arXiv subjects

Peter Schmelcher

Publications and source records attributed to Peter Schmelcher.

At least 19 recordsLinked to original sources

arXiv2026

Belief Propagation-based Disentanglers for Tensor Network State Preparation

We develop a quantum circuit synthesis method for preparing a class of tensor network states. The scheme applies to states tractable with belief propagation (BP), a tensor network gauging scheme which recently allowed for classical simulations at large scales. The problem is reduced to independent, strictly local, classical variational optimizations: each nearest-neighbor two-qubit "disentangler" gate minimizes the entropy defined on an edge. Disentanglers drive the state to a product state and their Hermitian conjugate prepares the target. Each disentangling layer has depth at most $z+1$ (with $z$ the maximal number of nearest neighbors per site), the optimization has no barren plateaus, and the bond dimension stays bounded. As a demonstration, with only $3$-$5$ disentangling layers we prepare a $102$-qubit tree tensor network encoding a $17$-dimensional normal distribution and the transverse-field Ising model ground states on a $64$- to $127$-qubit heavy-hex lattice with fidelities of order $0.9-0.999$. The method opens new possibilities for quantum applications by transferring classical tensor network states onto hardware.

quant-ph↗

arXiv2026

Spin Textures and Eigenstate Evolution of Isospectrally Patterned Lattices

Isospectrally patterned lattices exhibit a composite band structure with a tunable ratio of localized versus delocalized eigenstates that is controlled by the underlying phase gradient. We show that the lattice Hamiltonian can be interpreted as that of a single spin exposed to a rotating magnetic field which is allowed to hop with a spin-flip across the lattice. In the low- and high-energy part of the band the localized states show an envelope of oscillatory character separated by quasi-nodes. Spin peaks occur at the locations of these quasi-nodes and provide a unique spin texture to the eigenstates which becomes increasingly complex with increasing degree of excitation. The crossover from localization to delocalization and vice versa leaves its fingerprints in the Fourier spectrum of the eigenstates: the original bimodal frequency distribution widens with increasing degree of excitation, moves across the spectral window and finally culminates in an extremely narrow frequency peak. In the course of this evolution the spin texture undergoes a rearrangement transition involving different characteristic (ir)regular patterns which we quantify by considering the total variation of the local spin fluctuations. Our results demonstrate the variety of the spectral properties of isospectrally patterned lattices which holds great prospect in particular when considering higher lattice or cell dimensions.

quant-ph↗

arXiv2026

Charge-Conjugation Violation and Population Asymmetry in Bipartite Fermionic Lattices

Charge conjugation violation (CCV) is a central concept in particle physics and appears also for quasiparticles in quantum many-body systems, which typically relies on an embedded external symmetry breaking to the underlying system. An open question is how an intrinsic CCV mechanism could emerge and what its macroscopic consequences would be. We establish sublattice kinks in bipartite fermionic lattices as a concrete setup showing intrinsic CCV. The intrinsic CCV of the sublattice kink is based on the graph-topological nature of the underlying Hamiltonian, with no explicit symmetry breaking taking place. It leads to a population asymmetry of different configurations and imprints a hidden leaf-like structure in the eigenenergy spectrum. The population asymmetry also leads to an imbalanced sublattice-kink production triggered by the vacuum-instability in the quench dynamics. Our work demonstrates the graph topology as the microscopic origin of intrinsic CCV, with the population asymmetry as the macroscopic consequence, of which the proposed setup is highly amenable to experimental implementation via cold-atom quantum simulators.

cond-mat.quant-gas↗

arXiv2026

Symmetry and integrability in the anyon-Hubbard model

Recent cold atom experiments have realized one-dimensional anyons and enabled the tuning of 1D~statistics between bosons and fermions. Here, we analyze the symmetries, integrability, and resulting degeneracies of the underlying anyon-Hubbard model of finite length. Our results reveal a switching between symmetry classes AI, BDI, and CI in dependence on system size, particle number, and boundary conditions, and show that two anyons with periodic boundaries are integrable, while two anyons with open boundary conditions are not. We include a comprehensive analysis of all model limits, especially of interacting bosons and pseudofermions and resolve spectral signatures. We additionally reveal an exactly solvable doublon state that hides in the continuum of scattering states and the exact solution of the nullspace of two noninteracting anyons. The uncovered symmetries shape the fundamental properties of the one-dimensional anyons at hand, and the predicted states are accessible in state-of-the-art experiments.

cond-mat.quant-gas↗

arXiv2026

A Unified Local Light-shifts Encoding For Solving Optimization Problems on a Rydberg Annealer

Combinatorial optimization problems play a central role in computer science with many real world applications. A number of relevant problems remain computationally difficult to solve as they lie in the NP-hard complexity class. We present a unified framework for solving such optimization problems represented in the quadratic unconstrained binary optimization (QUBO) formalism, namely two-SAT, XOR-SAT, mixed-two-XOR-SAT, set packing, quadratic assignment, binary clustering, and protein folding, by expanding the domain of applications of \textit{PRR, 6(2), 023031}. A direct mapping from the QUBO form of these problems onto the Rydberg quantum platform is demonstrated as our first step. This mapping to the Rydberg system depends on distance-dependent long-range interactions and configurable local detuning, thus reducing resource overhead and improving scalability. Following-up on the encoding, the solution is reached by steering the system toward the ground state of the target Hamiltonian using an optimized quantum annealing protocol that controls the time-dependent detuning and Rabi frequency profiles. The framework can handle a variety of problems, each with different complexity. To quantify the complexity of any problem, a generalized hardness parameter is introduced that compares different problems based on the structure of their optimization landscapes. This is a proceedings contribution to the Athens Workshop in Theoretical Physics: 10th Anniversary, held at the National and Kapodistrian University of Athens on December 17-19 2025.

quant-ph↗

arXiv2026

Phases and dynamics of an impurity immersed in one-dimensional quantum droplets

We explore the ground-state properties of a single impurity immersed in a one-dimensional quantum droplet medium formed by a two-component Bose mixture. Relying on ab-initio simulations, we demonstrate that tuning the impurity-droplet interactions allows to controllably reshape the droplets density profiles and associated correlation patterns. For attractive impurity-medium couplings, the impurity becomes localized within the droplet which exhibits a density hump at the vicinity of the impurity, while repulsive interactions facilitate their phase-separation. Comparing our many-body results to the appropriate extended Gross-Pitaevskii description, we find adequate agreement for the droplet density profiles, with the effective field approach systematically overestimating impurity localization. Following a release of the external trap, we unveil that the sign and magnitude of the interactions between the impurity and the droplet hosts dictate the response of the three-component setting which experiences expansion unless strongly attractive intercomponent couplings are present. These results corroborate the role and presence of correlations in impurity-droplet mixtures and inspire future investigations on impurity physics for probing droplet configurations.

cond-mat.quant-gas↗

arXiv2026

Adaptive Tensor Network Sampling for Quantum Optimal Control

Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly fall into two categories: gradient-based and gradient-free algorithms. The associated optimization landscape is often high-dimensional, non-convex, and populated by numerous local minima, making efficient gradient-free search strategies essential. To address this, we introduce a gradient-free matrix product state/tensor train (MPS/TT) sampling heuristic for discrete quantum optimal control. In our approach, the MPS defines a score function over the space of discrete control parameters, which in turn induces a sampling distribution over candidate control sequences. This distribution is iteratively refined through selection of better performing sequences and local tensor updates to bias the search toward high-performing sequences. We evaluate the method on a range of benchmark problems, including single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer. Across these tasks, the method exhibits stable convergence behavior and competitive empirical performance relative to established gradient-free baselines. These results suggest that tensor network sampling offers a viable heuristic framework for discrete quantum control.

quant-ph↗

arXiv2026

Partial solvability induced by dark states in a box trap with decentered two-body interaction

We consider a generalization of the two-body contact interaction for nonrelativistic particles confined to a one-dimensional box, in which the interaction is decentered, i.e., the particles interact only when they are separated by a distance c. In contrast to the harmonically trapped system, this model is nonintegrable. Despite this, we demonstrate that the system exhibits partial solvability due to the presence of dark states, i.e., bosonic or fermionic states unaffected by the interaction. These states form exactly solvable subspaces embedded within an interacting spectrum. We characterize the stationary properties of the system, identify the conditions for the appearance of dark states, and show how they structure the spectrum and delineate interacting and noninteracting sectors.

quant-ph↗

arXiv2026

Core-Hole Excitation Dynamics of One-Dimensional Ultracold Trapped Fermions

We investigate the nonequilibrium dynamics of core-hole excitations in a one-dimensional fermionic few-body system consisting of a spin-polarized Fermi bath coupled to a single heavy mobile impurity. The bath is initially prepared in a particle-hole configuration by emptying a selected bath single-particle orbital, while the impurity is displaced with respect to the center of the bath confinement potential. The quench dynamics are initialized by suddenly switching on the impurity-bath interaction. To resolve the resulting dynamics, we combine two complementary \textit{ab initio} approaches, namely the Multi-Layer Multi-Configuration Time-Dependent Hartree method for mixtures and a multi-channel Born-Oppenheimer framework. We show that the postquench response is governed by the interaction strength, impurity confinement, mass imbalance, and the location of the initially prepared hole within the Fermi sea. The density evolution and impurity center-of-mass motion reveal a competition between mixing and demixing of impurity and bath, while the von Neumann entropy demonstrates the buildup of pronounced many-body correlations. Most importantly, the occupation dynamics of the initially emptied orbital identifies deep core holes as substantially more robust against refilling than bulk or edge vacancies. Our results establish core-hole excitations as robust dynamical many-body features in trapped ultracold fermions and provide a controlled route towards probing orthogonality response, correlation buildup, and hole refilling in real time.

cond-mat.quant-gas↗

arXiv2026

Recurrence analysis of quantum many-body dynamics

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a nonlinear time-series analysis framework long established for classical dynamical systems - to investigate correlated quantum many-body dynamics. Recurrence plots provide a qualitative fingerprint of simulated or experimental data, while recurrence quantification analysis extracts corresponding numerical descriptors. Applying this framework to quenches from the paramagnetic ground state in the one-dimensional transverse-field Ising model, we observe a clear progression in the recurrence plots of two-site correlations: nearly periodic patterns in the deeply ferromagnetic phase give way to multiscale temporal structures at criticality. Recurrence quantifiers further recover the critical field strength without prior knowledge of the model, establishing recurrence analysis as a versatile tool for characterizing quantum many-body dynamics, including unsupervised detection of quantum phase transitions.

quant-ph↗

arXiv2026

Vibronic quantum dynamics of ultralong-range high-$\ell$ Rydberg molecules

We investigate the non-adiabatic quantum dynamics of ultralong-range Rydberg molecules using a vibronically coupled two-channel treatment. The two-channels are composed of coupled trilobite and butterfly electronic states, formed as a result of $S$-wave and $P$-wave scattering of high angular momentum Rydberg electrons with perturbing ground state atoms. Within the Born-Oppenheimer treatment, the $P$-wave scattering channel introduces an adiabatic decay pathway that affects the stability and lifetimes of trilobite states. Our numerical results show that the vibronic coupling is dependent on the principal quantum number $n$, and for certain $n$ there is non-adiabatic stabilization against internal molecular decay, facilitating previously studied dynamical effects in pure trilobite molecules. Apart from the internal diffraction effect caused by the backscattering of vibrational wavepackets from the trilobite potential, we also observe interesting multi-well tunneling effects during low-energy oscillations for a range of $n$-values. Our work serves to highlight that the unique vibrational coordinate dependent electronic structure of these polar molecules, along with high level densities, promise many exciting dynamical effects.

physics.atom-ph↗

arXiv2026

The helical quantum two-body problem and its wave packet dynamics

We explore the helical quantum two-body problem i.e. two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well which can be seen also by analyzing the individual wells energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multi-well potential landscape. We show that there exists a rich pattern forming transient evolution which depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats and pulsed emission from single well localized wave packets due to their intrawell dynamics.

quant-ph↗

arXiv2026

High-fidelity non-adiabatic dark state gates for neutral atoms

Rydberg blockade gates are the most experimentally mature entangling operations in neutral-atom quantum processors, combining fast gate times with simple control, but their performance degrades at larger interatomic separations and remains sensitive to motional and technical noise. Non-blockade gate schemes, such as dark-state and geometric protocols, offer complementary robustness but typically rely on complex and experimentally demanding control. Here we show that quantum optimal control enables non-blockade gate schemes to be implemented using the experimentally established pulse-shaping techniques developed for blockade-based gates. Focusing on the dark-state gate, we construct non-adiabatic implementations that preserve the intrinsic robustness of adiabatic dark-state protocols while achieving gate times comparable to time-optimal blockade gates using only smooth, experimentally feasible pulses. The resulting gates exhibit enhanced resilience to motional coupling, laser noise, and interaction inhomogeneity, particularly near and beyond the blockade radius. This work establishes a practical route to fast, robust two-qubit gates without increased experimental complexity.

quant-ph↗

arXiv2026

Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits

Preparing arbitrary quantum states requires exponential resources. Matrix Product States (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly rely on heuristic circuits that are deterministic but quickly saturate in accuracy, or on variational optimization methods that reach high fidelities but scale poorly. This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline. Heuristic staircase-like and brick wall disentangler circuits provide warm-start initializations for variational optimization, enabling high-fidelity state preparation for large systems. Target MPSs are either specified as physical quantum states or constructed from classical datasets via amplitude encoding, using step-by-step singular value decompositions or tensor cross interpolation. The framework incorporates entanglement-based qubit reordering, reformulated as a quadratic assignment problem, and low-level optimizations that reduce depths by up to 50% and CNOT counts by 33%. We evaluate the full pipeline on datasets of varying complexity across systems of 19-50 qubits and identify trade-offs between fidelity, gate count, and circuit depth. Optimized brick wall circuits typically achieve the lowest depths, while the optimized staircase-like circuits minimize gate counts. Overall, our results provide principled and scalable protocols for preparing MPSs as quantum circuits, supporting utility-scale applications on near-term quantum devices.

quant-ph↗

arXiv2025

Two-Body Kapitza-Dirac Scattering of One-Dimensional Ultracold Atoms

Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here we develop a numerically-exact two-body description of Kapitza-Dirac scattering for two contact-interacting atoms in a one-dimensional harmonic trap subjected to a pulsed optical lattice, enabling us to obtain the numerically exact dynamics. We map how interaction strength, lattice depth, lattice wavenumber, and pulse duration reshape the diffraction pattern, leading to an interaction-dependent population redistribution in real and momentum-space. By comparing the exact dynamics to an impulsive sudden-approximation description, we delineate the parameter regimes where it remains accurate and those, notably at strong attraction and small lattice wavenumber, where it fails. Our results provide a controlled few-body benchmark for interacting Kapitza-Dirac scattering and quantitative guidance for Kapitza-Dirac-based probes of ultracold atomic systems.

cond-mat.quant-gas↗

arXiv2025

Observation of spin singlet butterfly Rydberg molecules in an ultracold atomic Rb gas

We report the observation of spin-singlet ultra-long range Rydberg butterfly molecules consisting of a ground-state atom bound to a Rydberg atom by $P$-wave scattering of $^{87}$Rb Rydberg electrons from $^{87}$Rb(5s) atoms. A three-photon excitation scheme enables the photoassociation of these molecules by weakly admixing Rb($18f_{7/2}$) states. The measured binding energies, kilo-Debye permanent electric dipole moments, and lifetimes are in excellent agreement with theory. Two long-lived vibrational levels, red detuned from the Rb($18f_{7/2}$) threshold, are observed. This experiment is a foundational step in the production of ultra-cold anions and heavy Rydberg ion-pair systems.

physics.atom-ph↗

arXiv2025

Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm

Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical simulation of quantum circuits is vital not only for validating and benchmarking quantum hardware but also for gaining deeper insights into the behavior of quantum algorithms. A promising framework for classical simulation is provided by tensor networks. Recently, the Density-Matrix Renormalization Group (DMRG) algorithm was developed for simulating quantum circuits using matrix product states (MPS). Although MPS is efficient for representing quantum states with one-dimensional correlation structures, the fixed linear geometry restricts the expressive power of the MPS. In this work, we extend the DMRG algorithm for simulating quantum circuits to tree tensor networks (TTNs). The framework employs a variational compression scheme that optimizes the TTN to approximate the evolved quantum state. To benchmark the method, we simulate random circuits and the quantum approximate optimization algorithm (QAOA) with various two-qubit gate connectivities. For the random circuits, we devise tree-like gate layouts that are suitable for TTN and show that TTN requires less memory than MPS for the simulations. For the QAOA circuits, a naive TTN construction that exploits graph structure significantly improves the simulation fidelities. Our findings show that the DMRG algorithm with TTNs provides a promising framework for simulating quantum circuits, particularly when gate connectivities exhibit clustering or a hierarchical structure.

quant-ph↗

arXiv2025

Qudit-based scalable quantum algorithm for solving the integer programming problem

Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It is a hard problem to solve using classical algorithms, as its complexity increases exponentially with problem size. Most quantum algorithms for solving IP are highly resource inefficient because they encode integers into qubits. In [1], the issue of resource inefficiency was addressed by mapping integer variables to qudits. However, [1] has limited practical value due to a lack of scalability to multiple qudits to encode larger problems. In this work, by extending upon the ideas of [1], a circuit-based scalable quantum algorithm is presented using multiple interacting qudits for which we show a quantum speed-up. The quantum algorithm consists of a distillation function that efficiently separates the feasible from the infeasible regions, a phase-amplitude encoding for the cost function, and a quantum phase estimation coupled with a multi-controlled single-qubit rotation for optimization. We prove that the optimal solution has the maximum probability of being measured in our algorithm. The time complexity for the quantum algorithm is shown to be $O(d^{n/2} + m\cdot n^2\cdot \log{d} + n/ε_{QPE})$ for a problem with the number of variables $n$ taking $d$ integer values, satisfying $m$ constraints with a precision of $ε_{QPE}$. Compared to the classical time complexity of brute force $O(d^n)$ and the best classical exact algorithm $O((\log{n})^{3n})$, it incurs a reduction of $d^{n/2}$ in the time complexity in terms of $n$ for solving a general polynomial IP problem.

quant-ph↗