum games are presented. In one game, the optimal quantum strategy is achieved when players share a $GHZ$-state, breaking the traditional 10\% gain observed in 2 and 3 qubit CHSH games and achieving a 22.5\% gap. In the other game, players gain a greater advantage using a $W$-state as their quantum resource. Quantum games with other four-qubit entangled states are also explored. To demonstrate the results, these game scenarios are implemented on an online quantum computer, and the advantage of the respective quantum resource for each game is experimentally verified.

quant-ph↗

arXiv2024

A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals

We introduce and describe a new heuristic method for finding an upper bound on the degree of contextuality and the corresponding unsatisfied part of a quantum contextual configuration with three-element contexts (i.e., lines) located in a multi-qubit symplectic polar space of order two. While the previously used method based on a SAT solver was limited to three qubits, this new method is much faster and more versatile, enabling us to also handle four- to six-qubit cases. The four-qubit unsatisfied configurations we found are quite remarkable. That of an elliptic quadric features 315 lines and has in its core three copies of the split Cayley hexagon of order two having a Heawood-graph-underpinned geometry in common. That of a hyperbolic quadric also has 315 lines but, as a point-line incidence structure, is isomorphic to the dual $\mathcal{DW}(5,2)$ of $\mathcal{W}(5,2)$. Finally, an unsatisfied configuration with 1575 lines associated with all the lines/contexts of the four-qubit space contains a distinguished $\mathcal{DW}(5,2)$ centered on a point-plane incidence graph of PG$(3,2)$. The corresponding configurations found in the five-qubit space exhibit a considerably higher degree of complexity, except for a hyperbolic quadric, whose 6975 unsatisfied contexts are compactified around the point-hyperplane incidence graph of PG$(4,2)$. The most remarkable unsatisfied patterns discovered in the six-qubit space are a couple of disjoint split Cayley hexagons (for the full space) and a subgeometry underpinned by the complete bipartite graph $K_{7,7}$ (for a hyperbolic quadric).

quant-ph↗

arXiv2024

New and improved bounds on the contextuality degree of multi-qubit configurations

We present algorithms and a C code to reveal quantum contextuality and evaluate the contextuality degree (a way to quantify contextuality) for a variety of point-line geometries located in binary symplectic polar spaces of small rank. With this code we were not only able to recover, in a more efficient way, all the results of a recent paper by de Boutray et al [(2022). Journal of Physics A: Mathematical and Theoretical 55 475301], but also arrived at a bunch of new noteworthy results. The paper first describes the algorithms and the C code. Then it illustrates its power on a number of subspaces of symplectic polar spaces whose rank ranges from 2 to 7. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension 2 and higher, (ii) non-existence of negative subspaces of dimension 3 and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for rank 4, as well as for a particular subgeometry of the three-qubit space whose contexts are the lines of this space, (iv) proof for the non-contextuality of perpsets and, last but not least, (v) contextual nature of a distinguished subgeometry of a multi-qubit doily, called a two-spread, and computation of its contextuality degree. Finally, in the three-qubit polar space we correct and improve the contextuality degree of the full configuration and also describe finite geometric configurations formed by unsatisfiable/invalid constraints for both types of quadrics as well as for the geometry whose contexts are all 315 lines of the space.

quant-ph↗

arXiv2024

Exploiting Finite Geometries for Better Quantum Advantages in Mermin-Like Games

Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and contextuality. The Mermin-Peres game is a simple example, demonstrating how two players can utilise shared quantum information to win a no - communication game with certainty, where classical players cannot. In this paper we look at the geometric structure behind such classical strategies, and borrow ideas from the geometry of symplectic polar spaces to maximise this quantum advantage. We introduce a new game called the Eloily game with a quantum-classical success gap of $0.2\overline{6}$, larger than that of the Mermin-Peres and doily games. We simulate this game in the IBM Quantum Experience and obtain a success rate of $1$, beating the classical bound of $0.7\overline{3}$ demonstrating the efficiency of the quantum strategy.

quant-ph↗

arXiv2023

Two new non-equivalent three-qubit CHSH games

In this paper, we generalize to three players the well-known CHSH quantum game. To do so, we consider all possible 3 variables Boolean functions and search among them which ones correspond to a game scenario with a quantum advantage (for a given entangled state). In particular we provide two new three players quantum games where, in one case, the best quantum strategy is obtained when the players share a $GHZ$ state, while in the other one the players have a better advantage when they use a $W$ state as their quantum resource. To illustrate our findings we implement our game scenarios on an online quantum computer and prove experimentally the advantage of the corresponding quantum resource for each game.

quant-ph↗

arXiv2023

Implementing 2-qubit pseudo-telepathy games on noisy intermediate scale quantum computers

It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games with a guaranteed quantum strategy, when classically no such guarantee can exist. This phenomenon, also called quantum pseudo-telepathy, has been studied in the case of the so-called Mermin Magic square game. In this paper we review in detail two different ways of implementing on a quantum computer such a game and propose a new Doily game based on the geometry of 2-qubit Pauli group. We show that the quantumness of these games are almost revealed when we play them on the IBM Quantum Experience, however the inherent noise in the available quantum machines prevents a full demonstration of the non-classical aspects.

quant-ph↗

arXiv2023

Maximally entangled real states and SLOCC invariants: the 3-qutrit case

The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as measures of entanglement. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the point of view of maximizing the hyperdeterminant). We also study the basic fundamental invariants and find real 3-qutrit states that maximize their absolute values. It is notable that the Aharonov state is a simultaneous maximizer for all 3 fundamental invariants. We also study the evaluation of these invariants on random real 3-qutrit systems and analyze their behavior using histograms and level-set plots. Finally, we show how to evaluate these invariants on any 3-qutrit state using basic matrix operations.

quant-ph↗

arXiv2023

Contextuality degree of quadrics in multi-qubit symplectic polar spaces

Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker Theorem, we formulate the contextuality property as the absence of solutions to a linear system and define for a contextual configuration its degree of contextuality. Then we explain why subgeometries of binary symplectic polar spaces are candidates for contextuality proofs. We report the results of a software that generates these subgeometries, decides their contextuality and computes their contextuality degree for some small symplectic polar spaces. We show that quadrics in the symplectic polar space $W_n$ are contextual for $n=3,4,5$. The proofs we consider involve more contexts and observables than the smallest known proofs. This intermediate size property of those proofs is interesting for experimental tests, but could also be interesting in quantum game theory.

quant-ph↗

arXiv2023

A hyperdeterminant on Fermionic Fock Space

Twenty years ago Cayley's hyperdeterminant, the degree four invariant of the polynomial ring $\mathbb{C}[\mathbb{C}^2\otimes\mathbb{C}^2\otimes \mathbb{C}^2]^{{\text{SL}_2(\mathbb{C})}^{\times 3}}$, was popularized in modern physics as separates genuine entanglement classes in the three qubit Hilbert space and is connected to entropy formulas for special solutions of black holes. In this note we compute the analogous invariant on the fermionic Fock space for $N=8$, i.e. spin particles with four different locations, and show how this invariant projects to other well-known invariants in quantum information. We also give combinatorial interpretations of these formulas.

quant-ph↗

arXiv2022

Multi-qubit doilies: enumeration for all ranks and classification for ranks four and five

For $N \geq 2$, an $N$-qubit doily is a doily living in the $N$-qubit symplectic polar space. These doilies are related to operator-based proofs of quantum contextuality. Following and extending the strategy of Saniga et al. (Mathematics 9 (2021) 2272) that focused exclusively on three-qubit doilies, we first bring forth several formulas giving the number of both linear and quadratic doilies for any $N > 2$. Then we present an effective algorithm for the generation of all $N$-qubit doilies. Using this algorithm for $N=4$ and $N=5$, we provide a classification of $N$-qubit doilies in terms of types of observables they feature and number of negative lines they are endowed with. We also list several distinguished findings about $N$-qubit doilies that are absent in the three-qubit case, point out a couple of specific features exhibited by linear doilies and outline some prospective extensions of our approach.

quant-ph↗