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The stability of the solid electrolyte interphase (SEI) layer during the charging–discharging cycles is reasonably related to its microscopic elasticity. For the first time, it was theoretically revealed that each component of the elastic moduli takes a maximum at an optimal concentration of 1.0 vol % of fluoroethylene carbonate (FEC) for the SEI layer formed in the FEC-added NaPF6/PC-based electrolyte. The elastic constants indicated that the SEI layer formed at lower FEC concentrations is more resistant to tensile and shear deformations. The optimal hardness is sensitive in the lower FEC concentrations although it simply decreases as the FEC concentration increases. This is due to the formation of a denser SEI structure with small cavities in the lower concentrations. The results are excellently consistent with the experimental one, justifying the microscopic understanding of the FEC additive effect on the mechanical stability of the SEI layers designed through the Red Moon simulation.

International audience; The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has recently attracted interest due to its use in Variation Quantum Eigensolver (VQE) molecular simulations on quantum computers. However, when the size of molecules increases, UCCSD becomes less interesting as it cannot achieve sufficient accuracy. Including higher-order excitations is therefore mandatory to recover the UCC's missing correlation effects. In this Letter, we extend the Trotterized UCC approach via the addition of (true) Triple T excitations introducing UCCSDT. We also include both spin and orbital symmetries. Indeed, in practice, these later help to reduce unnecessarily circuit excitations and thus accelerate the optimization process enabling to tackle larger molecules. Our initial numerical tests (12-14 qubits) show that UCCSDT improves the overall accuracy by at least two-orders of magnitudes with respect to standard UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be competitive with the CCSD(T) gold-standard classical method of quantum chemistry.

Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of edges to near-linear in the number of nodes, while approximately preserving the cut and spectral structure of the graph. In this work we demonstrate a polynomial quantum speedup for spectral sparsification and many of its applications. In particular, we give a quantum algorithm that, given a weighted graph with $n$ nodes and $m$ edges, outputs a classical description of an $\epsilon$-spectral sparsifier in sublinear time $\tilde{O}(\sqrt{mn}/\epsilon)$. This contrasts with the optimal classical complexity $\tilde{O}(m)$. We also prove that our quantum algorithm is optimal up to polylog-factors. The algorithm builds on a string of existing results on sparsification, graph spanners, quantum algorithms for shortest paths, and efficient constructions for $k$-wise independent random strings. Our algorithm implies a quantum speedup for solving Laplacian systems and for approximating a range of cut problems such as min cut and sparsest cut., Comment: v2: several small improvements to the text. An extended abstract will appear in FOCS'20; v3: corrected a minor mistake in Appendix A; v4: final version as published in SICOMP

International audience; The computation of hyperfine resolved cross sections and rate coefficients for open-shell molecules in collision with H2 is a true methodological and numerical challenge. Such collisional data are however required to interpret astrophysical observations. We report the first hyperfine resolved rate coefficients for (de-)excitation of 13CCH and C13CH isotopologues induced by collisions with para-H2. These calculations have been performed using a recently published C2H-H2 potential energy surface. Hyperfine resolved cross sections and rate coefficients between the first 98 energy levels of the two isotopologues were determined using a recoupling technique for temperatures ranging from 5 to 100 K. Significant isotopic substitution effects were found, showing the necessity of computing isotopologue specific collisional data. These rate coefficents have then been used in a simple radiative transfer modelling for typical molecular cloud conditions. © 2023 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.

The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several ad hoc computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher order quantum computations. To this end, we generalise the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps., Comment: 6+11 pages

Quantum Internetworking is a recent field that promises numerous interesting applications, many of which require the distribution of entanglement between arbitrary pairs of users. This work deals with the problem of scheduling in an arbitrary entanglement swapping quantum network - often called first generation quantum network - in its general topology, multicommodity, loss-aware formulation. We introduce a linear algebraic framework that exploits quantum memory through the creation of intermediate entangled links. The framework is then employed to mathematically derive a natural class of quadratic scheduling policies for quantum networks by applying Lyapunov Drift Minimization, a standard technique in classical network science. Moreover, an additional class of Max-Weight inspired policies is proposed and benchmarked, reducing significantly the computation cost, at the price of a slight performance degradation. The policies are compared in terms of information availability, localization and overall network performance through an ad-hoc simulator that admits user-provided network topologies and scheduling policies in order to showcase the potential application of the provided tools to quantum network design., Comment: 18 pages, 7 figures. To be submitted to the journal "IEEE Transactions on Quantum Engineering"

International audience; We exhibit a strong connection between the matchgate formalism introduced by Valiant and the ZW-calculus of Coecke and Kissinger. This connection provides a natural compositional framework for matchgate theory as well as a direct combinatorial interpretation of the diagrams of ZW-calculus through the perfect matchings of their underlying graphs. We identify a precise fragment of ZW-calculus, the planar W-calculus, that we prove to be complete and universal for matchgates, that are linear maps satisfying the matchgate identities. Computing scalars of the planar W-calculus corresponds to counting perfect matchings of planar graphs, and so can be carried in polynomial time using the FKT algorithm, making the planar W-calculus an efficiently simulable fragment of the ZW-calculus, in a similar way that the Clifford fragment is for ZX-calculus. This work opens new directions for the investigation of the combinatorial properties of ZW-calculus as well as the study of perfect matching counting through compositional diagrammatical technics.

We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an unfolding procedure and their stabilizers form so-called $\ell$-orthogonal spaces meaning that the joint overlap between any $\ell$ stabilizer elements is always even. This last feature makes them interesting for devising magic-state distillation protocols, for instance by using puncturing techniques. We study examples of these codes and their properties., 21 pages, 10 figures

International audience; Underground nuclear explosions generate non-isothermal two-phase flow, heat and mass transfer, and tracer transport through fractured porous media. The governing equations of these coupled phenomena on the Darcy scale are presented and the corresponding numerical code is briefly described. Two configurations are considered. In the first one, the damaged zone generated by the explosion is replaced by equivalent macroscopic boundary conditions at the bottom of the medium. Vapor condensation at distance from this zone plays a crucial role and slows down the tracer transport to the ground surface, while the presence of hot liquid water and of hot rubble particles in it accelerates it. In the second configuration, the damaged zone itself is treated as a porous medium with specific properties and is integrated in the simulation domain. Several regions can be distinguished with different properties, such as the chimney, the cavity, the solidified magma, the fractured porous medium, and the intact porous medium. Phase change, heat transfer and tracer transport can be detailed in these regions and at the boundaries between them. Among the most important conclusions, the role of phase change, of the thermal properties and therefore of the temperature, is pointed out.

International audience; We introduce and study a class of entanglement criteria based on the idea of applying local contractions to an input multipartite state, and then computing the projective tensor norm of the output. More precisely, we apply to a mixed quantum state a tensor product of contractions from the Schatten class $S_1$ to the Euclidean space $\ell_2$, which we call entanglement testers. We analyze the performance of this type of criteria on bipartite and multipartite systems, for general pure and mixed quantum states, as well as on some important classes of symmetric quantum states. We also show that previously studied entanglement criteria, such as the realignment and the SIC POVM criteria, can be viewed inside this framework. This allows us to answer in the positive two conjectures of Shang, Asadian, Zhu, and G\"uhne by deriving systematic relations between the performance of these two criteria.

Entanglement and spontaneous emission are fundamental quantum phenomena that drive many applications of quantum physics. During the spontaneous emission of light from an excited two-level atom, the atom briefly becomes entangled with the photonic field. Here, we show that this natural process can be used to produce photon-number entangled states of light distributed in time. By exciting a quantum dot -- an artificial two-level atom -- with two sequential pi pulses, we generate a photon-number Bell state. We characterise this state using time-resolved intensity and phase correlation measurements. Furthermore, we theoretically show that applying longer sequences of pulses to a two-level atom can produce a series of multi-temporal mode entangled states with properties intrinsically related to the Fibonacci sequence. Our work demonstrates that spontaneous emission is a powerful entanglement resource and it can be further exploited to generate new states of quantum light with potential applications in quantum technologies., Main: 7 pages, 3 figures; Supplementary: 11 pages, 5 figures

How many copies of a quantum process are necessary and sufficient to construct an approximate classical description of it? We extend the result of Surawy-Stepney, Kahn, Kueng, and Guta (2022) to show that $\tilde{\mathcal{O}}(d_{\text{in}}^3d_{\text{out}}^3/\varepsilon^2)$ copies are sufficient to learn any quantum channel $C^{d_{\text{in}}\times d_{\text{in}}} \rightarrow C^{d_{\text{out}}\times d_{\text{out}}}$ to within $\varepsilon$ in diamond norm. Moreover, we show that $\Omega(d_{\text{in}}^3 d_{\text{out}}^3/\varepsilon^2)$ copies are necessary for any strategy using incoherent non-adaptive measurements. This lower bound applies even for ancilla-assisted strategies.

We present a theoretical study of electrical current fluctuations and finite-frequency noise in a double quantum dot connected to two electron reservoirs with the aim of deriving the Fano factor, the $\Delta T$-noise and the cross-correlations. This allows one to highlight several interesting features. Firstly the possibility of getting a significant reduction of current noise and Fano factor either when the system is placed in a given operating regime, or when a temperature gradient is applied between the two reservoirs, resulting from the fact that a negative $\Delta T$-noise is generated. The second feature is the sign change found in the cross-correlator between the two reservoirs with increasing frequencies. This study clarifies the understanding of the results obtained experimentally in such systems., Comment: 5 pages, 6 figures

We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of N qubits. Such states are locally equivalent to an N-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time., Comment: 14 pages, 10 figures

Magnetic resonance is a branch of science that aims to detect spins via their absorption and emission of electromagnetic radiation. There are two sub-branches : Nuclear Magnetic Resonance (NMR), which applies to atomic spins, and Electronic Paramagnetic Resonance (EPR), which applies to unpaired electron spins. In both cases, commercial instruments are limited to measuring large ensembles of spins and only provide averages of their collective response. In this thesis, we perform EPR of individual Erbium ions inserted in a scheelite crystal using a new detec-tion method based on the microwave fluorescence emitted by the spins during their relaxation. To promote photon emission, the spins are coupled to a superconducting resonator with a small mode volume and low losses, generating a Purcell effect. The output of the resonator is connected to a microwave photon detector based on a superconducting qubit and a 4-wave micing. The high sensitivity of this detector S = 10⁻²² W/√Hz is one of the keys to the success of this experiment. Our method is applicable to all types of paramagnetic impurities without requiring an optical transition or a large coherence time. We measure the characteristics of several individual spins, the results vary strongly from one spin to another, highlighting the inhomogeneity of their electromagnetic environments. The coherence times reach several milliseconds and are radiatively limited. Finally, we perform an experiment to probe the magnetic environment of a particular impurity using a dynamic decoupling sequence. The resonance signal allows us to demonstrate the presence of ¹⁸³W nuclear spin. We finally make some preliminary hypotheses on their arrangement around the erbium ion studied.; La résonance magnétique est une branche de la science qui vise à détecter les spins via leur absorption et émission de rayonnement électromagnétique. On distingue deux sous-branches : la Résonance Magnétique Nucléaire (RMN) qui s’applique aux spins atomiques et la Résonance Paramagnétique Electronique (RPE) qui s’applique aux spins électroniques non appariés. Dans les deux cas, les appareils commerciaux sont limités à la mesure de vastes ensembles de spins et ne fournissent que des moyennes de leur réponse collective. Dans cette thèse, nous réalisons la RPE d’ion Erbium individuels insérés dans un cristald e scheelite en utilisant une nouvelle méthode de détection basée sur la fluorescence micro-onde émise par les spins pendant leur relaxation. Pour favoriser l’émission de photon, les spins sont couplés à un résonateur supraconducteur ayant un petit volume de mode et de faibles pertes, générant un effet Purcell. La sortie du résonateur est connectée à un compteur de photon micro-onde basé sur un qubit supraconducteur et un mélange à 4 ondes. La grande sensibilité de ce détecteur S = 10⁻²² W/√Hz est une des clés de la réussite de cette expérience. Notre méthode s’applique à tous types d’impuretés paramagnétiques sans nécessiter une transition optique ni un grand temps de cohérence. Nous mesurons les caractéristiques de plusieurs spins individuels, les résultats varient fortement d’un spin à l’autre, mettant en avant l’inhomogénéité de leurs environnements électromagnétiques. Les temps de cohérence atteignent plusieurs millisecondes et sont limités radiativement. Finalement, nous réalisons une expérience visant à sonder l’environnement magnétique d’une impureté particulière grâce à une séquence de découplage dynamique. Le signal à résonance nous permet de mettre en évidence la présence de spin nucléaire de ¹⁸³W. Nous émettons finalement quelques hypothèses préliminaires sur leur disposition autour de l’ion erbium étudié.

This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported on semialgebraic sets and subject to moment polynomial constraints is investigated. A positive solution to Hilbert's 17th problem for pseudo-moments is given. On the other hand, moment polynomials positive on actual measures are shown to be sums of squares and formal moments of squares up to arbitrarily small perturbation of their coefficients. When only measures supported on a bounded semialgebraic set are considered, a stronger algebraic certificate for moment polynomial positivity is derived. This result gives rise to a converging hierarchy of semidefinite programs for moment polynomial optimization. Finally, as an application, two nonlinear Bell inequalities from quantum physics are settled., 26 pages

A case study of the non-equilibrium dynamics of open quantum systems in the markovian approximation is presented for two dynamical models based on a single harmonic oscillator in an external field. Specified through distinct forms of ohmic damping, their quantum Langevin equations are derived from an identical set of physical criteria, namely the canonical commutator between position and momentum, the Kubo formula, the virial theorem and the quantum equilibrium variance. The associated Lindblad equations are derived but only one of them is completely positive. Transforming those into Fokker-Planck equations for the Wigner functions, both models are shown to evolve towards the same Gibbs state, for a vanishing external field. The phenomenological differences between the models are illustrated through their quantum relaxations and through the phase diagrammes derived from their re-interpretation as mean-field approximations of an interacting many-body system., Comment: 4 figures

How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measurements. We show that demanding that a theory exhibits {a composite} measurement imposes a hierarchy of constraints on the structure of its sets of states and effects, which translate to a hierarchy of constraints on the allowed correlations themselves. We moreover focus on the particular case where one demands the existence of a correlated measurement that reads out the parity of local fiducial measurements. By formulating a non-linear Optimisation Problem, and semidefinite relaxations of it, we explore the consequences of the existence of such a parity reading measurement for violations of Bell inequalities. In particular, we show that in certain situations this assumption has surprisingly strong consequences, namely, that Tsirelson's bound can be recovered., Comment: 43 pages. V3 -- new numerical results

International audience; Cold Rydberg atoms are a promising platform for quantum technologies and combining them with optical waveguides has the potential to create robust quantum information devices. Here, we experimentally observe the excitation of cold rubidium atoms to a large range of Rydberg S and D states through interaction with the evanescent field of an optical nanofiber. We develop a theoretical model to account for experimental phenomena present such as the AC Stark shifts and the Casimir-Polder interaction. This work strengthens the knowledge of Rydberg atom interactions with optical nanofibers and is a critical step toward the implementation of all-fiber quantum networks and waveguide QED systems using highly excited atoms.

We study the time evolution of the density matrix of a high energy quark propagating in a dense QCD medium where it undergoes elastic collisions (radiation is ignored in the present study). The medium is modeled as a stochastic color field with a Gaussian correlation function. This allows us to eliminate the medium degrees of freedom and obtain a simple master equation for the evolution of the reduced density matrix of the high energy quark, making use of approximations that are familiar in the description of open quantum systems. This master equation is solved analytically, and we demonstrate that its solution can be reconstructed from a simple Langevin equation. At late times, one finds that only the color singlet component of the density matrix survives the quark's propagation through the medium. The off-diagonal elements of the density matrix are suppressed successively in transverse position space and in momentum space, and become independent of the details of the initial condition. This behavior is reflected in the corresponding von Neumann entropy, whose growth at late time is related to the increase of the classical phase space explored by the high energy quark in its motion through the medium. The interpretation of the Wigner transform as a classical distribution is further supported by the fact that the associated classical entropy coincides at late time with the von Neumann entropy., 15 pages, 6 figures

International audience; In this paper we introduce a novel noise model for quantum measurements motivated by an indirect measurement scheme with faulty preparation. Averaging over random dynamics governing the interaction between the quantum system and a probe, a natural, physical noise model emerges. We compare it to existing noise models (uniform and depolarizing) in the framework of incompatibility robustness. We observe that our model allows for larger compatibility regions for specific classes of measurements.

Despite a very good understanding of single-particle Anderson localization in one-dimensional (1D) disordered systems, many-body effects are still full of surprises, a famous example being the interaction-driven many-body localization (MBL) problem, about which much has been written, and perhaps the best is yet to come. Interestingly enough the non-interacting limit provides a natural playground to study non-trivial multiparticle physics, offering the possibility to test some general mechanisms with very large-scale exact diagonalization simulations. In this work, we first revisit the 1D many-body Anderson insulator through the lens of extreme value theory, focusing on the extreme polarizations of the equivalent spin chain model in a random magnetic field. A many-body-induced chain breaking mechanism is explored numerically, and compared to an analytically solvable toy model. A unified description, from weak to large disorder strengths $W$ emerges, where the disorder-dependent average localization length $\xi(W)$ governs the extreme events leading to chain breaks. In particular, tails of the local magnetization distributions are controlled by $\xi(W)$. Remarkably, we also obtain a quantitative understanding of the full distribution of the extreme polarizations, which is given by a Fr\'echet-type law. In a second part, we explore finite interaction physics and the MBL question. For the available system sizes, we numerically quantify the difference in the extreme value distributions between the interacting problem and the non-interacting Anderson case. Strikingly, we observe a sharp "extreme-statistics transition" as $W$ changes, which may coincide with the MBL transition., Comment: 18 + 6 pages; 13 + 4 figures

DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since then, they have been widely used as models and subsampling tools in statistics and computer science. Most applications require sampling from a DPP, and given their quantum origin, it is natural to wonder whether sampling a DPP on a quantum computer is easier than on a classical one. We focus here on DPPs over a finite state space, which are distributions over the subsets of $\{1,\dots,N\}$ parametrized by an $N\times N$ Hermitian kernel matrix. Vanilla sampling consists in two steps, of respective costs $\mathcal{O}(N^3)$ and $\mathcal{O}(Nr^2)$ operations on a classical computer, where $r$ is the rank of the kernel matrix. A large first part of the current paper consists in explaining why the state-of-the-art in quantum simulation of fermionic systems already yields quantum DPP sampling algorithms. We then modify existing quantum circuits, and discuss their insertion in a full DPP sampling pipeline that starts from practical kernel specifications. The bottom line is that, with $P$ (classical) parallel processors, we can divide the preprocessing cost by $P$ and build a quantum circuit with $\mathcal{O}(Nr)$ gates that sample a given DPP, with depth varying from $\mathcal{O}(N)$ to $\mathcal{O}(r\log N)$ depending on qubit-communication constraints on the target machine. We also connect existing work on the simulation of superconductors to Pfaffian point processes, which generalize DPPs and would be a natural addition to the machine learner's toolbox. Finally, the circuits are empirically validated on a classical simulator and on 5-qubit machines., Comment: 48 pages, 8 figures. Additional results about parity of cardinality of PfPP samples

We examine evaluations of the contributions of Matrix Mechanics and Max Born to the formulation of quantum mechanics from Heisenberg's Helgoland paper of 1925 to Born's Nobel Prize of 1954. We point out that the process of evaluation is continuing in the light of recent interpretations of the theory that deemphasize the importance of the wave function., 58 pages

Quantum mechanics allows processes to be superposed, leading to a genuinely quantum lack of causal structure. For example, the process known as the quantum switch applies two operations ${\cal A}$ and ${\cal B}$ in a superposition of the two possible orders, ${\cal A}$ before ${\cal B}$ and ${\cal B}$ before ${\cal A}$. Experimental implementations of the quantum switch have been challenged by some on the grounds that the operations ${\cal A}$ and ${\cal B}$ were implemented more than once, thereby simulating indefinite causal order rather than actually implementing it. Motivated by this debate, we consider a situation in which the quantum operations are physically described by a light-matter interaction model. While for our model the two processes are indistinguishable in the infinite energy regime, restricting the energy available for the implementation of the operations introduces imperfections, which allow one to distinguish processes using different number of operations. We consider such an energetically-constrained scenario and compare the quantum switch to one of its natural simulations, where each operation is implemented twice. Considering a commuting-vs-anticommuting unitary discrimination task, we find that within our model the quantum switch performs better, for some fixed amount of energy, than its simulation. In addition to the known computational or communication advantages of causal superpositions, our work raises new questions about their potential energetic advantages., Comment: Updated version with a slightly modified abstract and conclusion emphasizing more on the exact assumptions and outcomes of the work. The Fig1 has a rewritten legend. Minor details were also added on various parts

The quantum critical properties of interacting fermions in the presence of disorder are still not fully understood. While it is well known that for Dirac fermions, interactions are irrelevant to the non-interacting infinite randomness fixed point (IRFP), the problem remains largely open in the case of Majorana fermions which further display a much richer disorder-free phase diagram. Here, pushing the limits of DMRG simulations, we carefully examine the ground-state of a Majorana chain with both disorder and interactions. Building on appropriate boundary conditions and key observables such as entanglement, energy gap, and correlations, we strikingly find that the non-interacting Majorana IRFP is very stable against finite interactions, in contrast with previous claims., 5+2 pages, 5+4 figures

Lawrence et al. have presented an argument purporting to show that "relative facts do not exist" and, consequently, "Relational Quantum Mechanics is incompatible with quantum mechanics". The argument is based on a GHZ-like contradiction between constraints satisfied by measurement outcomes in an extended Wigner's friend scenario. Here we present a strengthened version of the argument, and show why, contrary to the claim by Lawrence et al., these arguments do not contradict the consistency of a theory of relative facts. Rather, considering this argument helps clarify how one should not think about a theory of relative facts, like RQM., 4 pages

Single spins in solids are good candidates for implementing quantum bits for quantum information processing thanks to their long coherence times. However, being individual atomic-scale quantum objects, they are difficult to address and to entangle with one another. This thesis work explores two distinct but related approaches for manipulating and detecting single spins, both involving comparable hybrid circuit quantum electrodynamics platforms operated at millikelvin temperatures. In the first approach, single electron spin resonance (ESR) is demonstrated by spin fluorescence detection: a microwave photon counter is used to detect the photon emitted by an excited spin. The spins are paramagnetic erbium ions in a scheelite crystal, and are coupled magnetically to a high-quality factor planar superconducting resonator. They are detected individually with a signal-to-noise ratio of 1.9 in a one second-integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the engineered spin radiative lifetime. This single-spin quantum control experiment also opens the route to new applications of ESR, in particular for microscopic object characterization. In the second approach, the detection of spins is based on leveraging the charge degree of freedom of hole spins and their strong intrinsic spin-orbit interaction. We demonstrate a compact novel platform made of electrostatically defined quantum dots in AlGaAs/GaAs heterostructure, filled with hole spins by optical illumination. The spins are coupled electrically to a superconducting resonator for probing their charge and spin states. Using this resonator as a dispersive readout, we show that single charge tunneling events in the dots can be detected after illumination. This represents a critical step towards addressing single hole spin in a semiconductor. Overall, the two methods reported in this thesis open new avenues for the development of quantum sensing and quantum computing applications.; Les spins uniques dans les solides sont de bons candidats pour la mise en œuvre de bits quantiques pour le traitement de l'information quantique grâce à leurs longs temps de cohérence. Cependant, en tant qu'objets quantiques individuels à l'échelle atomique, ils sont difficiles à traiter et à enchevêtrer les uns avec les autres. Ce travail de thèse explore deux approches distinctes mais liées pour manipuler et détecter des spins uniques ; toutes deux utilisent des circuits quantiques hybrides fonctionnant à des températures de l'ordre du millikelvin. Dans la première approche, la résonance paramagnétique électronique (RPE) de spins individuels est démontrée en détectant leur fluorescence : un compteur de photons micro-onde détecte le photon émis par un spin excité. Les spins utilisés sont des ions paramagnétiques d'erbium dans un cristal de scheelite, et sont couplés magnétiquement à un résonateur planaire supraconducteur de facteur de qualité élevé. Ils sont détectés individuellement avec un rapport signal/bruit de 1,9 en une seconde. Le signal de fluorescence présente de l'antibunching (dégroupement), prouvant ainsi qu'il provient d'émetteurs individuels. Des temps de cohérence allant jusqu'à 3 ms sont mesurés, limités par le temps de vie radiatif du spin. Cette expérience de contrôle quantique d'un spin unique ouvre également la voie à de nouvelles applications de RPE, notamment pour la caractérisation d'objets microscopiques. Dans la seconde approche, la détection des spins est basée sur l'exploitation du degré de liberté de charge des spins de trous et de leur forte interaction spin-orbite intrinsèque. Nous démontrons une nouvelle plateforme compacte composée de boîtes quantiques définis électrostatiquement dans l'AsGa, et pré-remplis de spins de trous par illumination dans le domaine optique ; les spins sont couplés électriquement à un résonateur supraconducteur pour sonder leurs états de charge et de spin. En utilisant ce résonateur en régime de lecture dispersive, nous montrons que des sauts de charge unique dans les boîtes quantiques peuvent être détectées après l'illumination. Il s'agit d'une étape cruciale dans l'étude du spin d'un trou unique dans un semi-conducteur. Dans l'ensemble, les deux méthodes présentées dans cette thèse ouvrent de nouvelles voies pour le développement des capteurs quantiques et du traitement quantique de l'information.

Quantum memories represent one of the main ingredients of future quantum communication networks. Their certification is therefore a key challenge. Here we develop efficient certification methods for quantum memories. Considering a device-independent approach, where no a priori characterisation of sources or measurement devices is required, we develop a robust self-testing method for quantum memories. We then illustrate the practical relevance of our technique in a relaxed scenario by certifying a fidelity of 0.87 in a recent solid-state ensemble quantum memory experiment. More generally, our methods apply for the characterisation of any device implementing a qubit identity quantum channel., 5+11 pages, 1 figure

An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of freedom describing the shape of the wave-packet and its fluctuations. These quantum dressing are independent degrees of freedom, mathematically encoded in the higher moments of the wave-function. We review how to extract the effective dynamics for Gaussian wave-packets evolving according to the Schrodinger equation with time-dependent potential in a 1+1-dimensional spacetime, and derive the equations of motion for the quadratic uncertainty. We then show how to integrate the evolution of all the higher moments for a general wave-function in a time-dependent harmonic potential., 7 pages, v2: references and footnotes added

While strong system-bath coupling produces rich and interesting phenomena, applications to quantum thermal engines have been so far pointing mainly at detrimental effects. The delicate trade-off between efficiency loss due to strong coupling and power increase due to faster equilibration, while acknowledged, remained largely unexplored owing to the challenge of assessing precisely the equilibration time. Here, we overcome this obstacle by exploiting exact numerical simulations based on the hierarchical equations of motion (HEOM) formalism. We show that a quantum Otto cycle can perform better at strong (but not ultrastrong) coupling in that the product of the efficiency times the output power is maximized in this regime. In particular, we show that strong coupling allows one to obtain engines with larger efficiency than their weakly coupled counterparts, while sharing the same output power. Conversely, one can design strongly coupled engines with larger power than their weakly coupled counterparts, while sharing the same efficiency. Overall, our results provide situations where strong coupling can directly enhance the performance of thermodynamic operations, re-enforcing the importance of studying quantum thermal engines beyond standard configurations., 10 + 10 pages, 9 + 3 figures. Slight changes in the introduction. Comments are welcome

Temporal-to-spatial demultiplexing routes non-simultaneous events of the same spatial mode to distinct output trajectories. This technique has now been widely adopted because it gives access to higher-number multi-photon states when exploiting solid-state quantum emitters. However, implementations so far have required an always-increasing number of active elements, rapidly facing resource constraints. Here, we propose and demonstrate a demultiplexing approach that utilizes only a single active element for routing to, in principle, an arbitrary number of outputs. We employ our device in combination with a high-efficiency quantum dot based single-photon source, and measure up to eight demultiplexed highly indistinguishable single photons. We discuss the practical limitations of our approach, and describe in which conditions it can be used to demultiplex, e.g., tens of outputs. Our results thus provides a path for the preparation of resource-efficient larger-scale multi-photon sources., 7 pages, 7 figures

We discuss a construction of a microcanonical projection WOW of a quantum operator O, its spectrum, and the retrieval of canonical many-time correlations from it., 18 pages, 4 figures

37 pages, 3 figures; Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its dual). In this article, we generalize this idea and introduce the notion of polytope compatibility, by considering arbitrary polytopes. We find that semiclassical magic squares correspond to Birkhoff polytope compatibility. In general, we prove that polytope compatibility is in one-to-one correspondence with measurement compatibility, when the measurements have some elements in common and the post-processing of the joint measurement is restricted. Finally, we consider how much tuples operators with appropriate joint numerical range have to be scaled in the worst case in order to become polytope compatible and give both analytical sufficient conditions and numerical ones based on linear programming.

International audience; Previous experiments on cubic UO2 have suggested that the temperature dependences of the nearest-neighbour U–O and U–U distances are different. We have acquired total-scattering neutron diffraction patterns out to Q=23.5 Å−1 for 50 < T < 1023 K and produced via Fourier transform a pair-distribution function PDF(r). The PDF(r) shows quite clearly that r(U–O), defined by the maximum of the U–O peak in the PDF(r), does in fact decrease with increasing temperature, whereas r(U–U) follows the lattice expansion, as expected. We also observe that the r(U–O) contraction accelerates continuously above T ≈ 400 K, consistent with earlier experiments by others. Furthermore, by analysing the eigenvectors of the phonon modes, we show that the Δ5(TO1) phonon tends to separate the eight equivalent U–O distances into six shorter and two longer distances, where the longer pair contribute to a high-r tail observed in the U–O distance distribution becoming increasingly anisotropic at higher T. These results have significance for a wide range of materials in which heavy and light atoms are combined in a simple atomic structure [1].[1] L. Desgranges et al. J. Physics: Condensed Matter 35 10LT01 (2023)

A case study of the non-equilibrium dynamics of open quantum systems in the markovian approximation is presented for two dynamical models based on a single harmonic oscillator in an external field. Specified through distinct forms of ohmic damping, their quantum Langevin equations are derived from an identical set of physical criteria, namely the canonical commutator between position and momentum, the Kubo formula, the virial theorem and the quantum equilibrium variance. The associated Lindblad equations are derived but only one of them is completely positive. Transforming those into Fokker-Planck equations for the Wigner functions, both models are shown to evolve towards the same Gibbs state, for a vanishing external field. The phenomenological differences between the models are illustrated through their quantum relaxations and through the phase diagrammes derived from their re-interpretation as mean-field approximations of an interacting many-body system.; Une étude de cas de la dynamique hors équilibre de systèmes quantiques ouverts dans l'approximation markovienne est présentée pour deux modèles dynamiques basés sur un seul oscillateur harmonique, dans un champ externe. Spécifiées par des formes distinctes d'amortissement ohmique, leurs équations quantiques de Langevin sont dérivées à partir de critères physiques identiques, à savoir le commutateur canonique entre position et quantité de mouvement, la formule de Kubo, le théorème du viriel et la variance d'équilibre quantique. Les équations de Lindblad associées sont dérivées mais qu'une seule d'entre elles n'est complètement positive. En les transformant en équations de Fokker-Planck pour les fonctions de Wigner, les deux modèles évoluent vers le même état de Gibbs, pour un champ externe nul. Les différences phénoménologiques entre les modèles sont illustrées par leurs relaxations quantiques et par les diagrammes de phase dérivés de leur réinterprétation comme approximations de champ moyen d'un système à plusieurs corps en interaction.; Um estudo de caso da dinâmica fora do equilíbrio de sistemas quânticos abertos na aproximação markoviana é apresentado para dois modelos dinâmicos baseados em um único oscilador harmônico em um campo externo. Especificadas por meio de formas distintas de amortecimento ôhmico, suas equações quânticas de Langevin são derivadas de um conjunto idêntico de critérios físicos, ou seja, o comutador canônico entre posição e momento, a fórmula de Kubo, o teorema do virial e a variância do equilíbrio quântico. As equações de Lindblad associadas são derivadas, mas apenas uma delas é completamente positiva. Transformando-os em equações de Fokker-Planck para as funções de Wigner, ambos os modelos mostram evoluir para o mesmo estado de Gibbs, para um campo externo que desaparece. As diferenças fenomenológicas entre os modelos são ilustradas através de suas relaxações quânticas e através dos diagramas de fase derivados de sua reinterpretação como aproximações de campo médio de um sistema interativo de muitos corpos.

In this paper we study the transitions of entanglement complexity in an exemplary family of states - the Rokhsar-Kivelson-sign wavefunctions - whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with sub-extensive scaling of entanglement, reminiscent of the many-body-localization transition of disordered quantum Hamiltonians [Physical Review B 92, 214204 (2015)]. We study the singularities of the Rokhsar-Kivelson-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric; entanglement spectrum statistics; entanglement entropy fluctuations; stabilizer R\'enyi Entropy; and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a "super-universal" regime appears for small values of the control parameter in which all metrics become independent of the parameter itself; the entanglement entropy as well as the stabilizer R\'enyi entropy appear to approach their theoretical maximum; the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a non-universal scaling; and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates., Comment: Journal version. Added 1 paragraph and 1 image

We demonstrate that absorption saturation of a mid-infrared intersubband transition can be engineered to occur at moderate light intensities of the order of 10-20 kW.cm$^{-2}$ and at room temperature. The structure consists of an array of metal-semiconductor-metal patches hosting a judiciously designed 253~nm thick GaAs/AlGaAs semiconductor heterostructure. At low incident intensity the structure operates in the strong light-matter coupling regime and exhibits two absorption peaks at wavelengths close to 8.9 $\mu$m. Saturation appears as a transition to the weak coupling regime - and therefore to a single-peaked absorption - when increasing the incident power. Comparison with a coupled mode theory model explains the data and permits to infer the relevant system parameters. When the pump laser is tuned at the cavity frequency, the reflectivity decreases with increasing incident power. When instead the laser is tuned at the polariton frequencies, the reflectivity non-linearly increases with increasing incident power. At those wavelengths the system therefore mimics the behavior of a saturable absorption mirror (SESAM) in the mid-IR range, a technology that is currently missing.

The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of fault-tolerant quantum computing it is then crucial to minimize the number of $T$ gates. Many algorithms, yielding effective results, have been designed to address this problem. It has been demonstrated that performing a pre-processing step consisting of reducing the number of Hadamard gates in the circuit can help to exploit the full potential of these algorithms and thereby lead to a substantial $T$-count reduction. Moreover, minimizing the number of Hadamard gates also restrains the number of additional qubits and operations resulting from the gadgetization of Hadamard gates, a procedure used by some compilers to further reduce the number of $T$ gates. In this work we tackle the Hadamard gate reduction problem, and propose an algorithm for synthesizing a sequence of $\pi/4$ Pauli rotations with a minimal number of Hadamard gates. Based on this result, we present an algorithm which optimally minimizes the number of Hadamard gates lying between the first and the last $T$ gate of the circuit.

We propose a novel approach to generate, protect and control GKP qubits. It employs a microwave frequency comb parametrically modulating a Josephson circuit to enforce a dissipative dynamics of a high impedance circuit mode, autonomously stabilizing the finite-energy GKP code. The encoded GKP qubit is robustly protected against all dominant decoherence channels plaguing superconducting circuits but quasi-particle poisoning. In particular, noise from ancillary modes leveraged for dissipation engineering does not propagate at the logical level. In a state-of-the-art experimental setup, we estimate that the encoded qubit lifetime could extend two orders of magnitude beyond the break-even point, with substantial margin for improvement through progress in fabrication and control electronics. Qubit initialization, readout and control via Clifford gates can be performed while maintaining the code stabilization, paving the way toward the assembly of GKP qubits in a fault-tolerant quantum computing architecture., 61 pages, 20 figures, 1 table

Funding Information: The authors thank S Pirandola, and S Gasparinetti for useful discussions, and thank the support from Project QMiCS (820505) of the EU Flagship on Quantum Technologies. M C, E Z C, R A, G F, S G, and Y O thank the support from FCT—Fundação para a Ciência e a Tecnologia (Portugal), namely through Projects UIDB/50008/2020 and UIDB/04540/2020, as well as from Project TheBlinQC supported by the EU H2020 QuantERA ERA-NET Cofund in Quantum Technologies and by FCT (QuantERA/0001/2017). M C acknowledges support from the DP-PMI and FCT through scholarship PD/BD/135186/2017. G F acknowledges support from FCT through scholarship SFRH/BD/145572/2019. T G-R, M R and M S acknowledge financial support from Basque Government QUANTEK Project from ELKARTEK program (KK-2021/00070), Spanish Ramón y Cajal Grant RYC-2020-030503-I, as well as from OpenSuperQ (820363) of the EU Flagship on Quantum Technologies, and the EU FET-Open Projects Quromorphic (828826) and EPIQUS (899368), and IQM Quantum Computers under the Project ‘Generating quantum algorithms and quantum processor optimization’. M R acknowledges support from UPV/EHU PhD Grant PIF21/289. M M and G C acknowledge funding from the European Research Council under Consolidator Grant No. 681311 (QUESS), and from the Academy of Finland through its Centers of Excellence Program (Project Nos. 312300 and 336810) and QEMP Project (319579). M R, K G F, and F D acknowledge support by the German Research Foundation via Germany’s Excellence Strategy (EXC-2111-390814868), the Elite Network of Bavaria through the program ExQM, the EU Flagship Project QMiCS (Grant No. 820505), the German Federal Ministry of Education and Research via the Projects QUARATE (Grant No. 13N15380) and QuaMToMe (Grant No. 16KISQ036), and the State of Bavaria via the Munich Quantum Valley and the Hightech Agenda Bayern Plus. | openaire: EC/H2020/820505/EU//QMiCS | openaire: EC/H2020/820363/EU//OpenSuperQ | openaire: EC/H2020/681311/EU//QUESS The field of propagating quantum microwaves is a relatively new area of research that is receiving increased attention due to its promising technological applications, both in communication and sensing. While formally similar to quantum optics, some key elements required by the aim of having a controllable quantum microwave interface are still on an early stage of development. Here, we argue where and why a fully operative toolbox for propagating quantum microwaves will be needed, pointing to novel directions of research along the way: from microwave quantum key distribution to quantum radar, bath-system learning, or direct dark matter detection. The article therefore functions both as a review of the state-of-the-art, and as an illustration of the wide reach of applications the future of quantum microwaves will open.

It is of folkloric belief that the security of classical cryptographic protocols is automatically broken if the Adversary is allowed to perform superposition queries and the honest players forced to perform actions coherently on quantum states. Another widely held intuition is that enforcing measurements on the exchanged messages is enough to protect protocols from these attacks. However, the reality is much more complex. Security models dealing with superposition attacks only consider unconditional security. Conversely, security models considering computational security assume that all supposedly classical messages are measured, which forbids by construction the analysis of superposition attacks. Boneh and Zhandry have started to study the quantum computational security for classical primitives in their seminal work at Crypto'13, but only in the single-party setting. To the best of our knowledge, an equivalent model in the multiparty setting is still missing. In this work, we propose the first computational security model considering superposition attacks for multiparty protocols. We show that our new security model is satisfiable by proving the security of the well-known One-Time-Pad protocol and give an attack on a variant of the equally reputable Yao Protocol for Secure Two-Party Computations. The post-mortem of this attack reveals the precise points of failure, yielding highly counter-intuitive results: Adding extra classical communication, which is harmless for classical security, can make the protocol become subject to superposition attacks. We use this newly imparted knowledge to construct the first concrete protocol for Secure Two-Party Computation that is resistant to superposition attacks. Our results show that there is no straightforward answer to provide for either the vulnerabilities of classical protocols to superposition attacks or the adapted countermeasures., 46 pages

We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity., Comment: 25 pages, 9 figures, 3 tables

This paper demonstrates the capability to simulate EPR experiments in a realistic way (i.e. without transmission of information between the source and the detector) and confirms even more the Bell’s theorem, by demonstrating that effectively non-local variables are required to violate the Bell’s inequality. Unlike all EPR experiments, this modeling instead of simply noting the inadequacy of a local modeling proposes a new way of non-local idealization. These simulations work on spreadsheet by idealizing objects with a non-linear notion, the extended object. This allows to set up a new principle of locality (or non-locality) and a new meaning on the loopholes of EPR experiments. It sheds new light on several concepts of Quantum Mechanics (QM): the quantum states (would represent an equivalence class of many different indistinguishable objects seen as equivalent in terms of measurement), the wave function (would represent a probability on this equivalence class seen as a single set despite different probabilities of happening for the individual objects composing this equivalence class), the measurement (in our simulation, the measured object is not modified), the superposition of states (in our simulation, Schrödinger's cat is never both dead and alive). These simulations lead to several kinds of EPR experiments with violations of the Bell’s inequalities with values different from the QM, allow to realize entanglements with more than 2 objects (whatever the number of Alice and Bob) or even with more than 2 results (beyond the only “+1” or “-1” outputs). Many questions remain to be explored in the physics domain on quantum phenomena (teleportation, encryption, quantum computing, etc.…), but this theoretical approach also reveals the necessity of developing new non-linear tools in mathematics domain and seems to show that QM could finally be a limit case of a more fundamental nonlinear physics theory founded on these extended objects. This observation is strangely reminiscent of developments such as string theory.

A quantum repeater node is presented based on trapped ions that act as single photon emitters, quantum memories and an elementary quantum processor. The node’s ability to establish entanglement across two 25 km-long optical fibers independently, then to swap that entanglement efficiently to extend it over both fibers, is demonstrated. The resultant entanglement is established between telecom-wavelength photons at either end of the 50 km channel. Finally, the system improvements to allow for repeater-node chains to establish stored entanglement over 800 km at Hertz rates are calculated, revealing a near-term path to distributed networks of entangled sensors, atomic clocks and quantum processors., This work was financially supported by the START prize of the Austrian FWF project Y 849-N20, the Aus- trian FWF Standalone project QMAP with project num- ber P 34055, the Institute for Quantum Optics and Quan- tum Information (IQOQI) of the Austrian Academy Of Sciences (OeAW) and the European Union's Horizon 2020 research and innovation program under grant agree- ment No 820445 and project name 'Quantum Internet Alliance'. We acknowledge funding for V. Krutyanskiy by the Erwin Schr ̈odinger Center for Quantum Science & Technology (ESQ) Discovery Programme, for N.S. by the Commissariat `a l'Energie Atomique et aux Energies Alternatives (CEA), and for B.P.L. by the CIFAR Quan- tum Information Science Program of Canada.

We show that conditional expectations, optimal hypotheses, disintegrations and adjoints of unital completely positive maps are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita–Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional $C^{\ast}$-algebras.

The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems in order to enhance the precision of measurements beyond the standard quantum limit. To do so, one can reshape the quantum projection noise -- a strategy known as squeezing. In the context of many-body spin systems, one typically utilizes all-to-all interactions (e.g. the one-axis twisting model) between the constituents to generate the structured entanglement characteristic of spin squeezing. Motivated by recent theoretical work, here we explore the prediction that short-range interactions -- and in particular, the two-dimensional dipolar XY model -- can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of -3.5 dB (prior to correcting for detection errors, or approximately -5 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by approximately 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics., 12 pages, 10 figures

We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which encode logical oscillators. Unlike for qubits or oscillators, homological quantum rotor codes allow one to encode both logical rotors and logical qudits, depending on the homology of the underlying chain complex. In particular, such a code based on the chain complex obtained from tessellating the real projective plane or a M\"{o}bius strip encodes a qubit. We discuss the distance scaling for such codes which can be more subtle than in the qubit case due to the concept of logical operator spreading by continuous stabilizer phase-shifts. We give constructions of homological quantum rotor codes based on 2D and 3D manifolds as well as products of chain complexes. Superconducting devices being composed of islands with integer Cooper pair charges could form a natural hardware platform for realizing these codes: we show that the $0$-$\pi$-qubit as well as Kitaev's current-mirror qubit -- also known as the M\"{o}bius strip qubit -- are indeed small examples of such codes and discuss possible extensions., Comment: 47 pages, 10 figures, 2 tables

We study a semi-classical model of the mixmaster universe. We first derive the quantum model and then introduce its semi-classical approximation. We employ a general integral quantization method that respects the symmetries of the model given by the affine and the Weyl-Heisenberg groups, and can produce a wide class of quantum models. The semi-classical approximation is based on the coherent states. The semi-classical dynamics is complex and can not be solved by analytical methods. We focus on a key qualitative feature of the dynamics, namely, we investigate whether the primordial anisotropic universe can undergo a spontaneous inflationary phase driven by the anisotropic energy combined with semi-classical corrections. The answer to this question provides a useful perspective on the inflationary paradigm as well as on alternative bouncing models., 15 pages, 6 figures