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Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks., Comment: 10 + 14 pages, 4 + 7 figures

Metastable states arise in a range of quantum systems and can be observed in various dynamical scenarios, including decay, bubble nucleation, and long-lived oscillations. The phenomenology of metastable states has been examined in quantum many-body systems, notably in 1D ferromagnetic Ising spin systems and superfluids. In this paper, we study long-lived oscillations of metastable and ground states in 1D antiferromagnetic neutral atom chains with long-range Rydberg interactions. We use a staggered local detuning field to achieve confinement. Using theoretical and numerical models, we identify novel spectral signatures of quasiparticle oscillations distinct to antiferromagnetic neutral atom systems and interpret them using a classical energy model of short-range meson repulsion. Finally, we evaluate the experimental accessibility of our proposed setup on current neutral-atom platforms and discuss experimental feasibility and constraints., Comment: 15 pages, 5 figures

Metastable states of quantum many-body systems with confinement offer a means to simulate false vacuum phenomenology, including non-equilibrium dynamical processes like decay by nucleation, in truncated limits. Recent work has examined the decay process in 1D ferromagnetic Ising spins and superfluids. In this paper, we study nucleation dynamics in 1D antiferromagnetic neutral atom chains with Rydberg interactions, using both numerical simulations and analytic modeling. We apply a staggered local detuning field to generate the metastable and ground states. Our efforts focus on two dynamical regimes: decay and annealing. In the first, we corroborate the phenomenological decay rate scaling and determine the associated parameter range for the decay process; in the second, we uncover and elucidate a procedure to anneal the metastable state from the initial to the final system, with intermediate nucleation events. We further propose experimental protocols to prepare the required states and perform quenches on near-term neutral atom quantum simulators, examining the experimental feasibility of our proposed setup and parameter regime., Comment: 15 pages, 8 figures

Aquila, an analog quantum simulation platform developed by QuEra Computing, supports control of the position and coherent evolution of up to 256 neutral atoms. This study details novel experimental protocols designed for analog quantum simulators that generate Bell state entanglement far away from the blockade regime, construct a $Z_2$ state with a defect induced by an ancilla, and optimize the driving fields schedule to prepare excited states with enhanced fidelity. We additionally evaluate the effectiveness of readout error mitigation techniques in improving the fidelity of measurement results. All experiments were executed on Aquila from QuEra and facilitated by the AWS Braket interface. Our experimental results closely align with theoretical predictions and numerical simulations. The insights gained from this study showcase Aquila's capabilities in handling complex quantum simulations and computations, and also pave the way for new avenues of research in quantum information processing and physics that employ programmable analog hardware platforms., Comment: 7 pages, 6 figures, IEEE QCE24 - QTEM Best Paper Award - 1st Place

We investigate the physical properties of $G_2$-symmetric integrable chains with local degrees of freedom in the fundamental representation; given the typical connection between integrability and critical points, we test the model's properties against a hypothesis of conformal-invariant long-distance behavior. Leveraging an embedding between the $G_2$ exceptional Lie algebra and $SU(2)$-symmetric chains with local spin-3 representations, we perform numerical analyses via exact diagonalization (ED) targeted at specific spin sectors, as well as via non-Abelian density-matrix renormalization group (DMRG). A basic study of the momentum-resolved ED spectrum suggests the low-energy system is effectively described by a $(G_2)_1$ Wess--Zumino--Witten (WZW) theory, but we find challenges in further numerical characterization of conformal data. The study and control of the phenomenology of this model may have implications for the development of accessible models for Fibonacci anyons., Comment: 13 pages, 5 figures

Architectures for quantum computing based on neutral atoms have risen to prominence as candidates for both near and long-term applications. These devices are particularly well suited to solve independent set problems, as the combinatorial constraints can be naturally encoded in the low-energy Hilbert space due to the Rydberg blockade mechanism. Here, we approach this connection with a focus on a particular device architecture and explore the ubiquity and utility of independent set problems by providing examples of real-world applications. After a pedagogical introduction of basic graph theory concepts of relevance, we briefly discuss how to encode independent set problems in Rydberg Hamiltonians. We then outline the major classes of independent set problems and include associated example applications with industry and social relevance. We determine a wide range of sectors that could benefit from efficient solutions of independent set problems -- from telecommunications and logistics to finance and strategic planning -- and display some general strategies for efficient problem encoding and implementation on neutral-atom platforms., Comment: 30 pages, 10 example applications

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity-spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the inter-impurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.

It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $\mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is highly unexpected for a spin-2 system and, as we argue, would imply an unconventional mechanism for symmetry emergence. Yet, the absence of convenient critical points for renormalization group perturbative expansions, allied with the usual difficulty in the convergence of numerical methods in critical or small-gapped phases, renders the verification of this hypothetical SU$(3)$-symmetric phase a non-trivial matter. By tracing parallels with the well-understood phase diagram of spin-1 chains and searching for signatures robust against finite-size effects, we draw criticism on the existence of this phase. We perform non-Abelian density matrix renormalization group studies of multipolar static correlation function, energy spectrum scaling, single-mode approximation, and entanglement spectrum to shed light on the problem. We determine that the hypothetical SU$(3)$ spin-2 phase is, in fact, dominated by ferro-octupolar correlations and also observe a lack of Luttinger-liquid-like behavior in correlation functions that suggests that is perhaps not critical. We further construct an infinite family of spin-$S$ systems with similar ferro-octupolar-dominated quasi-SU$(3)$-like phenomenology; curiously, we note that the spin-3 version of the problem is located in a subspace of exact G$_2$ symmetry, making this a point of interest for search of Fibonacci topological properties in magnetic systems., Comment: 13 pages, 9 figures

Amplifiers based on Josephson junctions allow for a fast and noninvasive readout of superconducting qubits. Motivated by the ongoing progress toward the realization of fault-tolerant qubits based on Majorana bound states, we investigate the topological counterpart of the Josephson bifurcation amplifier. We predict that the bifurcation dynamics of a topological Josephson junction driven in the appropriate parameter regime may be used as an additional tool to detect the emergence of Majorana bound states., Comment: 16 pages, 11 figures

Fractionalized quasiparticles - anyons - bear a special role in present-day physics. At the same time, they display properties of interest both foundational, with quantum numbers that transcend the spin-statistics laws, and applied, providing a cornerstone for decoherence-free quantum computation. The development of platforms for realization and manipulation of these objects, however, remains a challenge. Typically these entail the zero-temperature ground-state of incompressible, gapped fluids. Here, we establish a strikingly different approach: the development and probing of anyon physics in a gapless fluid. The platform of choice is a chiral, multichannel, multi-impurity realization of the Kondo effect. We discuss how, in the proper limit, anyons appear at magnetic impurities, protected by an asymptotic decoupling from the fluid and by the emerging Kondo length scale. We discuss possible experimental realization schemes using integer quantum Hall edges. The gapless and charged degrees of freedom coexistent with the anyons suggest the possibility of extracting quantum information data by transport and simple correlation functions. To show that this is the case, we generalize the fusion ansatz of Cardy's boundary conformal field theory, now in the presence of multiple localized perturbations. The generalized fusion ansatz captures the idea that multiple impurities share quantum information non-locally, in a way formally identical to anyonic zero modes. We display several examples supporting and illustrating this generalization and the extraction of quantum information data out of two-point correlation functions. With the recent advances in mesoscopic realizations of multichannel Kondo devices, our results imply that exotic anyon physics may be closer to reach than presently imagined., Comment: 19 pages, 5 figures

We revisit the importance of collective-mode fluctuations and gauge invariance in the electromagnetic response of superconducting systems. In particular, we show that order-parameter fluctuations, gapless or not, have no contribution to the Meissner effect in both $s$- and $p$-wave superconductors. More generally, we extend this result to uniform and nonuniform superfluids with no external wavevector scale. To facilitate this analysis, we formulate a path-integral-based matrix methodology for computing the electromagnetic response of fermionic fluids in the presence of concomitantly fluctuating collective modes. Closed-form expressions for the electromagnetic response in different scenarios are provided, including the case of fluctuations of electronic density and the phase and amplitude of the order parameter. All microscopic symmetries and invariances are manifestly satisfied in our formalism, and it can be straightforwardly extended to other scenarios.

In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, there exist two types of vortices which are distinct by the presence or absence of zero energy states in their core. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. Weak Zeeman fields are found to suppress the intra-orbital spin-singlet pairing, known to localize the states at the ends of the vortices on the surface. On the other hand, an orbital-triplet pairing is shown to be stable against Zeeman interactions, but leads to delocalized zero-energy Majorana modes which extend through the vortex. In contrast, the finite-energy vortex modes remain localized at the vortex ends even when the pairing is of orbital-triplet form. Phenomenologically, this manifests as an observed disappearance of zero-bias peaks within the cores of topological vortices upon increase of the applied magnetic field. The presence of magnetic impurities in FeTe$_{(1-x)}$Se$_x$, which are attracted to the vortices, would lead to such Zeeman-induced delocalization of Majorana modes in a fraction of vortices that capture a large enough number of magnetic impurities. Our results provide an explanation to the dichotomy between topological and non-topological vortices recently observed in FeTe$_{(1-x)}$Se$_x$., Comment: 16 pages including the supplementary materials. 4 figures

Through a theoretical coupled wire model, we construct strongly correlated electronic \emph{integer} quantum Hall states. As a distinguishing feature, these states support electric and thermal Hall transport violating the Wiedemann-Franz law as $\left(\kappa_{xy}/\sigma_{xy}\right)/\left[\left(\pi^{2}k_{B}^{2}T\right)/3e^{2}\right]<1$.We propose a new Abelian incompressible fluid at filling $\nu=16$ that supports a bosonic chiral $(E_{8})_{1}$ conformal field theory at the edge and is intimately related to topological paramagnets in (3+1)D. We further show that this topological phase can be partitioned into two non-Abelian quantum Hall states at filling $\nu=8$, each carrying bosonic chiral $(G_{2})_{1}$ or $(F_{4})_{1}$ edge theories, and hosting Fibonacci anyonic excitations in the bulk. Finally, we discover a new notion of particle-hole conjugation based on the $E_{8}$ state that relates the $G_{2}$ and $F_{4}$ Fibonacci states., Comment: 12 pages. 3 figures

Weyl semimetals display unusual electronic transport properties when placed under magnetic fields. Here, we investigate how magnetic fields alter the dynamics of long wavelength lattice vibrations in these materials. To that end, we develop a theory for the phonon dispersion, which incorporates contributions from chiral and nonchiral Landau levels, electron-phonon interactions, electron-electron interactions, and disorder. We predict (i) a magnetic-field-induced hybridization between optical phonons and plasmons, (ii) avoided crossings between pseudoscalar optical phonons and electronic excitations originating from nonchiral Landau levels, (iii) a sharp dependence of the sound velocity on the relative angle between the sound propagation and the magnetic field. We compare our results to recent theoretical studies on the signatures of the chiral anomaly in phonon dynamics., Comment: 12 pages plus appendices, 7 figures. Published version

We present a many-body exact diagonalization study of the $\mathbb{Z}_2$ and $\mathbb{Z}_4$ Josephson effects in circuit quantum electrodynamics architectures. Numerical simulations are conducted on Kitaev chain Josephson junctions hosting nearest-neighbor Coulomb interactions. The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements., Comment: 16 pages, 11 figures

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems., Comment: 26 pages, 12 figures

Strongly disordered spin chains invariant under the SO(N) group are shown to display random-singlet phases with emergent SU(N) symmetry without fine tuning. The phases with emergent SU(N) symmetry are of two kinds: one has a ground state formed of randomly distributed singlets of strongly bound pairs of SO(N) spins (a `mesonic' phase), while the other has a ground state composed of singlets made out of strongly bound integer multiples of N SO(N) spins (a `baryonic' phase). The established mechanism is general and we put forward the cases of $\mathrm{N}=2,3,4$ and $6$ as prime candidates for experimental realizations in material compounds and cold-atoms systems. We display universal temperature scaling and critical exponents for susceptibilities distinguishing these phases and characterizing the enlarging of the microscopic symmetries at low energies., Comment: 5 pages, 2 figures, Contribution to the Topical Issue "Recent Advances in the Theory of Disordered Systems", edited by Ferenc Igl\'oi and Heiko Rieger

We demonstrate a topological classification of vortices in three dimensional time-reversal invariant topological superconductors based on superconducting Dirac semimetals with an s-wave superconducting order parameter by means of a pair of numbers $(N_\Phi,N)$, accounting how many units $N_\Phi$ of magnetic fluxes $hc/4e$ and how many $N$ chiral Majorana modes the vortex carries. From these quantities, we introduce a topological invariant which further classifies the properties of such vortices under linking processes. While such processes are known to be related to instanton processes in a field theoretic description, we demonstrate here that they are, in fact, also equivalent to the fractional Josephson effect on junctions based at the edges of quantum spin Hall systems. This allows one to consider microscopically the effects of interactions in the linking problem. We therefore demonstrate that associated to links between vortices, one has the exchange of quasi-particles, either Majorana zero-modes or $e/2$ quasi-particles, which allows for a topological classification of vortices in these systems, seen to be $\mathbb{Z}_8$ classified. While $N_\Phi$ and $N$ are shown to be both even or odd in the weakly-interacting limit, in the strongly interacting scenario one loosens this constraint. In this case, one may have further fractionalization possibilities for the vortices, whose excitations are described by $SO(3)_3$-like conformal field theories with quasi-particle exchanges of more exotic types., Comment: 25 pages, 9 figures

Discovered in high-energy physics, the chiral anomaly has recently made way to materials science by virtue of Weyl semimetals (WSM). Thus far, the main efforts to probe the chiral anomaly in WSM have concentrated on electronic phenomena. Here, we show that the chiral anomaly can have a large impact in the $A_1$ phonons of enantiomorphic WSM. In these materials, the chiral anomaly produces an unusual magnetic-field-induced resonance in the effective phonon charge, which in turn leads to anomalies in the phonon dispersion, optical reflectivity, and the Raman scattering., Comment: 5 pages, 1 figure

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for defining quantum pumps, demonstrating that, as opposed to the conventional two-dimensional case, pumped quantities depend not only on the initial and final points of Hamiltonian evolution but also on the class of the chosen path and preserved symmetries. As such, we distinguish the scenarios of closed/open paths of Hamiltonian evolution, finding that different closed cycles can lead to the pumping of different quantum numbers, and that different open paths may point to distinct scenarios for surface physics. As explicit examples, we consider models similar to simple models used to describe topological insulators, but with doubled degrees of freedom compared to a minimal topological insulator model. The extra fermionic flavors from doubling allow for extra gapping terms/adiabatic parameters - besides the usual topological mass which preserves the topology-protecting discrete symmetries - generating an enlarged adiabatic parameter-space. We consider cases in one and three \emph{spatial} dimensions, and our results in three dimensions may be realized in the context of crystalline topological insulators, as we briefly discuss., Comment: 21 pages, 7 Figures

We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the RG to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. I.e., if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA does not faithfully reproduce the exact ground state at all length scales., Comment: 24 pages, many figures

Motivated by an apparent paradox in [X L. Qi, E.Witten, S-C. Zhang, Phys. Rev. B 87 134519 (2013)] we use the method of gauged Wess-Zumino-Witten functionals to construct an effective action for a Weyl fermion whose Majorana mass arises from coupling to a charged condensate. We obtain expressions for the current induced by an external gauge field and observe that the topological part of the current is only one-third of that that might have been expected from the gauge anomaly. The anomaly is not changed by the induced mass gap however. The topological current is supplemented by a conventional supercurrent that supplies the remaining two-thirds of the anomaly once the equation of motion for the Goldstone mode is satisfied. We apply our formula for the current to resolve the apparent paradox, and also to the chiral magnetic effect (CME) where it predicts a reduction of the CME current to one third of its value for a free Weyl gas in thermal equilibrium. We attribute this reduction to a partial cancelation of the CME by a chiral vortical effect (CVE) current arising from the persistent rotation of the fluid induced by the external magnetic field., Comment: 29 pages, no figures. Revised version has three new references

We analyze the problem of electronic transmission through different regions of a graphene sheet that are characterized by different types of connections between the Dirac points. These valley symmetry breaking Hamiltonians might arise from electronic self-interaction mediated by the dielectric environment of distinct parts of the substrate on which the graphene sheet is placed. We show that it is possible to have situations in which we can use these regions to select or filter states of one desired chirality., Comment: Final version of work published in PRB in 2011

In this letter we show that the zero-point motion of the vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level and the corresponding effects manifest in the density of states at energies which are of the order of the fluctuations frequency. This frequency might be much larger than the electronic energy gap in the spectrum generated by a stationary vortex. As a result the quantum zero-point motion can move the spectral signature of the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. Moreover, the phenomena studied in this letter present novel effects of Magnus force on the vortex spectrum which are not present in the ordinary s-wave superconductors. Our results show that quantum zero point fluctuations can bring the fingerprints of topological phase transitions to more experimentally accessible grounds and point to the importance of study of quantum fluctuations in different candidates for realizing topological phase transitions., Comment: 11 pages (including the supplementary materials), 3 figures

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU(2)_2$ Kac-Moody current running along the defect line. The $SU(2)_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-anti-hedgehog pairs., Comment: 7 pages, 3 figures

Thermodynamic measurements of magnetic fluxes and I-V characteristics in SQUIDs offer promising paths to the characterization of topological superconducting phases. We consider the problem of macroscopic quantum tunneling in an rf-SQUID in a topological superconducting phase. We show that the topological order shifts the tunneling rates and quantum levels, both in the parity conserving and fluctuating cases. The latter case is argued to actually enhance the signatures in the slowly fluctuating limit, which is expected to take place in the quantum regime of the circuit. In view of recent advances, we also discuss how our results affect a $\pi$-junction loop., Comment: 10 pages, 11 figures