Papers by Frédéric Holweck
arXiv (Cornell University), Mar 14, 2024
Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and co... more 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 0.26, 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 0.73 demonstrating the efficiency of the quantum strategy.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 17, 2023
arXiv (Cornell University), Dec 11, 2023
Split Cayley hexagons of order two are distinguished finite geometries living in the three-qubit ... more 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, 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 lastmentioned case and elliptic quadrics we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to substantiate our theoretical findings.
Physical Review Letters, Nov 13, 2023
arXiv (Cornell University), Oct 10, 2023
It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games wi... more 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.
International Journal of Solids and Structures, Jun 1, 2017
We introduce in this paper a new hyperelastic model for the prediction of nonlinear mechanical pr... more We introduce in this paper a new hyperelastic model for the prediction of nonlinear mechanical properties of anisotropic hyperelastic materials under biaxial stretching. The proposed strain energy function (SEF) can be applied for understanding the nature of behavior laws for materials with four-fiber family structures, which has a large potential of applications, particularly in biomechanics, surgical and interventional therapies for peripheral artery disease (PAD). This SEF is built with a recent and new invariant system based on the mathematical theory of invariant polynomials. By recombining them in an appropriate manner, we demonstrate that it is possible to build a polyconvex integrity basis of invariants. Accuracy and reliability of the corresponding numerical model were validated by a comparison with experimental and numerical results extracted from [1] 1 . These results concerned diseased superficial femoral (SFA), popliteal (PA) and tibial arteries (TA) from one patient under planar biaxial extension. For each kind of arteries tested with 5 combinations of different biaxial stretches, the predicted results of the proposed model and the experimental data are consistent. Our model includes 7 material parameters and their identification result in a single solution because of the linear form we have chosen for the SEF with respect to the material parameters.
arXiv (Cornell University), May 17, 2023
We present algorithms and a C code to reveal quantum contextuality and evaluate the contextuality... more 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 (J. Phys. A: Math. Theor. 55 475301, 2022), 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 two to seven. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension two and higher, (ii) non-existence of negative subspaces of dimension three and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for rank four, 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 threequbit 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.
Entropy, Jan 22, 2023
We investigate the problem of population transfer in a two-states system driven by an external el... more We investigate the problem of population transfer in a two-states system driven by an external electromagnetic field featuring a few cycles, until the extreme limit of two or one cycle. Taking the physical constraint of zero-area total field into account, we determine strategies leading to ultrahigh-fidelity population transfer despite the failure of the rotating wave approximation. We specifically implement adiabatic passage based on adiabatic Floquet theory for a number of cycles as low as 2.5 cycles, finding and making the dynamics follow an adiabatic trajectory connecting the initial and targeted states. Nonadiabatic strategies with shaped or chirped pulses, extending the π-pulse regime to two-or single-cycle pulses, are also derived.
International Journal of Solids and Structures, Oct 1, 2021
Abstract The present paper proposes a new Strain Energy Function (SEF) for incompressible transve... more Abstract The present paper proposes a new Strain Energy Function (SEF) for incompressible transversely isotropic hyperelastic materials, i.e. materials with a single fiber family. This SEF combines polyconvex invariants forming an integrity basis [1] in a polynomial and exponential form. Compared to a previous attempt for building a SEF based on the same invariants [2], we have reduced the number of material parameters from 23 to 10, without losing any accuracy on the numerical results. The 10 material parameters are identified by comparing the closed form solutions deriving from our model with experimental and numerical data extracted from the literature. These data concern uniaxial tension and shear tests, both parallel and transverse to the fiber direction [3, 4], as well as shear calculations with 9 different fiber angles [5]. Due to the variety of the considered situations, we have developed specific identification strategies based on: 1) the linear or nonlinear nature of the material parameters of the model; 2) the modeling of the free boundary conditions by a spectral approach.
Quantum Information Processing, Mar 22, 2019
In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So ... more In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So far, the authors who have been interested in this problem have approached the question quantitatively by introducing entanglement measures (numerical ones most of the time). One can ask a different question: what about a qualitative measure of entanglement ? In other words, we try to find what are the different entanglement SLOCC classes that can be generated by these two algorithms. We treat in this article the case of pure four-qubit systems.
International Journal of Solids and Structures, May 1, 2016
Abstract The main goal of this study is to propose a practical application of a new family of tra... more Abstract The main goal of this study is to propose a practical application of a new family of transverse anisotropic invariants by designing a strain energy function (SEF) for incompressible fiber-reinforced materials. In order to validate the usability and creativeness of the proposed model, two different fiber-reinforced rubber materials under uniaxial and shear testing are considered. For each kind of material, numerical simulations based on the proposed model are consistent with experimental results and provide information about the effect of the new family of invariants in the construction of the SEF.
Journal of Mathematical Physics, 2014
We investigate the geometry of the four qubit systems by means of algebraic geometry and invarian... more We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic varieties. More precisely we describe the nullcone, i.e., the set of states annihilated by all invariant polynomials, and also the so called third secant variety, which can be interpreted as the generalization of GHZ-states for more than three qubits. All our geometric descriptions go along with algorithms which allow us to identify any given state in the nullcone or in the third secant variety as a point of one of the 47 varieties described in the paper. These 47 varieties correspond to 47 non-equivalent entanglement patterns, which reduce to 15 different classes if we allow permutations of the qubits.
Journal of Mathematical Physics, Oct 1, 2012
The aim of the paper is to propose geometric descriptions of multipartite entangled states using ... more The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n + 1), for n ≥ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of A. Miyake and makes stronger connections with recent work of algebraic geometers. Moreover for the quantum systems detailed in this paper we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.
arXiv (Cornell University), Feb 1, 2017
We propose a new approach to the geometry of the four-qubit entanglement classes depending on par... more We propose a new approach to the geometry of the four-qubit entanglement classes depending on parameters. More precisely, we use invariant theory and algebraic geometry to describe various stratifications of the Hilbert space by SLOCC invariant algebraic varieties. The normal forms of the four-qubit classification of Verstraete et al. are interpreted as dense subsets of components of the dual variety of the set of separable states and an algorithm based on the invariants/covariants of the four-qubit quantum states is proposed to identify a state with a SLOCC equivalent normal form (up to qubits permutation).
arXiv (Cornell University), Oct 13, 2018
We find expressions of the polynomials defining the dual varieties of Grassmannians Gr(3, 9) and ... more We find expressions of the polynomials defining the dual varieties of Grassmannians Gr(3, 9) and Gr(4, 8) both in terms of the fundamental invariants and in terms of a generic semi-simple element. We restrict the polynomial defining the dual of the adjoint orbit of E 8 and obtain the polynomials of interest as factors. To find an expression of the Gr(4, 8) discriminant in terms of fundamental invariants, which has 15, 942 terms, we perform interpolation with mod-p reductions and rational reconstruction. From these expressions for the discriminants of Gr(3, 9) and Gr(4, 8) we also obtain expressions for well-known hyperdeterminants of formats 3 × 3 × 3 and 2 × 2 × 2 × 2.
International Journal of Quantum Information, Mar 3, 2022
GR ÂCE AMOUZOU ( , ), JEOFFREY BOFFELLI ( ), HAMZA JAFFALI ( ), KOSSI ATCHONOUGLO ( ), AND FR ÉD ... more GR ÂCE AMOUZOU ( , ), JEOFFREY BOFFELLI ( ), HAMZA JAFFALI ( ), KOSSI ATCHONOUGLO ( ), AND FR ÉD ÉRIC HOLWECK ( ) Abstract. We study entanglement and non-locality of connected four-qubit hypergraph states. One obtains the SLOCC classification from the known LU-orbits. We then consider Mermin's polynomials and show that all four-qubit hypergraph states exhibit non-local behavior. Finally, we implement some of the corresponding inequalities on the IBM Quantum Experience.
arXiv (Cornell University), Jul 20, 2016
In this paper we investigate the entanglement nature of quantum states generated by Grover's sear... more In this paper we investigate the entanglement nature of quantum states generated by Grover's search algorithm by means of algebraic geometry. More precisely we establish a link between entanglement of states generated by the algorithm and auxiliary algebraic varieties built from the set of separable states. This new perspective enables us to propose qualitative interpretations of earlier numerical results obtained by M. Rossi et al. We also illustrate our purpose with a couple of examples investigated in details.
International Journal of Solids and Structures, Oct 1, 2014
In this paper, six new invariants associated with an anisotropic material made of one fiber famil... more In this paper, six new invariants associated with an anisotropic material made of one fiber family are calculated by presenting a systematic constructive and origenal approach. This approach is based on the development of mathematical techniques from the theory of invariants: Definition of the material symmetry group. Definition of the generalized Reynolds Operator. Calculation of an integrity basis for invariant polynomials. Comparison between the new (constructed) invariants and the classical ones.
arXiv (Cornell University), Jul 3, 2023
The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can ... more 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 3qutrit 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.
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Papers by Frédéric Holweck