From Quantum Matter to Quantum Computers

We argue that moiré bilayer graphene at charge neutrality hosts a continuous semimetal-to-insulator quantum phase transition that can be accessed experimentally by tuning the twist angle between the two layers. For small twist angles near the first magic angle, the system realizes a Kramers intervalley-coherent insulator, characterized by circulating currents and spontaneously broken time reversal and U(1) valley symmetries. For larger twist angles above a critical value, the spectrum remains gapless down to the lowest temperatures, with a fully symmetric Dirac semimetal ground state. Using self-consistent Hartree-Fock theory applied to a realistic model of twisted bilayer graphene, based on the Bistritzer-MacDonald Hamiltonian augmented by screened Coulomb interactions, we find that the twist-tuned quantum phase transition is continuous. We argue that the quantum critical behavior belongs to the relativistic Gross-Neveu-XY universality class, and we characterize it through an effective field theory analysis. Our theoretical predictions can be directly tested using current experimental setups incorporating the recently developed quantum twisting microscope.

Multiterminal superconducting junctions have revitalized the investigation of the Josephson effect. One of the most interesting aspects of these hybrid systems is the occurrence of multi-Cooper pair tunneling processes that have no analog in two-terminal devices. Such correlated tunneling events are also intimately connected to the Andreev bound states (ABSs) supported by these structures. Josephson junctions with four superconducting terminals have attracted special attention because they are predicted to support ABSs with nontrivial topological properties. Here, we present a theoretical study of sextets, which are correlated tunneling processes involving three Cooper pairs and four different superconducting terminals. We investigate how sextets can be identified from the analysis of the current-phase relation, we show how sextets are connected to the hybridization of ABSs, and we discuss their existence in recent experiments on four-terminal devices realized in hybrid Al/InAs heterostructures.

Variational Quantum Eigensolvers (VQEs) are a class of hybrid classical quantum algorithms used to determine an upper bound on the ground state energy of a Hamiltonian. Due to their relatively low circuit depth, they are a promising candidate for a near-term quantum advantage. A significant drawback, however, is the overhead due to measurement repetitions. To combat this, an iterative measurement protocol, designed for molecular Hamiltonians, was introduced [1]. It relies on cheaply measuring commuting groups of operators, while the residual (non-commuting) elements are grouped in a different basis and then measured. This work builds upon that measurement protocol by combining it with nonperturbative analytical diagonalization techniques inspired by [2] to define a unitary transformation that specifically targets residual elements, rotating them into the commuting groups. Using this transformation, faster convergence of the energy approximation can be achieved, further reducing the measurement overhead. [1] Bincoletto, D.; Kottmann, J. S.; arXiv:2504.03019. [2] Li, B.; Calarco, T.; Motzoi, F.; PRX Quantum 3, 030313.

The simulation of quantum many-body systems is central to condensed matter physics, chemistry, and quantum information. However, the exponentially growing Hilbert space in these systems renders exact solutions intractable for moderately large system sizes and thus motivates the adoption of approximate numerical methods. In a 2017 seminal work, Carleo & Troyer [1] proposed the use of a Restricted Boltzmann Machine (RBM) neural network for variational Monte Carlo simulations, introducing neural-network quantum states (NQSs). NQSs leverage the power of modern deep learning while maintaining ab-initio accuracy—that is, they do not rely on external data—and have shown promising results over a range of systems. Here, we apply NQSs to the central-spin model that captures the interaction of a central spin with a bath of surrounding spins. This model represents, for example, the hyperfine coupling of electron and nuclear spins in semiconductor nanostructures, and a linear combination of such models yields the BCS model in the Anderson pseudospin formalism [2,3]. Understanding this model is therefore relevant for studying the decoherence of spin-qubit systems due to hyperfine coupling [4] and for simulating nonequilibrium superconductivity without mean-field theory. Despite the success of NQSs, their application to central-spin models has remained largely unexplored, apart from a recent study by Wei at al. [5]. In this work, we investigate the possibility for NQSs to learn and exploit the integrability of these models: The Hamiltonian admits many symmetries and associated conserved quantities [6], which may provide enhanced structure to the network. We evaluate this by comparing the performance of the networks under integrable and non-integrable conditions and by analyzing their learned internal representations. Additionally, we propose and explore novel neural network architectures which may provide greater expressiveness, flexibility, and generalizability. Overall, this work aims to improve the simulation of quantum many-body systems relevant for spin qubits with state-of-the-art ab-initio machine learning methods while providing insights into explaining the effectiveness of such methods for these problems. [1] G. Carleo, M. Troyer, Science 355, 602-606 (2017). [2] M.C. Cambiaggio, A. M. F. Rivas, M. Saraceno, Nuc. Phys. A 624, 2, 157-167 (1997). [3] J. Ruh, R. Finsterhoelzl, and G. Burkard, Phys. Rev. A 107, 062604 (2023). [4] A. V. Khaetskii, D. Loss, L. Glazman, Phys. Rev. Lett. 88, 18, 186802 (2002). [5] V. Wei, A. Orfi, F. Fehse, W. A. Coish, Adv. Phys. Res. 3, 2300078 (2024). [6] M. Gaudin, J. Phys. 37, 10, 1087-1098 (1976).

The dynamics under a non-Hermitian Hamiltonian are not unitary, with the non-conservation of norms as the consequence. The metric framework is a consistent treatment of non-Hermitian quantum mechanics, in which the Hilbert space is deformed in a dynamical fashion [1]. The true richness of this theory is unveiled when time evolution is considered, which is found to give rise to profound physical implications not seen in dissipative systems [2]. In our work, we realize the first experimental observation of a dynamical metric operator and the dynamics within the non-stationary Hilbert space. We propose a general framework for the quantum simulation of non-Hermiticity in closed systems. [1]Mostafazadeh, Ali. "Time-dependent pseudo-Hermitian Hamiltonians and a hidden geometric aspect of quantum mechanics." \textit{Entropy} 22.4 (2020): 471. [2]Sim, Karin, et al. "Quantum metric unveils defect freezing in non-Hermitian systems." \textit{Physical Review Letters} 131.15 (2023): 156501.

A singular flat band (SFB), a distinct class of the flat band, has been shown to exhibit various intriguing material properties characterized by the quantum distance. We present a general construction scheme for a tight-binding model hosting an SFB, where the quantum distance profile can be controlled. We first introduce how to build a compact localized state (CLS), endowing the flat band with a band-touching point and a specific value of the maximum quantum distance. Then, we develop a scheme designing a tight-binding Hamiltonian hosting an SFB starting from the obtained CLS, with the desired hopping range and symmetries. We propose several simple SFB models on the square and kagome lattices. Finally, we establish a bulk-boundary correspondence between the maximum quantum distance and the boundary modes for the open boundary condition, which can be used to detect the quantum distance via the electronic structure of the boundary states.

Driven out of equilibrium, closed quantum systems generally undergo thermalization, meaning that their long-time evolution results in equilibration to the predictions of a thermal (Gibbs) ensemble. This process is now understood in terms of the Eigenstate Thermalization Hypothesis (ETH). However, integrable systems, due to an extensive number of conservation laws, fail to thermalize. Our work focuses on quantum-chaotic quadratic systems, which demonstrate single-particle version of ETH and are proven to undergo the so-called generalized thermalization. We numerically investigate two-body observables for the 3D Anderson model and the quadratic SYK model, showing that they equilibrate to the predictions of the generalized Gibbs ensemble, except in the localized phase. We also address the influence of non-Gaussianity of the initial state in the quantum quench protocol.

Devices of quantum information processing, which allow the realization of analogue quantum simulations, e.g., quantum annealing, hold the promise of solving complex computational challenges and combinatorial optimization problems. We propose a novel type of quantum information device based on a network of interacting PT-symmetric non-Hermitian qubits. Using various techniques, such as the dilation procedure involving digital coupling to an auxiliary qubit, the quantum dynamics of individual PT-symmetric non-Hermitian qubits have been demonstrated on different experimental platforms, including NV-centers, superconducting qubits, and superconducting and trapped-ion qutrits. Exceptional points of various orders, as well as PT-symmetry-preserving and -breaking quantum phases, have been observed. A natural next step in this field is to explore the coherent quantum dynamics of interacting PT-symmetric non-Hermitian qubits. In this work, we focus on both time-independent and time-dependent Hamiltonians, suitable for quantum annealing, for an exemplary network of a two-qubit non-Hermitian system operating in the PT-symmetry-preserved and -broken regimes of the XY model. Our goal is to determine the optimal sweep speed that maximizes the probability of the system ending in the ground state.

Adiabatic quantum computing (AQC) provides a framework for solving optimisation problems by initialising a quantum system in the ground state of a mixing Hamiltonian and evolving it slowly toward a problem Hamiltonian. However, practical implementations on noisy intermediate-scale quantum (NISQ) devices are limited by the need for long runtimes or deep digitized circuits, both of which are highly sensitive to noise and decoherence. To address these challenges, numerous methods have been proposed. Here we present a feedback-based approach to adiabatic optimisation that enhances performance by introducing longitudinal bias fields during the evolution. The bias strengths are updated iteratively based on measurement outcomes from a truncated trotter evolution, allowing the protocol to adaptively steer the dynamics toward the target ground state. This method increases the minimum energy gap and reduces the required circuit depth, improving robustness and convergence. We benchmark the approach on combinatorial problems such as MaxCut and Sherrington-Kirkpatrick (SK) spin glasses, showing significantly improved ground-state fidelity compared to conventional discretized AQC. Importantly, our protocol, relying instead on classical post-processing between iterations for efficient initialisation of the circuit and few Trotter layers. This makes it readily compatible with current superconducting and trapped-ion platforms, offering a viable route to scalable quantum optimisation on near-term hardware.

Quantum simulators have the potential to solve quantum many-body problems, even involving long-range entanglement, which is out of reach for any classical computer. However, most of today's quantum simulators lack complete controllability for precise tuning of their physical parameters. In particular, accurately positioning the optical tweezers in Rydberg atom simulators is impossible with the current laser technology, which may, however, be corrected for with new tools driven by machine learning. In the paper Learning interactions between Rydberg atoms, the authors introduced a scalable approach to Hamiltonian learning using graph neural networks (GNNs), which demonstrated an impressive ability to extrapolate beyond its training domain, both in terms of the size and shape of the system, while exhibiting minimal decrease in accuracy. We continue this line of work by testing whether the same property of size extrapolation exists for systems where spins interact even more strongly. We introduce the long-range transverse field Ising model (LR TFIM), whose spin-spin interactions are proportional to $J_{ij} \propto R_{ij}^{-\alpha}$, allowing us to test much more correlated systems up to $\alpha = 1$. We use the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model across various Hamiltonian parameters. The correlation functions from these snapshots serve as input data for training. Remarkably, we demonstrate that the accuracy only slightly decreases with an increase in the interaction range, while still exhibiting very good performance, $R^2>0.90$. This work represents another step towards the potential application of GNNs in feedback control of optical tweezers' positions, thereby offering a significant enhancement of analog quantum simulators. Additionally, it deepens our understanding of the remarkable extrapolation properties of graph neural networks described in the original paper.

J. Mędrzycka$^1$, M. Muszyński$^1$, P. Kapuściński$^1$, P. Oliwa$^1$, E. Oton$^2$, P. Morawiak$^2$, R. Mazur$^2$, W. Piecek$^2$, J. Szczytko$^1$ $^1$ Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland; $^2$ Institute of Applied Physics, Military University of Technology, ul. Gen. S. Kalińskiego 2, 00-908, Warsaw, Poland Liquid crystals embedded within a microcavity (LCMC) offer unique tuning capabilities attributed to their fluid-like nature and self-organization properties. While these self-assembly properties remain largely unexplored in liquid crystal microcavity systems, they present exceptional opportunities for photonic potential engineering [1]. Among these, chiral nematic phase topological defects provide a particularly promising platform for such applications. One such defect is a toron, a self-assembled topological defect structure that occurs within chiral nematic (cholesteric) liquid crystals. It can be visualized as a toroidal configuration where the liquid crystal director field twists around both the major and minor axes of the torus. This results in a continuous, non-singular director field, except at the central defect core. In this study, we investigate chiral liquid-crystalline torons—ranging from approximately 2 $\mu$m to 6 $\mu$m in size—doped with a lasing dye and embedded within a planar microcavity. The resulting spatially varying refractive index induces a synthetic magnetic field that forms a binding photonic potential, effectively confining cavity modes. This confinement yields a non-trivial ladder of discrete energy states, shaped by the toron's structure and spin-orbit coupling. The dispersion relation exhibits strong polarization dependence, giving rise to uniquely polarized confined states observable as polarization quadrupoles in the S$_1$ and S$_2$ Stokes parameters. The evolution of the dispersion relation with toron size enables precise photonic potential engineering, achievable either dynamically via an applied electric field – leveraging the field-responsive nature of liquid crystals – or statically through tailoring the microcavity thickness. The proposed platform offers a versatile route for dynamic photonic control in soft-matter systems and lays the groundwork for advanced applications such as polarization-structured or orbital angular momentum (OAM) lasers, as well as single-site elements in polarization-sensitive photonic lattices. [1] M. Muszyński, et al., Laser & Photonics Reviews, 2400794 (2024)

We have studied the Haldane model on the fractal geometry of the Sierpi\'nksi gasket. As a consequence of the fractal geometry, we observe a fractality driven gap opening mechanism, leading to the opening of multiple gaps. In addition, the introduction of a complex next-nearest neighbor hopping causes the opening of multiple flux-induced gaps. We discuss a topological marker applicable to these fractal systems to quantify the topology, despite the lack of translational invariance. Finally, we present the phase diagram of this structure. Here, very intricate and complex patterns will emerge, in contrast with previous results. Therefore, we show that the fractality of the model greatly influences the phase space of these structures, and how the combination of topological phases of matter and fractal dimensions is an extremely compelling area of research.

The purpose of this thesis is to investigate the behavior of \textit{quantum magic} in many-body systems. According to the Gottesman-Knill theorem, the particular class of quantum states referred to as stabilizer states can be efficiently simulated on a classical computer. The property of non-stabilizerness, or magic, can be broadly defined as the distance between a general state and a stabilizer state, serving as a measure of classical hardness as well as a resource for quantum computation. Numerical studies of this property, as a feature of many-body systems, are classically hard. This work uses a combination of quantum circuit simulations and tensor-network methods to study the spread and characteristic features of magic in quantum systems. We demonstrate that this can be done with relative efficiency, while addressing questions about the characterization of non-local magic and its relation to quantum computational complexity.

We study the interplay of superconductivity and altermagnetism on a square lattice. Calculating susceptibilities in linear response theory, we observe that isotropic band structures favor s-wave coupling, while spin-nematic band structures favor instabilities in unconventional pairing channels. The ground state of the system is examined with mean-field calculations in dependence of different altermagnetic and electron-electron couplings. In the future, we aim to complement the analysis with Quantum Monte Carlo simulations.

Superconductivity in nickelates was first discovered in 2019 in the infinite-layer compound Nd$_{0.8}$Sr$_{0.2}$NiO$_2$, which shows a transition temperature of about 10–15$\,$K. More recently, in 2023, the family of high-temperature superconductors was extended by the nickelate La$_3$Ni$_2$O$_7$ which shows signatures of superconductivity around 80$\,$K, although it requires high pressure of about 15$\,$GPa. A related compound La$_4$Ni$_3$O$_{10}$ of the so-called Ruddlesden–Popper (RP) series undergoes a superconducting transition at 20–30$\,$K, also under high pressure. Motivated by these discoveries, we investigate a hypothetical class of nickelates modeled with Ni$^{2+}$ ions, where the essential physics is captured by electrons in partially filled $e_g$ orbitals, while fully occupied $t_{2g}$ orbitals are considered inactive. This motivates a two-orbital Hubbard model based on $e_g$ orbitals. The model is studied in the parameter regime enabling spin-state crossover, using numerical exact diagonalization for small periodic clusters. The aim is to contribute to the formulation of an effective low-energy model and to assess the validity of results obtained by mostly analytical approaches. To this end, cluster ground states, depending on model parameters, are analyzed by evaluating various averages and probabilities of selected electron configurations.

The Lindblad description of an open quantum system gives rise to two types of integrability, since the nonequilibrium steady state can be integrable independently of the Liouvillian. Taking boundary-driven and dephasing spin chains as a representative example, we discriminate Liouvillian and steady-state chaos by combining level spacing statistics and an extension of the eigenstate thermalization hypothesis to open quantum systems. Moreover, we analyze the structure of the steady states by expanding it in the basis of Pauli strings and comparing the weight of strings of different lengths. We show that the natural expectation that integrable steady states are "simple" (i.e., built from few-body local operators) does not hold: the steady states of both chaotic and integrable models have relevant contributions coming from Pauli strings of all possible lengths, including long-range and many-body interactions. Nevertheless, we show that one can effectively use the operator-size distribution to distinguish chaotic and integrable steady states.

We numerically study the formation of topological domains in the Haldane model on a honeycomb lattice in the presence of an external trapping potential. To map out topological domains in real space we calculate the local Chern number of the system as a function of position. The local Chern number was introduced by Bianco and Resta [1] as a topological marker of the Chern number. In order to test our implementation, we calculate the local Chern number of the Haldane model without external potential and confirm the results in [1]. By adding an external potential to the system, we find different topological domains which are indicated by a spatial variation of the local Chern number across the honeycomb lattice. We investigate the formation of topologically non-trivial domains, both as a function of the Fermi energy and for different shapes of the trapping potential. Related results were obtained for the Hofstadter model in [2]. [1] R. Bianco and R. Resta, Phys. Rev. B 84, 24 (2011) [2] U. Gebert, B. Irsigler, and W. Hofstetter, Phys. Rev. A 101, 6 (2020)

Neutral atoms in optical tweezer arrays have shaped the research frontier in quantum simulation, quantum metrology, and quantum computation in recent years. In particular, breakthroughs have been achieved in scaling array sizes, implementing close-to-unity fidelity manipulation, and fast, high-fidelity entanglement generation through the coupling to high-lying Rydberg states [1]. In our experiment, we leverage these developments to realize a novel experimental platform aimed at coupling an atom array to a high-finesse optical resonator [2], with the goal of strongly coupling the individual atoms to the cavity mode. We will present our compact and versatile experimental design, our ability to trap and manipulate individual rubidium atoms in optical tweezers inside the resonator, and our progress towards coupling the atoms to the optical mode and exciting them to their Rydberg states. In addition, we introduce our plan towards a dual-species array [3] integrating an alkaline-earth-like (AEL) atom (Ytterbium) with an Alkali (Rubidium). AEL atoms like Yb provide a unique level structure that one could leverage to improve the system performance by using the narrow cooling transitions, optical clock transitions, and techniques like erasure conversion. The dual-species array paired with an optical cavity would allow us to implement novel error correction, mitigation, and distributed quantum computing protocols. Our platform opens new perspectives in various directions, including fast readout and feedback for cyclic error correction in tweezer arrays, remote entanglement generation in or between atom arrays, and the quantum simulation of open-system dynamics. [1] S. Evered et al., "High-fidelity parallel entangling gates on a neutral-atom quantum computer," Nature, 622, 268–272 (2023). [2] E. Deist et al., "Mid-Circuit Cavity Measurement in a Neutral Atom Array," Phys. Rev. Lett.129, 203602 (2022). [3] S. Anand et al., "A dual-species Rydberg array" Nature Physics, Volume 20, 1744–1750 (2024)

Frustrated multipolar exchange interactions between spin-S local moments ($S > \frac{1}{2}$) have been suggested to possibly give rise to quantum spin liquid-like ground states featuring an emergent gauge structure and fractionalized excitations. However, only little is known about characteristic features and experimental signatures of such ``multipolar spin liquids". To this end, in this work we turn to the ``Quadrupolar Kitaev model" of $S=1$ moments on a honeycomb lattice as a drosophila, for which recent numerical studies have indicated a signature of deconfined ground state with $\mathbb{Z}_2$ topological order. As the quadrupolar spin-1 Kitaev model, similar to the spin-$S$ generalization of the Kitaev honeycomb model, is not exactly solvable, we use a combination of mean-field theory and exact symmetry analysis to investigate competing ground states, including multipolar liquids, and their (fractionalized) excitations. Our work suggests that for isotropic couplings $\left(J_x=J_y=J_z\right)$, there exists a extensive set of ground state configurations at the mean field level. Using a generalized parton construction, we identify an exact gauge structure using $1$-form symmetries of the model.

We investigate analogy between quantum signal processing (QSP) and the adiabatic-impulse model (AIM) in order to implement the QSP algorithm with fast quantum logic gates. QSP is an algorithm that uses single-qubit dynamics to perform a polynomial function transformation. AIM effectively describes the evolution of a two-level quantum system under strong external driving field. We can map parameters from QSP to AIM to implement QSP-like evolution with non-adiabatic, high-amplitude external drives. By choosing AIM parameters that control non-adiabatic transition parameters (such as amplitude A, frequency ω, and signal timing), one can achieve polynomial approximations and increase robustness in quantum circuits. The analogy presented here between QSP and AIM can be useful as a way to directly implement the QSP algorithm on quantum systems and obtain all the benefits from the fast Landau-Zener-Stückelberg-Majotana (LZSM) quantum logic gates.

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall systems, where the interplay of particle interactions and topological effects leads to the emergence of interesting many-body phenomena, such as long-range entanglement and anyonic excitations. These features make such systems of significant interest, especially due to their potential for quantum information technology. The purpose of investigating FCIs in a clean and highly controllable setting motivates efforts toward their realization in quantum simulations. A key difficulty in this context is, on the one hand, how to implement the relevant Hamiltonian through quantum simulation schemes and, on the other hand, how to drive the system towards the correlated FCI ground state. We explore the use of reservoir engineering, as can be realized in superconducting circuits, to stabilize the FCI ground state of the Harper-Hofstadter-Hubbard model. In particular, we consider realizations of the Hamiltonian based on Floquet engineering, as experimentally realized in quantum gas microscopes [1] and superconducting qubits [2]. Additionally, these systems are then coupled to driven leaky cavity modes. It has been shown that these ingredients can be successfully combined to effectively prepare target Floquet states [3]. Here, they are applied to prepare small-scale bosonic Laughlin states. [1] J. Léonard et al., Nature 619, 495-499 (2023) [2] C. Wang et al., Science 384, 579-584 (2024) [3] F. Petiziol, A. Eckardt, Phys. Rev. Lett. 129, 233601

M. Szyszko$^{1}$, T. Woźniak${^1}$, and M. Birowska$^{1}$ $^{1}$University of Warsaw, Faculty of Physics, 00-092 Warsaw, Pasteura 5, Poland Two-dimensional (2D) materials, with their distinctive electronic, optical, and mechanical properties, have significantly influenced semiconductor research. Among these, transition metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS$_2$) and tungsten diselenide (WSe$_2$), exhibit a layer-dependent band structure, strong spin–orbit coupling, excitonic properties and are stable in ambient conditions. Alloying—wherein one transition metal is substituted for another—provides a powerful method to tailor properties such as bandgap energy, carrier effective mass and phase stability. As a result, TMD alloys have gathered attention for next-generation optoelectronic (e.g., photodetectors and light-emitting devices) [1], valleytronics (due to spin–valley coupling)[2], and catalytic applications (such as hydrogen evolution reactions)[3], where fine-tuning electronic and optical properties is critical for device performance. Herein, we present an improved computational workflow for investigating the electronic and structural physical quantities of 2D TMD alloys, with a particular focus on the Mo\(_{1-x}\)W\(_x\)S\(_2\) system. By combining density functional theory (DFT) calculations with symmetry-based reduction of alloy configurations our approach significantly lowers computational overhead while retaining high accuracy. A central feature is the use of symmetry analysis to eliminate equivalent dopant configurations, thus providing comprehensive coverage of dopant distributions without exhaustive enumeration of all combinatorial variants. Applying this methodology to a 3×3 supercell reveals that the doping concentration is the dominant factor in determining key material parameters—most notably the bandgap energy, charge-carrier effective masses and the number of observed optical transition. We observe that the bandgap remains direct at the K point for all alloy compositions, exhibiting a pronounced non-linear dependence on the doping fraction, characterised by a clear bowing effect. In addition, subtle correlations emerge between atomic arrangements, total energy, and bandgap values, as well as between dopant distribution and slight anisotropies in carrier effective masses. Our results reveal that while different arrangements of the dopant atoms for particular alloy concentration display minor variations in their properties, none are significantly more energetically favourable than the others. The approach outlined here provides a systematic and efficient method to explore the composition–property relationships in 2D materials, facilitating the rational design and optimization of next-generation of optoelectronic devices. [1] K. F. Mak and J. Shan, Nature Photonics 10, 216-226 (2016). [2] J. R. Schaibley, et al., Nature Reviews Materials 1, 1–15 (2016). [3] D. Voiry, J. Yang, and M. Chhowalla, Advanced materials 28, 6197–6206 (2016)

A simple parametrized family of quantum systems consisting of two entangled subsystems, dubbed left and right ones, both of them featuring N qubits is considered in the thermofield double formalism. We assume that the system evolves in a purely geometric manner based on the parallel transport condition due to Uhlmann. We explore the different interpretations of this evolution relative to observers either coupled to the left or to the right subsystems. The Uhlmann condition breaks the symmetry between left and right by regarding one of the two possible sets of local unitary operations as gauge degrees of freedom. Then gauging the right side we show that the geometric evolution on the left manifests itself via certain local operations reminiscent of non-unitary filtering measurements. On the other hand on the right the basic evolutionary steps are organized into a sequence of unitary operations of a holonomic quantum computation. We calculate the Uhlmann connection governing the transport for our model which turns out to be related to higher dimensional instantons. Then we evaluate the anholonomy of the connection for geodesic triangles with geodesic segments defined with respect to the Bures metric. By analysing the explicit form of the local filtering measurements showing up on the left side we realize that they are also optimal measurements for distinguishing two given mixed states in the statistical sense. We also point out that by conducting an interference experiment on the right side one can observe the physical effects of the anholonomic quantum computation. We demonstrate this by calculating explicit examples for phase shifts and visibility patterns arising in such interference experiments. Finally a path consisting of geodesic segments producing the iSWAP gate via anholonomy is presented, to demonstrate computational universality.

Understanding how a mobile impurity interacts with a quantum many-body environment is an active area of research in condensed matter physics. A particle immersed in a weakly interacting Bose-Einstein condensate becomes dressed by excitations, forming a polaron. The host system is a quasi one-dimensional bosonic flux ladder, which serves as a minimal model for two-dimensional systems under magnetic flux. The system is described by the Bose-Hubbard Hamiltonian with Peierls substitution and is studied at zero temperature in the thermodynamic limit. It exhibits three phases: Meissner,vortex, and biased ladder, each characterized by distinct current patterns and symmetry-breaking properties. The phase diagram is obtained using mean-field theory and is confirmed numerically by Gross-Pitaevskii evolution. Bogoliubov theory is used to compute the collective excitations of the bath above the condensate, and the corresponding dynamical structure factor is computed in each phase. An impurity is then introduced and treated within the Chevy approximation, a variational truncation of the many-body wavefunction. The polaron spectral function is computed across all three phases. To isolate the role of flux, the spectral function is also computed for the one-dimensional Bose gas on a lattice. In this case, the impurity-boson correlation function is used to identify the nature of the dressed quasi-particles. The spectral functions show clear signatures of the underlying background. These are new results and are testable in cold-atom experiments.