arXiv subjects

Peter Schmelcher

Publications and source records attributed to Peter Schmelcher.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2025

Computational Study of the Spectral Behaviour of Different Isospectrally Patterned Lattices

We perform a computational spectral analysis of different isospectrally patterned lattices (IPL). Having been introduced very recently, the lattice Hamiltonian of IPL consist of coupled cells which possess all the same set of eigenvalues. The latter is achieved in a controllable manner by parametrizing the cells via the phases of the involved orthogonal (or unitary) transformations. This opens the doorway of systematically designing lattice Hamiltonians with unique properties by choosing correspondingly varying phases across the lattice. Here we focus on two-dimensional cells and explore symmetric as well as asymmetric IPL w.r.t. a given center. A tunable fraction of localized vs. delocalized eigenstates belonging to the three subdomains of the corresponding energy bands is demonstrated and analyzed with different measures of localization. In the asymmetric case the center of localization can be shifted arbitrarily by shifting the underlying phase grid. Introducing a complete phase revolution leads for low and high energies to two well-separated branches of localized states which finally merge with increasing energy into the branch of delocalized states. Remarkably, the localized states appear in near-degenerate pairs and this near-degeneracy is lifted upon entering the delocalization regime. A corresponding generalization to several phase revolutions is provided showing a characteristic nodal pattern among the near-degenerate eigenstates.

quant-ph↗

arXiv2025

Dynamical probe of the pseudo Jahn-Teller effect in one-dimensional confined fermions

We investigate the real-time dynamics of a quenched quantum impurity immersed in a one-dimensional ultracold Fermi gas, focusing on the breakdown of the adiabatic Born-Oppenheimer approximation due to non-adiabatic effects. Despite a sizable impurity-bath mass imbalance, increasing interactions induce strong non-adiabatic couplings, disrupting adiabatic motion and enabling population transfer between the adiabatic potential energy curves. These transitions are governed by conical intersections arising from the pseudo Jahn-Teller effect, dynamically shaping the impurity's motion through the bath. Using ab initio simulations via the Multi-Layer Multi-Configuration Time-Dependent Hartree method and a multi-channel Born-Oppenheimer framework, we track the impurity's evolution and directly prove the dynamical manifestation of the pseudo Jahn-Teller effect. We analyze two key scenarios: (i) a small initial shift, where a single avoided crossing drives transitions, and (ii) a large shift, where multiple avoided crossings lead to enhanced non-adiabaticity, self-trapping, and energy redistribution. Our findings establish ultracold fermionic few-body systems as tunable platforms for studying non-adiabatic quantum dynamics, opening new avenues for controlled impurity transport in strongly correlated environments.

cond-mat.quant-gas↗

arXiv2025

Vibrationally highly excited trilobite molecules stabilized by non-adiabatic coupling

We report on the observation of highly excited ($ν\sim 100)$ vibrational states of a trilobite ultralong-range Rydberg molecule in $^{87}$Rb. These states manifest spectroscopically in a regularly spaced series of peaks red-detuned from the $25f_{7/2}$ dissociation threshold. The existence and observed stability of these states requires the almost complete suppression of the adiabatic decay pathway induced by the $P$-wave shape resonance of Rb. This stabilization is predicted to occur only for certain Rydberg levels where the avoided crossing between trilobite and $P$-wave dominated butterfly potential energy curves nearly vanishes, allowing the vibrational states to diabatically traverse the crossing with almost unit probability. This is the first direct measurement of beyond-Born-Oppenheimer physics in long-range Rydberg molecules, and paves the way for future experiments to access and manipulate wavepackets formed from high-lying vibrational states.

physics.atom-ph↗

arXiv2025

High precision spectroscopy of trilobite Rydberg molecules

We perform three-photon photoassociation to obtain high resolution spectra of $^{87}$Rb trilobite dimers for the principal quantum numbers $n = 22,24,25,26$, and $27$. The large binding energy of the molecules in combination with a relative spectroscopic resolution of $10^{-4}$ provides a rigorous benchmark for existing theoretical models. A recently developed Green's function framework, which circumvents the convergence issues that afflicted previous studies,, is employed to theoretically reproduce the vibrational spectrum of the molecule with high accuracy. The relatively large molecular binding energy are primarily determined by the low energy $S$-wave electron-atom scattering length, thereby allowing us to extract the $^3S_1$ scattering phase shift with unprecedented accuracy, at low energy regimes inaccessible to free electrons.

physics.atom-ph↗

arXiv2025

Isospectrally Patterned Lattices

We introduce and explore patterned lattices consisting of coupled isospectral cells that vary across the lattice. The isospectrality of the cells is encapsulated in the phase that characterizes each cell and can be designed at will such that the lattice exhibits a certain phase gradient. Focusing on the specific example of a constant phase gradient on a given finite phase interval we show that the resulting band structure consists of three distinct energy domains with two crossover edges marking the transition from single center localized to delocalized states and vice versa. The characteristic localization length emerges due to a competition of the involved phase gradient on basis of a local rotation and the coupling between the cells which allows us to illuminate the underlying localization mechanism and its evolution. The fraction of localized versus delocalized eigenstates can be tuned by changing the phase gradient between the cells of the lattice. We outline the perspectives of investigation of this novel class of isospectrally patterned lattices.

quant-ph↗

arXiv2025

Ab-Initio Approach to Many-Body Quantum Spin Dynamics

A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison with the discrete truncated Wigner approximation (DTWA) highlights that ML-MCTDH is particularly well-suited for handling anisotropic models and provides more reliable results for two-point observables across all tested cases. The behavior of the corresponding entanglement dynamics is analyzed to reveal the complexity of the quantum states. Our findings indicate that the rate of entanglement growth strongly depends on the interaction range and the presence of disorder. This particular relationship is then used to examine the convergence behavior of ML-MCTDH. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.

quant-ph↗

arXiv2025

State Transfer in Latent-Symmetric Networks

The transport of quantum states is a crucial aspect of information processing systems, facilitating operations such as quantum key distribution and inter-component communication within quantum computers. Most quantum networks rely on symmetries to achieve an efficient state transfer. A straightforward way to design such networks is to use spatial symmetries, which severely limits the design space. Our work takes a novel approach to designing photonic networks that do not exhibit any conventional spatial symmetries, yet nevertheless support an efficient transfer of quantum states. Paradoxically, while a perfect transfer efficiency is technically unattainable in these networks, a fidelity arbitrarily close to unity is always reached within a finite time of evolution. Key to this approach are so-called latent, or 'hidden', symmetries, which are embodied in the spectral properties of the network. Latent symmetries substantially expand the design space of quantum networks and hold significant potential for applications in quantum cryptography and secure state transfer. We experimentally realize such a nine-site latent-symmetric network and successfully observe state transfer between two sites with a measured fidelity of 75%. Furthermore, by launching a two-photon state, we show that quantum interference is preserved by the network. This demonstrates that the latent symmetries enable efficient quantum state transfer, while offering greater flexibility in designing quantum networks.

quant-ph↗

arXiv2024

Internal diffraction dynamics of trilobite molecules

Trilobite molecules are ultralong-range Rydberg molecules formed when a high angular momentum Rydberg electron scatters off of a ground-state atom. Their unique electronic structure and highly oscillatory potential energy curves support a rich variety of dynamical effects yet to be explored. We analyze the vibrational motion of these molecules using a framework of adiabatic wavepacket propagation dynamics and observe that for appropriate initial states, the trilobite potential acts as molecular diffraction grating. The quantum dynamic effects observed are explained using a Fourier analysis of the scattering potential and the associated scattered wavepacket. Furthermore, vibrational ground-states of the low angular momentum ultralong-range Rydberg molecules are found to be particularly suitable to prepare the relevant wavepackets. Hence, we propose a time resolved pump-probe scheme designed for the realization of the effect in question, and advertise the utilization of a single diatomic Rydberg molecule as a testbed for the study of exaggerated quantum dynamical phenomena.

physics.atom-ph↗

arXiv2024

Solving The Travelling Salesman Problem Using A Single Qubit

The travelling salesman problem (TSP) is a popular NP-hard-combinatorial optimization problem that requires finding the optimal way for a salesman to travel through different cities once and return to the initial city. The existing methods of solving TSPs on quantum systems are either gate-based or binary variable-based encoding. Both approaches are resource-expensive in terms of the number of qubits while performing worse compared to existing classical algorithms even for small-size problems. We present an algorithm that solves an arbitrary TSP using a single qubit by invoking the principle of quantum parallelism. The cities are represented as quantum states on the Bloch sphere while the preparation of superposition states allows us to traverse multiple paths at once. The underlying framework of our algorithm is a quantum version of the classical Brachistochrone approach. Optimal control methods are employed to create a selective superposition of the quantum states to find the shortest route of a given TSP. The numerical simulations solve a sample of four to nine cities for which exact solutions are obtained. The algorithm can be implemented on any quantum platform capable of efficiently rotating a qubit and allowing state tomography measurements. For the TSP problem sizes considered in this work, our algorithm is more resource-efficient and accurate than existing quantum algorithms with the potential for scalability. A potential speed-up of polynomial time over classical algorithms is discussed.

quant-ph↗

arXiv2024

Classical scattering and fragmentation of clusters of ions in helical confinement

We explore the scattering dynamics of classical Coulomb-interacting clusters of ions confined to a helical geometry. Ion clusters of equally charged particles constrained to a helix can form many-body bound states, i.e. they exhibit stable motion of Coulomb-interacting identical ions. We analyze the scattering and fragmentation behavior of two ion clusters, thereby understanding the rich phenomenology of their dynamics. The scattering dynamics is complex in the sense that it exhibits cascades of decay processes involving strongly varying cluster sizes. These processes are governed by the internal energy flow and the underlying oscillatory many-body potential. We specifically focus on the impact of the collision energy on the dynamics of individual ions during and immediately after the collision of two clusters, and on the internal dynamics of ion clusters that are excited during a cluster collision.

physics.class-ph↗

arXiv2024

Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks

Quadratic Unconstrained Binary Optimization (QUBO) sits at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others. These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard. To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 seconds on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer by 72% on 200-variable random QUBO problems within a 100-second computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum-classical encoder-decoder (QCED) optimizer, aiming to further enhance the performance of FNNs in QUBO optimization.

quant-ph↗

arXiv2024

Integer Programming Using A Single Atom

Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form through the use of binary variables, which is an indirect and resource-consuming way of solving it. We develop an algorithm that maps and solves an IP problem in its original form to any quantum system possessing a large number of accessible internal degrees of freedom that are controlled with sufficient accuracy. This work leverages the principle of superposition to solve the optimization problem. Using a single Rydberg atom as an example, we associate the integer values to electronic states belonging to different manifolds and implement a selective superposition of different states to solve the full IP problem. The optimal solution is found within a few microseconds for prototypical IP problems with up to eight variables and four constraints. This also includes non-linear IP problems, which are usually harder to solve with classical algorithms when compared to their linear counterparts. Our algorithm for solving IP is benchmarked by a well-known classical algorithm (branch and bound) in terms of the number of steps needed for convergence to the solution. This approach carries the potential to improve the solutions obtained for larger-size problems using hybrid quantum-classical algorithms.

quant-ph↗

arXiv2024

Metastable doubly-charged Rydberg molecules

H$_3^{2+}$ is a one-electron system with three positive nuclei and is known to be unstable in its electronic ground-state. We examine an analogous one-electron system composed of a $^{87}$Rb Rydberg atom interacting with a pair of cations and predict the existence of metastable vibrationally-bound states of $^{87}$Rb$_3^{2+}$. These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favourable scaling of the Rydberg atom's quadrupole moment with the principal quantum number $n$. Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of $^{87}$Rb$_3^{2+}$ arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to $n$. We do not expect these states to exist below $n=24$ and for $n \leq 35$, their lifetime is limited by tunnelling of the Rydberg electron. In contrast, at very large $n$ the lifetime will be limited by tunnelling of the vibrational wavepacket. In between these limits, we expect a range of bound states at intermediate $n$ for which both tunnelling rates are smaller than the radiative decay rate of the Rydberg state.

physics.atom-ph↗

arXiv2024

Formation of Rydberg Crystals Induced by Quantum Melting in One-Dimension

Quantum fluctuations in frustrated systems can lead to the emergence of complex many-body phases. However, the role of quantum fluctuations in frustration-free lattices is less explored and could provide an interesting avenue for exploring new physics, and perhaps easier to realize compared to frustrated lattice systems. Using Rydberg atoms with tunable interactions as a platform, we leverage strong van der Waals interactions and obtain a constrained model in one dimension with non-local fluctuations given by dipolar interactions alongside local fluctuations. The combined effect of such processes leads to intrinsically quantum-ordered Rydberg crystals through the order-by-disorder mechanism. Finite-size analyses indicate that combined fluctuations drive the transition from disordered to ordered phases, contrary to the expected direction. We provide a theoretical description to understand the physics of order-by-disorder in one-dimensional systems, which are typically seen only in higher dimensions.

cond-mat.quant-gas↗

arXiv2024

Bond-Order Density Wave Phases in Dimerized Extended Bose-Hubbard Models

The Bose-Hubbard model (BHM) has been widely explored to develop a profound understanding of the strongly correlated behavior of interacting bosons. Quantum simulators not only allow the exploration of the BHM but also extend it to models with interesting phenomena such as gapped phases with multiple orders and topological phases. In this work, an extended Bose-Hubbard model involving a dimerized one-dimensional model of long-range interacting hard-core bosons is studied. Bond-order density wave phases (BODW) are characterized in terms of their symmetry breaking and topological properties. At certain fillings, interactions combined with dimerized hoppings give rise to an emergent symmetry-breaking leading to BODW phases, which differs from the case of non-interacting models that require an explicit breaking of the symmetry. Specifically, the BODW phase at filling $ρ=1/3$ possesses no analogue in the non-interacting model in terms of its symmetry-breaking properties and the unit cell structure. Upon changing the dimerization pattern, the system realizes topologically trivial BODW phases. At filling $ρ=1/4$, on-site density modulations are shown to stabilize the topological BODW phase. Our work provides the bridge between interacting and non-interacting BODW phases and highlights the significance of long-range interactions in a dimerized lattice by showing unique BODW phases that do not exist in the non-interacting model.

cond-mat.quant-gas↗

arXiv2024

Flipping electric dipole in the vibrational wave packet dynamics of carbon monoxide

Recently Rydberg atom-ion bound states have been observed using a high resolution ion microscope (Nature 605, 453 (2022)) and the corresponding vibrational dynamics has been spectroscopically analyzed. The atom-ion bond is created by an avoided crossing, which involves a flipping molecular dipole. Motivated by the discovery of this binding mechanism we address here the question whether a similar behavior can also occur for ground state diatomic molecules. Specifically, we investigate the vibrational wave packet dynamics within the $^1Σ^+_g$ electronic ground-state of carbon monoxide (CO), which shows a zero crossing of its dipole moment function close to its equilibrium. Via time-evolution of coherent states we demonstrate that indeed a flipping dipole is obtained and its dynamics can be controlled to some extent. Varying the coherent state parameter we explore different regions of the vibrational excitation spectrum thereby tuning the time scales of the rapid oscillatory motion of the relevant observables, their decay and revivals as well as the transition to a regime of irregular dynamics.

physics.atom-ph↗

arXiv2024

Active adaptolates: motility-induced percolating structures with an adaptive packing geometry

It is well known that periodic potentials can be used to induce freezing and melting in colloids. Here, we transfer this concept to active systems and find the emergence of a so-far unknown active matter phase in between the frozen solid-like phase and the molten phase. This phase of "active adaptolates" adopts the geometry of the underlying lattice like the frozen phase, maintains ballistic dynamics like the molten phase, and percolates. In particular, this finding creates a route to use external fields for designing the intrinsic structure of active systems without qualitatively affecting their dynamics.

cond-mat.soft↗