Papers

We study the impact of a minimal length, implied by generalized uncertainty principles and quantum gravity models, on unbounded (scattering) trajectories in the Kepler problem. The analysis is based on the precession of the Hamilton vector, which serves as a sensitive probe of orbital perturbations. Within the framework of the deformed Heisenberg algebra, we derive the correction to the trajectory arising from minimal length effects. It is shown that these quantum-gravitational corrections lead to a reduction in the scattering angle. In particular, for massless particles such as photons, the quantization of space results in a weakening of the gravitational lensing effect. Using available experimental data from the observation of the Einstein ring, we estimate the deformation parameter and the corresponding minimal length for the electron and Mercury. These findings highlight potential observational signatures of minimal length scenarios in high-energy astrophysics and gravitational optics.

The strategic demand for quantum hardware currently outpaces the availability of near-term devices, necessitating high-performance software emulators to validate novel protocols. We introduce Hyperion, a massively parallel, GPU-accelerated quantum emulator architected to bypass the classical memory walls inherent in strongly correlated quantum chemistry simulations. Hyperion leverages custom-optimized Sparse Matrix-Sparse Vector (SpMspV) kernels to natively accelerate exact matrix-vector multiplications, enabling strictly accurate State-Vector (SV) ADAPT-VQE simulations for up to 32 qubits on multi-node platforms. To scale beyond this hardware limit, we address the trade-off in pure Matrix Product State (MPS) emulators, where standard compression yields severe truncation errors and strict compression triggers intractable tensor rank explosions. We propose a novel partitioned emulation, namely the SV-MPS strategy: by routing non-interacting terms into an exact sparse SV core and delegating interacting terms to the MPS engine, this approach achieves emulation of 36 to 40 qubits with controlled approximations. This partitioning significantly reduces GPU resource requirements while maintaining robust accuracy across ADAPT-VQE iterations. Ultimately, Hyperion offers a high-fidelity platform dedicated to the development of new quantum algorithms for chemistry, enabling the modeling of realistic chemical systems at accuracies approaching the exact Full Configuration Interaction (FCI) / Complete Basis Set (CBS) limit.

We introduce a variational method for simulating the dynamics of interacting open quantum spin systems. The method is based on the spin phase-space representation and variationally targets the Husimi-$Q$ function with an ansatz based on a multi-dimensional mixture of spin-coherent states. Crucially, the mixture coefficients are allowed to take negative values, enabling the faithful capture of quantum correlations beyond semiclassical descriptions. The resulting equations of motion are derived from the Dirac-Frenkel variational principle and can be evaluated efficiently without resorting to Monte Carlo sampling by exploiting the analytical structure of the ansatz. As a first application, we demonstrate that this approach accurately captures both the full quantum dynamics and the non-equilibrium steady states of the transverse-field quantum Ising model, in excellent agreement with exact diagonalization. Furthermore, we show that the method scales efficiently to large two-dimensional lattices, a regime that remains challenging for other techniques.

We investigate entanglement in and out of equilibrium in a one-dimensional Bose gas in its low-energy Bogoliubov regime. In this Gaussian setting, the state is fully characterized by its covariance matrix, which allows us to detect and quantify entanglement using a covariance-based framework and associated entanglement monotones. For thermal states, we determine the optimal entanglement witness arising from the covariance matrix criterion and show that it has a remarkably simple mode-resolved structure: it is diagonal in the normal-mode basis and admits a simple analytic form that can be expressed as a product of only two normal-mode uncertainties. We then study out-of-equilibrium dynamics induced by unitary compression and show that entanglement can be generated even from initially separable thermal states. When the evolution is fully adiabatic, the optimal witness retains the same two-mode structure as in the thermal case. Departing from this regime, i.e., performing increasingly rapid compression, the optimal witness becomes genuinely more intricate. Our methods and results provide a unified and physically intuitive picture of how entanglement emerges and evolves in 1D quantum Bose gases, and identify an optimal witness structure relevant more broadly to the analysis of entanglement in quadratic bosonic models and its role in thermodynamic cycles.

We propose a novel superconducting quantum circuit that should be robust against both relaxation and dephasing over a wide and experimentally accessible parameter range. The circuit consists of a parallel arrangement of a large inductance, a small capacitor, and a well-transmitting Josephson weak link. Protection against relaxation arises from the hybridization between the fermionic degree of freedom associated with Andreev levels in the weak link and the bosonic electromagnetic mode of the LC circuit, hence its name: FerBo. Furthermore, as in the fluxonium qubit, delocalization of the wavefunctions in phase space provides resilience against dephasing.

We study non-equilibrium quantum dynamics by performing principal component analysis on the data sets of wavefunction snapshots. We show that a specific transformation of the data sets maximizes the information content in the largest principal component and further enables its connection to certain observables. This connection enables us to explain the dynamical features revealed by such a dimensionality-reduction scheme. We demonstrate this using quantum dynamics of the Heisenberg spin chain, starting from different initial states, and further extend the approach to extract higher-order correlations. Our framework should also be applicable to other unsupervised machine-learning methods based on dimensionality-reduction schemes and is highly relevant to experiments with quantum simulators, including those in higher dimensions.

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.

One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably takes the quantum formalism as the starting point for philosophical reflection and analysis. I argue that this methodology is particularly inappropriate, for it invariably marginalizes much of the theory's content, both that implicit in modelling heuristics and experimental practices, and that encapsulated in the mathematical structures of its formalism. In addition, the prevailing methodology offers little protection against undue influence by metaphysically-laden language which invariably accompanies the formalism. Here, I summarize an alternative methodology whose goal is to ensure that an interpretational project take into account all forms of theoretic content. The methodology harnesses the recent results of the quantum reconstruction program. These results distil the mathematical content of the quantum formalism into physical principles and assumptions, which are more readily philosophically digestible than the formalism itself, and bracket much of its metaphysically-laden language. As a case study of reconstruction-based interpretation, I describe the reconstruction of the identical particle formalism, and its step-by-step interpretation, highlighting the key questions that drive the interpretation forwards and the techniques and stances that are employed in each step. The interpretation yields a novel metaphysical profile for systems of identical particles as potential parts of a whole, which can be traced step-by-step to elementary experimental data and the reconstruction's physical postulates and assumptions. I also describe some of the pitfalls that one faces in any attempt to directly interpret the identical particle formalism.

Utility-scale quantum computing requires the integration and operation of a large-scale qubit register. Semiconductor spin qubits are a primary candidate for this, due to the prospects of building integrated hybrid quantum-classical architectures. However, scaling spin-qubit systems while preserving performance and control has remained a challenge. Here, we demonstrate the operation of an 18-qubit array in germanium based on an extendable 2xN architecture. We achieve simultaneous initialization, control, and readout across the entire array, enabled by parallel operation of modular unit cells. Across the array, we achieve average and median single-qubit gate fidelities of 99.8% and 99.9%, respectively. Finally, we characterize the nearest-neighbor exchange couplings throughout the device and implement high-quality controlled-Z gates to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state. These results demonstrate that spin-qubit arrays can be scaled while maintaining high-fidelity operation and establish a modular, extendable architecture for planar semiconductor quantum processors.

We present Tsim, an open-source high-throughput simulator for universal noisy quantum circuits targeting quantum error correction. Tsim represents quantum circuits as ZX diagrams, where Pauli channels are modeled as parameterized vertices. Diagrams are simplified via parameterized ZX rules, and then compiled for vectorized sampling with GPU acceleration. After the one-time compilation, one can sample detector or measurement shots in linear time in the number of Clifford gates and exponentially only in the number of non-Clifford gates. Tsim implements the Stim API and fully supports the Stim circuit format, extending it with T and arbitrary single-qubit rotation instructions. For low-magic circuits, Tsim throughput can match the sampling performance of Stim.

Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $\kappa$-Poincaré $T$-matrix is explicitly worked out. Afterwards, motivated by recent results on the role of the Hopf algebra dual form of a quantum (1+1) centrally extended Galilei group as the algebraic object underlying non-relativistic quantum reference frame transformations, a new quantum deformation of the (1+1) centrally extended Poincaré Lie algebra is obtained, and its universal $T$-matrix is presented. Finally, the Hopf algebra dual form contraction is applied to this Poincaré $T$-matrix, showing that its corresponding non-relativistic counterpart is precisely the Galilei $T$-matrix associated with quantum reference frames. In this way, the Poincaré Hopf algebra dual form introduced here stands as a natural candidate for describing the symmetry structure of relativistic quantum reference frame transformations. In the appropriate basis, the associated quantum Poincaré group is recognized, remarkably, as a non-trivial central extension of the (1+1) spacelike $\kappa$-Poincaré dual Hopf algebra.

We introduce Simulated Bifurcation Quantum Annealing (SBQA), a quantum-inspired optimization algorithm that extends simulated bifurcation by incorporating inter-replica interactions to mimic quantum tunneling. SBQA retains the efficiency and parallelism of simulated bifurcation while improving performance on sparse and rugged energy landscapes. We derive its equations of motion, analyze parameter dependence, and propose a lightweight auto-tuning strategy. A comprehensive benchmarking study on both large-scale problems and smaller instances relevant for current quantum hardware shows that SBQA systematically improves on SBM in the sparse and rugged regimes where SBM is known to struggle, while remaining competitive and versatile across a diverse set of tested problem families. These results position SBQA as a practical quantum-inspired optimization heuristic and a stronger classical baseline for the sparse and rugged regimes studied here.

Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic execution of quantum algorithms requires a higher-order approach to mitigate errors on the operations themselves. In this work, we investigate universal unitary purification: the task of utilizing a quantum higher-order operation to partially restore the ideal action of an unknown unitary corrupted by a known noise model. We consider deterministic purification of unknown single-qubit unitaries under independent depolarizing noise with ideal auxiliary operations. We prove that within the indefinite causal order (ICO) framework, no nontrivial 2-slot higher-order operation can universally purify the set of single-qubit unitaries. Overcoming this strict limitation, we establish that a 3-slot parallel architecture provides the minimal realization for nontrivial purification. We analytically derive the optimal average fidelity over all 3-slot ICO strategies and show that a parallel strategy attains it, strictly surpassing trivial strategies through input encoding and joint decoding of the channel outputs and a quantum memory. Furthermore, we provide a concrete quantum circuit construction attaining this optimum. Our results clarify the possibilities and limitations of purifying unknown qubit unitaries under depolarizing noise, offering insights for robust gate design.

Routed geometry is a device-level choice in a fixed syndrome-extraction circuit. Two embeddings of the same code can set different physical separations between gate blocks active in the same time step, and these separations control the residual coupling between those blocks. We derive how this choice shapes the leading correlated-fault structure of the effective data channel, and we test the consequences at circuit level. Starting from a geometry-conditioned interaction Hamiltonian on disjoint blocks within one tick, we obtain a retained data channel of single and pair faults for bivariate-bicycle codes, with a truncation error controlled by the per-tick coupling strength. Two geometry metrics emerge. In the combinatorial limit, a matching argument on the logical support reduces the effective fault weight on that support. For strictly positive kernels, once every support pair contributes somewhere in the schedule, the induced support graph becomes complete. At that point the matching-number reduction is exhausted, and the embedding-dependent quantity is the total retained pair weight on the support, which we call the weighted exposure. Circuit-level Monte Carlo on the $[\![72,12,6]\!]$ and $[\![144,12,12]\!]$ benchmarks shows that a biplanar layout, with the schedule split across two routing planes, suppresses the geometry penalty incurred by the monomial layout in a single plane. On the BB72 baseline set of $101$ operating points, the reference-support weighted exposure is strongly correlated with the observed logical error rate (Spearman $\rho_\mathrm{S}=0.893$) in the tested window. A logical-aware two-swap local search over single-layer embeddings on BB72 reduces the worst-case family exposure by $26.11\%$ and lowers the logical error rate across the tested power-law window.

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes are available that achieve high accuracy while preserving key qualitative properties of the underlying dynamical system, and are successfully used across a broad range of fields. In this work, we present a systematic analysis of both local and global errors arising from arbitrary splitting methods applied to unitary problems. Two complementary types of error estimates are derived. The first is expressed in terms of operator norms, while the second is formulated using norms of commutators and can, under suitable assumptions, be extended to certain classes of unbounded operators. Special attention is devoted to the case where only two operators are involved. The theoretical results are illustrated by deriving explicit error bounds for some representative schemes.

The $q$-multinomial coefficient, a classical object in enumerative combinatorics, counts permutations of multisets weighted by the number of inversions, with a single deformation parameter $q$. We introduce the twisted multinomial coefficient, in which each inversion between letters $i$ and $j$ carries a pair-dependent weight $\omega_{ij}$ determined by a skew-symmetric matrix $\Omega$. In general, no closed-form evaluation is known. Our main result is that under a natural structural condition on $\Omega$ - predecessor-uniformity ($\omega_{ij} = q_j$ for all $i<j$) - the twisted multinomial factorizes as a product of Gaussian ($q$-deformed) binomials with site-dependent parameters: $\binom{k}{k_1,\ldots,k_m}_\Omega = \prod_j\binom{\ell_j}{k_j}_{q_j}$ where $\ell_j = k_1+\cdots+k_j$. This extends the standard product formula for the $q$-multinomial from a single parameter $q$ to $m-1$ independent parameters. The identity is purely combinatorial: it holds for arbitrary $q_j \in \mathbb{C}\setminus\{0\}$ without any algebraic constraints. We were led to this identity by studying pilot state preparation in Hamiltonian Decoded Quantum Interferometry (HDQI), a recently proposed quantum algorithm for preparing Gibbs and ground states. As an application, we show that the factorization yields an exact matrix product state (MPS) of bond dimension $k+1$ for the expansion coefficients of $h^k$ in a twisted algebra. We further show that the same site matrices deliver an exact MPS of bond dimension $\mathrm{deg}(\mathcal{P})+1$ for the expansion coefficients of $\mathcal{P}(h)$, for any polynomial $\mathcal{P}$, via a polynomial-dependent right boundary vector.

We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to graphs of arbitrary structure. In general case of quantum graph states of arbitrary structure we derive the geometric measure of entanglement and evaluate quantum correlators. It is shown that these quantities are related to the edge-weight structure around the corresponding vertices in the graph (i.e., edge weights incident to the vertices and vertex weights associated with their closed neighborhoods). In the special case of quantum states representing unweighted graphs, these quantities are related to the degrees of the corresponding vertices in the graph. As an example, we analyze the state associated with the star graph $K_{1,4}$ using noisy quantum computing on the AerSimulator. The results are in good agreement with theoretical predictions. These findings demonstrate a connection between graph structure and quantum properties, enabling the study of properties of classical graphs via quantum computing.

We report a proof-of-principle implementation of the quantum approximate optimization algorithm (QAOA) for the smallest nontrivial MAX-CUT instance on an NV-center-based quantum processor operating at room temperature. The two-qubit register is encoded in the electron spin and the ${}^{14}\mathrm{N}$ nuclear spin of a single NV$^-$ center. Using a minimization formulation of MAX-CUT, we implement a single-layer QAOA ansatz with native entangling and single-qubit control operations. Because the optical readout of the NV$^-$ center is not projective in the computational basis, we reconstruct computational-basis populations from averaged fluorescence signals and use them to determine the experimental QAOA cost landscape by scanning the variational parameters. These results show that the core elements of QAOA can be realized on this platform and establish a baseline for future improvements in phase tracking, coherence-preserving control, and scaling to larger problem sizes.

In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well–known Hidden Subgroup Problem, originally solved by Simon in a landmark work. The second is the Fully Balanced Image Problem, originally introduced by the authors (joint with J. Ossorio–Castillo), which is related to a certain class of mappings (which contains strictly, for instance, the family of group morphisms). Both problems are tackled using a combination of two techniques: first, a conversion into Boolean objects, better suited for quantum computing arguments, and subsequently a custom–tailored algorithm which takes advantage of the Generalised Phase–Kick Back technique.

Energy-based models provide a natural bridge between statistical physics and machine learning by representing data through structured energy landscapes. Boltzmann machines are a particularly compelling class of such models for capturing complex interactions among latent variables, but their use in modern generative learning has been limited by the classical intractability of sampling from general (non-restricted) Boltzmann distributions. Here we develop a quantum-annealing-based framework that enables variational autoencoders with general Boltzmann priors. The framework employs three complementary annealing modes tailored to different stages of learning and deployment: diabatic quantum annealing provides unbiased Boltzmann samples for efficient training, slower annealing concentrates samples near low-energy configurations of the learned prior for unconditional generation, and conditional annealing with external fields steers the learned energy landscape toward attribute-specific regions for conditional generation and semantic editing. Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable training and high-quality generation on MNIST, Fashion-MNIST, and CelebA, achieving faster convergence and lower reconstruction loss than a Gaussian-prior VAE with the same encoder-decoder architecture. Beyond generation, the learned energy function provides out-of-distribution detection signals that add discriminative power beyond reconstruction loss. We demonstrate that these scores separate in-distribution samples from held-out digit classes in one-class MNIST experiments and improve the detection of market regime shifts in financial data. These results establish quantum annealing as a practical and controllable physical mechanism for energy-based representation learning and generative modeling beyond the reach of tractable classical approaches.

We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the comb. Starting from an initial vertex, the walk has a nonzero probability to stay trapped in a finite region. These results are obtained by studying the spectrum and eigenstates of the random Hamiltonian for the graphand analysing its properties. We use both analytic and numerical methods, many of which come from the theory of Anderson localization in one dimension.

We investigate the spectral properties of the Su-Schrieffer-Heeger (SSH) model with sublattice-dependent onsite nonlinearity. Two complementary approaches are employed in our studies. First, Bloch state solutions under periodic boundary conditions are assumed to enable semi-analytical treatment, which allows us to obtain the system's energy band structure and further derive a general expression of the Zak phase that incorporates nonlinearity-induced correction (referred to as nonlinear Zak phase). This analysis reveals that, at sufficiently high nonlinearities, a nonlinearity-induced topological phase transition occurs, marked by a discontinuity in the nonlinear Zak phase. The second approach amounts to numerically obtaining other (non-Bloch) solutions under open boundary conditions, employing the Self-Consistent Field Iterative Method. Its main results include the observation of an edge state's energy that is independent of a nonlinear parameter, a persisting band touching point that only shifts in the presence of perturbations reminiscent of Weyl points in a Weyl semimetal, as well as delocalized solutions that persist even at extreme nonlinearity strengths. These findings illuminate the rich interplay between topology and nonlinearity in lattice models with potential realization in optical/acoustic waveguide settings.

In this paper, we present a systematic study on the ground state computation of quantum droplets in homonuclear Bose-Bose mixtures, governed by the extended Gross-Pitaevskii equations (eGPEs) with Lee-Huang-Yang (LHY) corrections. This model captures the formation of self-bound droplets stabilized by the delicate balance between the attractive mean-field interaction and the repulsive quantum fluctuations. We formulate dimensionless energy functionals for both the general two-component system and the reduced single-component density-locked model. To compute the ground states efficiently, we adapt and benchmark various gradient flow discretization schemes, identifying a backward-forward sine-pseudospectral scheme based on the gradient flow with Lagrange multiplier method (GFLM-BFSP) as the robust solver for our simulations. Utilizing this method, we report three main numerical observations: (i) the density-locked model is quantitatively validated as a reliable approximation for ground state properties; (ii) the dimension-dependent convergence rates of the Thomas-Fermi approximation are established in the strong-coupling regime; and (iii) the critical particle number for self-binding in free space is numerically determined, providing a precise correction to the analytical prediction by Petrov [Phys. Rev. Lett. 115, 155302 (2015)].

A system of three or four particle can be entangled in a number of different ways. It may be the case that only subsets of the particles are entangled, and these subsets are not entangled with each other. It may also be the case that the state is the sum of states in which entanglement only exists within subsets. If this is not the case, the state is said to be genuinely entangled. GHZ states, for example, are genuinely entangled. Deciding whether a state is genuinely entangled is not simple, but conditions do exist to detect it. Here we would like to propose additional sufficient conditions based on one for bipartite entanglement.

Simulating strongly correlated fermionic pairing in the presence of rotational and pair-breaking fields requires deep quantum circuits. We present a graph-structured variational quantum eigensolver whose pair-transfer and single-excitation rotations follow the nonzero pairing and one-body mixing edges of the Hamiltonian. The circuit conserves particle number exactly and uses one parameter per retained edge. We benchmark one layer against exact fixed-number diagonalization for 1500, $M=8$ Hamiltonians represented by 16 qubits. Its mean energy error rises from 0.86 keV without one-body driving to 691 keV at the strongest drive; the one-layer circuit loses accuracy as pair breaking strengthens. In a matched eight-qubit comparison, the graph circuit reaches the 0.42 keV high-drive error of a pair-plus-all-singles circuit with 8 instead of 34 parameters. Fixed-number Adaptive Derivative-Assembled Pseudo-Trotter VQE reaches 0.056 keV with 304 decomposed controlled-NOT gates and iterative pool screening, while a 52-parameter, single-repetition unitary coupled-cluster singles-and-doubles circuit gives 17.6 keV with 2752 such gates. At a separate twelve-qubit point, a second graph layer reduces the high-drive error from 378 to 35 keV. Across the exact grid, an off-diagonal pair-coherence scale tracks the leading pair-density eigenvalue, condensate fraction, and interaction energy. Cranked zirconium Hamiltonians provide the benchmark instances and tune the strength of one-body pair breaking.

Neutral atom quantum computers (NAQCs) are among the most promising computational platforms for quantum computing. Controlling and measuring individual atoms and their states, which often requires multiple imaging and image-analysis procedures, is typically the most time-consuming task during computation and contributes significantly to overall cycle times. To resolve this challenge, we propose a highly-parallel atom-detection accelerator for tweezer-based NAQCs. Our design builds on an existing state-reconstruction method and combines an algorithm-level optimization with a Field Programmable Gate Array (FPGA) implementation to maximize parallelism and reduce the run time of the image-analysis process. We identify and overcome several challenges for an FPGA implementation, such as introducing a prefetching mechanism to improve scalability and customizing bus transfers to support large bandwidths. Tested on a Xilinx UltraScale+ FPGA, our design can analyze a 256x256-pixel fluorescence image in just 115mus, achieving 34.9x and 6.3x speedups over the original and optimized CPU baseline, respectively. Moreover, our accelerator can maintain consistent resource utilization across various atom array sizes, contributing to the ongoing efforts toward scalable and fully integrated FPGA-based control systems for NAQCs.

Quantum computing has attracted the attention of the scientific community in the past few decades. However, despite some relevant advantages, near-term quantum devices remain severely limited by thermal effects, which induce decoherence and restrict coherent control at finite temperature. In this regard, this work reports a gate-based quantum algorithm that prepares the finite-temperature vacuum of Thermofield Dynamics (TFD) and tracks its real-time evolution. The circuit depth scales linearly with system size and requires only single-qubit rotations and nearest-neighbor CNOT gates, making it NISQ-friendly. We benchmark the protocol on the PennyLane simulator: magnetization of a spin-$1/2$ particle in a magnetic field agrees with the exact result $M(\beta)=\tanh(\beta\omega/2)$ to machine precision, and the coherent precession acquires a temperature-dependent damping that quantitatively matches the analytical TFD prediction. Our work provides a ready-to-deploy toolbox for thermal quantum simulations and opens a route to study dissipative phase transitions, quantum thermodynamics and thermal machine-learning models on near-term devices.

Optical circuits and light sources, such as lasers, undergo continuous miniaturization. In its extreme, nanolasers might be comprised of only a few molecules confined in plasmonic nanoresonators. Few-emitter lasers promise low energy requirements and fast responses in a footprint that can be inserted into any device or biological tissue. Utilizing the recently developed stacked hierarchy approach, informed from first principles, we demonstrate the impact of vibrational structure on lasing, using the example of few-molecule lasing in plasmonic cavities. Explicitly accounting for the entire vibrational manifold unveils resonances in the laser intensity that depend on the Stokes shift, drive strength, and the number of emitters. Our work identifies the limits of the omnipresent "incoherent drive"-approximation and paves the way for the understanding of nanolasers at the molecular scale.

The approximate coherent state rank is the minimal number of (classical) coherent states required to approximate a continuous-variable bosonic quantum state and directly relates to the classical complexity of simulating bosonic computations. Despite its importance, little is known about lower bounds on this quantity, even for basic families of states. In this work, we initiate a systematic study of lower bounds on the approximate coherent state rank. Our contributions are as follows. (i) We introduce a technique based on low-rank approximation theory yielding generic lower bounds on the approximate coherent state rank of arbitrary single-mode states. (ii) Using this technique, we find a complete characterization of all single-mode states of finite approximate coherent state rank, and we obtain in particular analytical expressions for the approximate coherent state rank of squeezed states and of finite superpositions of Fock states. (iii) We further show that our single-mode lower bounds can be lifted to multimode lower bounds for finite superpositions of multimode Fock states. (iv) Finally, we prove a super-polynomial lower bound on the approximate coherent state rank of the $n$-mode Fock state $|1\rangle^{\otimes n}$, by exploiting a connection to the permanent. To do so, we show that the algebraic complexity of approximate multi-linear formulas for the permanent is super-polynomial, building upon the proof of a lower bound for exact formulas due to [Raz, JACM 2009]. Our results establish an unconditional barrier to efficient classical simulation of Boson Sampling via coherent state decompositions and connect non-classicality of bosonic quantum systems to central questions in algebraic complexity.

Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold ground-state polar molecules are an ideal platform to encode synthetic dimensions, offering access to large Hilbert spaces of long-lived internal states associated with the rotational and hyperfine degrees of freedom, that can be coupled together with microwave fields to simulate tunnelling. Here, to benchmark the advantages of ultracold molecules, we encode a 1D synthetic lattice in the rotational states of ultracold RbCs molecules and use it to investigate the well-known Su-Schrieffer-Heeger (SSH) model, a minimal model displaying topological properties. To probe the system, we perform spectroscopy using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, typically ~500 times the lattice tunnelling period, even for a synthetic lattice using 8 rotational states. Observations of dynamics at long times with full site-resolved readout of the synthetic dimension allow us to test the effects of chiral and non-chiral perturbations on the topologically protected edge states. Our work lays the foundation for further quantum simulations using the rich internal structure of molecules, including dipolar string phases in interacting samples of molecules, and adiabatic state preparation of many-body Hamiltonians.