Papers

Entanglement can show fundamentally different behavior in fermionic systems. However, while bipartite measures of fermionic entanglement have been established, genuine multiparty entanglement (GME) in fermionic systems is much less understood. We introduce an efficiently computable measure (via semi-definite programming) of fermionic GME, fermion genuine multiparty negativity (fGMN), and show that it is an entanglement monotone and a natural multipartite extension of the fermionic negativity. Using this measure, we find many states which have fGMN but no non-fermionic GME, including large classes of fermionic stabilizer states. The fGMN also displays some major phenomenological differences to the bipartite fermionic negativity, such as finite sudden death points over separation and temperature.

We develop a geometric perturbation theory of Bloch states for perturbations coupling via the interband Berry connection. The gauge-invariant Bargmann trace builds the dressed dispersion and connection order by order as a hierarchy \(Q^{(N)}\), starting with the quantum geometric tensor. Higher members encode multiband geometry beyond the quantum metric and Berry curvature. Connected amplitudes control vertex-order corrections, while strict-order corrections reduce to disconnected products. For a uniform electric field we find the fully coherent, purely geometric sector of the third-order response.

We investigate a coherently driven exciton–photon microcavity with Kerr nonlinearity in the ultrastrong-coupling regime. When the lower and upper polariton branches are well separated in energy, the full Hopfield–Rabi–Kerr model reduces to an effective single-mode description of the lower polariton. We analyze the stability of the lower-polariton steady states. We show that the resulting bistability is qualitatively similar to that in the strong-coupling regime. However, in the ultrastrong-coupling regime counter-rotating processes and the diamagnetic $A^{2}$ term renormalize the polariton spectrum and composition, changing the effective detuning $\tilde{\Delta}_{1}$ and nonlinearity $U_{\mathrm{LP}}$ $g$-dependency beyond the strong-coupling (RWA) picture. As a result, although the semiclassical bistability criterion keeps its standard Kerr–oscillator form, the turning points and hysteresis window are shifted relative to the strong-coupling prediction.

Quantum key distribution (QKD) allows for the establishment of a secret key between two parties, secure against computationally unbounded adversaries. Most experimental and theoretical research in this area, investigates the performance of QKD over fiber or free space channels. A growing body of work, however, has begun to investigate its performance in underwater scenarios. Here, we consider the realistic finite key scenario, and evaluate the simulated performance of two different decoy state protocols. We show that there are certain underwater channels where "simpler" QKD protocols outperform more complex ones. Finally, we also investigate methods to improve QKD performance underwater, specifically looking at classical advantage distillation, which we show can greatly improve the maximal distance supported by QKD underwater.

In this work we study whether nonlinear models of quantum mechanics can avoid detection by strong measurements, if the nonlinear effects only exist as high frequency modes. A potential physical process which could hide such modes would be amplitude level time averaging over fundamentally indistinguishable times. To that end, we have defined a temporal indistinguishability postulate which describes the averaging process, and handcrafted a nonlinear toy model well suited to avoid detection. We have demonstrated that even in such an ideal setup, tabletop weak postselected measurements can still detect nonlinear behavior and put constraints on nonlinear high frequency modes of evolution, even at frequencies beyond fundamental minimal temporal resolution.

Unitary $k$-designs provide a resource-efficient framework for emulating Haar randomness up to the $k$-th order. Quench-based protocols have recently been shown to generate such designs, but achieving this typically requires multiple Hamiltonian realizations, even when using temporal ensembles. Here, we show that no independent Hamiltonians are required: a single chaotic Hamiltonian is sufficient to generate approximate unitary $k$-designs, even when that Hamiltonian is spatially local. We introduce a two-Pauli-kick (2PK) protocol, in which unitary evolution under a fixed Hamiltonian is interspersed with two Pauli operator insertions (kicks). We find that the resulting frame potential approaches the Haar value at long times, with deviations suppressed by the inverse Hilbert-space dimension. We verify this for single realizations of Gaussian random matrices, the Majorana and Spin Sachdev-Ye-Kitaev models, and deterministic local quantum spin chains. Remarkably, in deterministic spin systems, the 2PK protocol generates approximate unitary designs in regimes where quench-based protocols are either inapplicable or fail to converge. Furthermore, our protocol provides a finite-temperature extension of the frame potential and establishes an analytic bound in terms of the equilibrium partition function. We discuss a holographic perspective on this mechanism.

Server-centric quantum data-center architectures offer scalability by distributing communication tasks across QPUs rather than concentrating complexity in a centralized switching core. However, scaling such architectures increases the path length, the number of Bell-state measurements, and the loss of end-to-end fidelity. We ask whether the path diversity of a server-centric topology can be converted into a mechanism for preserving not only rate, but also fidelity. We study this through end-to-end purification as a fidelity-restoration mechanism. First, in a black-box model, we determine the minimum number of raw end-to-end Werner-state copies, each carrying the degraded Werner parameter of a distance-ell path, that purification must consume to recover a single copy matching an elementary link, comparing recursive 2-to-1 and optimized nested r-to-1 purification. Second, we instantiate these requirements in a probabilistic BCube architecture, whose edge-disjoint path diversity supplies the raw copies. Because purification imposes a lower bound on input fidelity, no path redundancy can raise the output below this threshold, which limits scaling. To address it we present the Hop-Independent Quantum Data Center (HI-QDC), an isometric, modular, scalable architecture in which purification transforms end-to-end entanglement across a module into an effective link-level resource for the inter-module topology. Our results identify the regimes in which a BCube module, under end-to-end purification, preserves both the fidelity and the yield of an elementary link. The module then hides its internal hop count and acts as an effective elementary link for a higher-level network. Thus topology supplies the path multiplicity purification requires, while purification converts it into fidelity recovery, enabling recursively scalable quantum data-center networks.

Learning compact, interpretable descriptions of quantum many-body states is an important task in quantum science. We study the task of learning the Slater determinant with maximum fidelity to an arbitrary fermionic many-body state, with motivation from both Hartree-Fock methods and agnostic tomography. Given an $n$-fermion wavefunction built from $m$ fermionic modes, we provide classical and quantum algorithms returning a Slater determinant with fidelity within $\varepsilon$ of maximal in time $m^{\text{poly}(n,1/\varepsilon)}$. We prove matching hardness lower bounds, assuming standard complexity conjectures, along some parameter axes. Given access to quantum copies, we prove this can be accomplished with $\text{poly}(m,n,1/\varepsilon)$ copies of $\rho$. We also show that above a fidelity of $2/3$ any stationary point is the unique global maximum while below $2/3$ the optimization landscape can have spurious stationary points, and hence $2/3$ marks a transition point in the optimization landscape for this problem. We apply the algorithm to the Fermi-Hubbard model, extracting the closest Slater determinant from neural quantum state solutions. Together, our results provide algorithmic tools with provable guarantees in understanding fermionic many-body systems with classical or quantum simulation.

Quantum computing is transitioning from an academic idea to a practical technology, driven by recent hardware advancements and clear paths toward real-world applications. Universal quantum ecosystems (e.g., Qiskit, Cirq, PennyLane) facilitate this transition by providing a consistent interface to diverse quantum devices, abstracting hardware-specific details through a device model that captures each device's computational capabilities. However, these device models have historically been shaped by superconducting hardware, assuming static qubit positions and fixed coupling maps. This prevents them from representing the unique computational capabilities of emerging technologies such as neutral atoms, which feature dynamic qubit rearrangement and zoned operations. As a result, although numerous specialized compilers for neutral atom devices already exist, they cannot retrieve the hardware information they need through these ecosystems - creating a technology lock that hinders or even prevents the integration of neutral atom devices. In this work, we demonstrate how this limitation leads to suboptimal compilation results and can exclude certain devices entirely. Motivated by this, we propose rethinking current device models to faithfully represent neutral atom devices, enabling their seamless integration into universal quantum ecosystems. Evaluations conducted within the Quantum Device Management Interface (QDMI) demonstrate that the proposed device model unlocks a routing overhead fidelity improvement by a factor of up to 100,000 on a circuit with 16 qubits and 600 gates.

We show that the self-correcting memory in 3d Wegner gauge theory is stable to arbitrary small enough perturbations of the Hamiltonian. Our proof relies on a new method we dub “gauge averaging”, which gives conditions under which explicitly broken gauge symmetries are effectively restored by fluctuations. These conditions show that the self-correcting memory phase is fluctuation stabilized, with its robustness to perturbations increasing with increasing temperature, up to some $T_c > 0$.

Estimation of work at the quantum scale remains a central challenge in quantum thermodynamics. Canonical approaches have a fundamental drawback: they assume classical control of the quantum system, as implicit in a time-dependent Hamiltonian. Yet the energetic cost of implementing this control is omitted and can exceed the system's energy scale by orders of magnitude, calling into question the operational significance of work values. We address this by autonomizing the controlled energy transfer, embedding the driven dynamics into an energy-conserving evolution on a larger quantum system. Work is then unambiguously identified with the energy transferred between the two systems, singling out a unique observable on the driven system: the work operator. We show that the quantum work operator evades a no-go theorem by deriving a quantum fluctuation theorem that recovers the Jarzynski equality in classical scenarios. We incorporate imperfect control and quantify corrections to work statistics. Extending the framework to open quantum systems, we obtain an operatorial first law in which work, heat, and internal-energy changes are represented by distinct operators on the reduced system. Together, these results settle the long-standing debate over whether work is a quantum observable: it is, once the controlling system is included in the description rather than treated as external.

Sample-based Quantum Diagonalization (SQD), an extension of Quantum Selected Configuration Interaction (QSCI), has emerged as a promising hybrid quantum-classical paradigm for computing molecular ground state energies. By leveraging quantum sampling instead of variational optimization, QSCI avoids barren plateaus and enables direct reconstruction of correlated electronic wavefunctions. However, existing configuration recovery techniques primarily enforce symmetry constraints without guaranteeing optimal selection of the most physically relevant configurations, often leading to unnecessarily large subspaces and increased classical diagonalization costs. In this work, we introduce a machine-learned compact subspace generation protocol based on Restricted Boltzmann Machines (RBMs), termed QSCI-RBM, and integrate it within the Density Matrix Embedding Theory (DMET) framework. The RBM is trained on quantum-sampled configurations to learn the underlying probability distribution of dominant determinants, enabling the targeted generation of high-probability configurations. We apply this framework to the simulation of a protein-ligand complex involving the inhibitor Carmofur bound to the SARS-CoV-2 main protease ($M^{\text{pro}}$). Our results demonstrate that DMET-QSCI-RBM achieves energies within the chemical accuracy threshold by accessing only approximately 4% of the configuration subspace. In contrast, standard DMET-SQD simulations failed to reach chemical accuracy while accessing up to 20% of the subspace, even as the chemical potential itself nearly converged. These findings highlight that RBM-assisted configuration generation produces significantly more compact subspaces while preserving physical accuracy, thereby reducing classical computational overhead and enabling the scalable quantum embedding simulation of complex biological systems.

Fermion pairing underlies collective quantum phenomena across widely different forms of matter. In extended systems such as ultracold Fermi gases, pairing is commonly understood through the BCS–BEC crossover, where the pair size evolves from large, overlapping Cooper pairs to tightly bound dimers. In finite systems such as atomic nuclei, superconducting grains and quantum dots, however, the same pairing tendency competes with confinement, shell filling and spatial inhomogeneity, making the microscopic structure of pairs much harder to access. Here, we image pair correlations in a finite, tunable system of few fermionic atoms with single-particle resolution and full counting statistics. We observe that confinement and shell structure re-organize pairing in real space: In the weakly interacting, confinement-dominated regime, closed-shell configurations suppress correlations in the high-density trap center. Pairing is mainly observed toward the low-density surface. Open-shell systems, however, support substantially stronger central pairing. Already for surprisingly small systems, increasing either interaction strength or particle number restores a locally bulk-like Cooper-pair profile in the trap center, whereas the edge retains dimer-like correlations. By resolving where pairs form and how their character changes from localized dimers to overlapping Cooper pairs, our measurements provide a microscopic view of pairing in finite fermionic matter and connect the physics of mesoscopic cold atoms to pairing phenomena in nuclei and superconducting nanostructures.

Pauli Correlation Encoding (PCE) is a heuristic framework for binary optimisation that encodes classical variables into many-body Pauli observables. While PCE requires fewer qubits than other approaches, it relies on estimating a large number of Pauli expectation values whose signs determine the variables' values, which can incur substantial measurement overhead. Here, we introduce efficiently simulable PCE, a class of dequantised PCE realisations where all expectation values needed can be computed efficiently classically. We instantiate this idea using free-fermionic evolutions, realised by matchgate circuits, and Instantaneous Quantum Polynomial (IQP) circuits. On MaxCut, Maximum Independent Set, Multi-Dimensional Knapsack, and Max3SAT benchmarks, these methods produce high-quality solutions across problem sizes ranging from tens to thousands of variables. Our results show that PCE is naturally understood as a correlation-based optimisation framework with both quantum and classically simulable realisations. This yields a dequantised baseline for evaluating future quantum PCE implementations.

Programming distributed quantum systems requires multiple actors to coordinate precise sequences of quantum operations, classical communication, and entanglement generation. Writing such protocols directly as distributed processes is tedious and error-prone, and subtle mismatches can cause deadlock or silently incorrect quantum states. We present Qoreo, a choreographic programming language for quantum distributed systems in which an entire protocol is expressed as single, global program (a choreography) rather than as a collection of independent actor processes. Qoreo includes a local quantum language with linear types that enforce the no-cloning principle; a choreographic language that combines local quantum computation with inter-actor classical and quantum communication; and a process language for individual network nodes. We prove type safety for choreographies, guaranteeing that well-typed programs implement well-defined quantum operations, and we define endpoint projection~(EPP), which automatically derives a network of independent processes from any choreography. We prove EPP sound and complete with respect to the choreographic semantics; as a corollary, every well-typed choreography projects to a deadlock-free process network. The metatheory of Qoreo is fully mechanized in Rocq, and we provide an extraction pipeline to NetQASM for simulation and deployment on quantum network hardware.

We deform the Carlen–Maas–Wirth framework for noncommutative dynamical optimal transport by an Arnold–Nielsen type complexity operator. A positive state-independent operator $G$ compatible with the Hilbert bimodule structure of a noncommutative differential calculus $\partial\colon\M\to\Hcal$ can be absorbed into the calculus itself, \[ \partial_G:=G^{1/2}\partial. \] The corresponding complexity-weighted transport problem is exactly the unweighted transport problem generated by $\partial_G$, whenever the deformed quadratic form remains Dirichlet. In finite dimensions we prove existence of minimizers for density-dependent Petz-class metrics and for fixed physical complexity weights, the latter without commutation between $G$ and the state-dependent mobility. On unitary orbits we identify the induced distance with a quotient metric coming from a right-invariant complexity geometry. This yields an exact Bell-state preparation result via Clairaut's relation and an exactly computed restricted-path upper bound for GHZ preparation; the Lindblad detailed-balance case is included only as entropy-gradient-flow background.

Hardware noise and finite sampling perturb the fidelity estimates forming a quantum-kernel Gram matrix. We measured how far three hardware-reconstructed Gram matrices depart from an exact statevector reference for one frozen four-qubit ZZ feature map on N=24 indoor air-quality windows, executed on ibm_fez at 1024 shots per circuit in three single, non-interleaved jobs: baseline, dynamical decoupling alone, and gate twirling alone. All were complete, finite, and positive-semidefinite. Off-diagonal root-mean-squared error (RMSE) against the reference was 0.0878, 0.0864, and 0.0427; full-matrix centered kernel alignment (CKA) ranged 0.933-0.989 and the post hoc diagonal-excluded (U-centered) CKA 0.816-0.986. The gate-twirled job deviated least on every reported geometry axis; its baseline contrasts are deletion-stable for the Spearman, mean-absolute-error, RMSE, and full-matrix CKA diagnostics, while the Pearson and diagonal-excluded contrasts fall just below that convention. Dynamical decoupling was not separated from the baseline. The observed error exceeded both finite-shot reference scales, so, under those sampling-only models, sampling does not explain it. Centered kernel-target alignment did not track reconstruction fidelity and stayed at or below each label-permutation reference: implementation fidelity and task relevance are distinct diagnostic axes. All configuration-level statements describe three realized jobs on one backend; no mitigation-efficacy, classifier-superiority, forecasting, or quantum-advantage claim is made.

Polaritonic architectures seek to engineer molecular properties by hybridizing localized degrees of freedom with delocalized optical cavity fields. However, scaling laws impose a severe bottleneck on N-molecule collective strong coupling: because each molecule contributes only a fractional share to the collective state, localized responses undergo O(1/N) ensemble dilution. We demonstrate a violation of this scaling using fluorescence-encoded infrared spectroscopy of molecular ensembles under vibrational strong coupling, where macroscopically synchronized electronic responses scale as O(1). This scale-invariance reveals a regime of vibronic quantum transduction, where non-local vibrational entanglement is translated into collective electronic entanglement. By demonstrating the generation of macroscopically entangled electronic states from vibro-polaritons without an O(1/N) penalty, these results provide a scalable framework for room-temperature quantum technologies and coherent steering of non-adiabatic chemical pathways.

Let $\mathbb{K}\in\{\mathbb{R},\mathbb{C},\mathbb{H}\}$, put $\beta=\dim_{\mathbb{R}}\mathbb{K}$, and let $G_n^{\mathbb{K}}$ be an $n\times n$ matrix with i.i.d. standard $\mathbb{K}$-Gaussian entries, namely a standard $\mathbb{K}$-Ginibre matrix. We prove that the normalized row-ordered permanent $W_n^{\mathbb{K}}=\operatorname{per}_{\mathbb{K}}G_n^{\mathbb{K}}/\sqrt{n!}$ has a radial density $p_n^{\mathbb{K}}$ satisfying $\|p_n^{\mathbb{K}}\|_\infty=p_n^{\mathbb{K}}(0)\lesssim_\beta n^{(\beta+2)/4}$ and $\sup_{z\in\mathbb{K}}\mathbb{P}(|W_n^{\mathbb{K}}-z|\leq\varepsilon)\lesssim_\beta n^{(\beta+2)/4}\varepsilon^\beta$. In particular, for $\mathbb{K}=\mathbb{C}$, this resolves the Permanent Anticoncentration Conjecture of Aaronson and Arkhipov. The proof compares the squared Gaussian permanent with the squared (Study) determinant in Laplace-transform order.

Quantum-state texture (QST) is an emerging quantum resource that has garnered increasing attention amid advances in quantum theory. In this work, we generalize the QST to quantum-state block texture (QSBT). This generalization provides profound operational interpretations for quantifying the advantages of quantum states in quantum information processing. We pioneer an alternative framework for characterizing and quantifying quantum-state block texture, and propose three types of block texture measures. By comparing these QSBT measures, we investigate their distinctions and interrelationships. We demonstrate that the geometric measure serves as an upper bound for the trace distance-based measure. For a specific family of quantum states, we evaluate the values of two trace distance-based measures. Then we sample four sets of data from this family of states, with each set comprising $5\times 10^4, 10^5, 5\times 10^5$ and $10^6 $ samples, respectively, and present the corresponding distributions. Our results reveal that the QSBT measures constructed via different approaches show distinct characteristics, indicating their potential roles in quantifying the block texture of quantum states.

We present a formulation of quantum field theory based entirely on real numbers, which we call real quantum field theory (RQFT). The construction is obtained from the standard complex-number formulation by replacing the imaginary unit i with a matrix J throughout all formulas. Here J is the real 2x2 matrix satisfying the condition J^2=-1. This extends the recently developed formulation of real quantum mechanics based on the real Kähler space to systems with infinitely many degrees of freedom. As the basic example, we construct the RQFT for a scalar field. We define a field operator acting on the real Kähler analogue of the bosonic Fock space. This operator satisfies the Klein-Gordon equation and the J-form of canonical commutation relation. To construct the RQFT we develop the corresponding J-calculus. In particular, we introduce the direct and inverse J-Fourier transforms and the associated J-valued distributions. In RQFT, the usual unitarity condition for the complex S-matrix is replaced by the statement that the real scattering operator is both orthogonal and symplectic. The physical observables in RQFT coincide with those of ordinary QFT. Thus RQFT does not change the physical predictions of scalar QFT, but provides an equivalent formulation. We explore the possibility of purely real formulations of the Standard Model of elementary particles. We show that it does admit this formulation and the resulting theory has ortho-symplectic symmetry. The choice of the Standard Model as the testbed for exploring the possibility of purely real formulations is related with the fact it provides a realistic description of all known fundamental particles. The real formulation of the Standard Model naturally suggests a possible exit beyond the Standard Model. In particular, we consider the implications of breaking the J-symmetry as a marker for new physics.

Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for $^{43}$Ca$^+$ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state ($\bar{n}\approx 0.16$) and benchmark an induced error on the data qubit of $1.7(4)\times 10^{-4}$ per cooling cycle.

The fractional angular momentum of a two-dimensional charge-flux composite is a well-established phenomenon usually derived from a semiclassical Hamiltonian. However, when the composite is treated as an isolated system in free two-dimensional space, the fundamental rotational and reflection symmetries of the $O(2)$ group demand that its total angular momentum is strictly quantized. We address this conceptual discrepancy by applying a full quantum electrodynamic (QED) approach combined with Noether's theorem. We demonstrate that the interaction between the charge and flux, mediated by the vacuum electromagnetic field, generates an intrinsic interaction angular momentum composed of both field momentum and hidden relativistic momentum. This gauge-invariant interaction angular momentum exactly compensates for the fractional part of the kinetic angular momentum. Consequently, the net angular momentum of the composite strictly follows the integer or half-integer quantization rule. Our formalism clarifies that the conventional fractional spin corresponds to the expectation value of the kinetic angular momentum within the perturbed QED ground state. It also elucidates why the standard classical field angular momentum definition fails to capture this in two dimensions, due to non-vanishing boundary terms.

Local unitary equivalence is central to entanglement quantification and classification. Identifying the local unitary equivalence remains a formidable challenge. We address this problem for a class of quantum states with one highly degenerate eigenvalue and the rest non-degenerate simple eigenvalues that are pivotal to structured resources in quantum resource theory. We introduce a “reduction" procedure that maps each state to a “reduced state" by nullifying the highest-multiplicity eigenvalue and prove that the local unitary equivalence of the original states is equivalent to that of their reduced counterparts. For the resulting pure or non-degenerate reduced states, we employ the existing invariants or fixed-point subgroup criteria to establish a complete discrimination framework, although the existing criteria can not directly identify the local unitary equivalence of the original states. We also verify the local unitary equivalence of two families of single-parameterized multipartite mixed states constructed by perturbing absolutely maximally entangled states from distinct combinatorial origins, demonstrating the efficacy and generality of our approach.

The fundamental interactions governed by quantum electrodynamics (QED) are intrinsically rich in quantum resources, yet how these resources dynamically redistribute during relativistic scattering is still not fully understood. In this work, we systematically investigate the tree-level Bhabha scattering process (e^- e^+ \rightarrow e^- e^+) within the framework of quantum resource theory, revealing how QED kinematics and Feynman amplitudes strictly dictate resource redistribution. Specifically, we demonstrate a strict anti-correlation between entropic uncertainty and dynamically generated entanglement across diverse initial states. We find that mass-induced single-helicity-flip transitions cause a pronounced geometric symmetry breaking in the non-relativistic regime, whereas the restoration of chiral symmetry in the ultra-relativistic limit ensures strict symmetry about the backward scattering angle. Furthermore, we analytically establish a rigorous equivalence between local wave-particle duality and global bipartite quantum coherence. Finally, evaluating the trade-off between local duality and Bell nonlocality, we show that in the ultra-relativistic limit, transverse scattering of basic factorized states equalizes the s- and t-channel amplitudes to optimize non-local correlations. However, pre-existing local coherence inevitably disrupts this delicate kinematic balance, significantly suppressing the Bell parameter and preventing the maximal violation of local realism. Therefore, we believe the present results provide deeper understanding of the fundamental quantum nature of QED processes.

We study the dynamics of quantum entanglement between two harmonically trapped electrons interacting via the electromagnetic force. Starting from two-mode Gaussian states at thermal equilibrium, we make use of the covariance matrix formalism in order to compute the logarithmic negativity of the evolved state as a quantitative measure of entanglement. We analyze two initial configurations: thermal single-mode and two-mode squeezed states, and describe the time evolution of entanglement in the system for different values of squeezing and temperature, while identifying the parameter regimes accessible to current and near-future single-electron trap experiments.

Coupling phases play a decisive yet often overlooked role in cavity magnonics, particularly in complex multimode systems. Here, we investigate phase-mediated interference effects in a cavity magnonics system comprising a four-post re-entrant microwave cavity coupled to Yttrium Iron Garnet (YIG) spheres. Using an input-output model that explicitly accounts for both internal and external coupling phases, we achieve agreement with experimental microwave transmission measurements. Our results unravel the emergence of a positionally-dependent uncoupled mode due to interference of cavity photon-magnon (internal) coupling phases. Further, we experimentally observed large nonreciprocity at the antiresonance frequencies and show that this feature arises due to the far-detuned modes' odd parity cavity photon-probe (external) coupling phase interfering with the internal coupling phases. Bridging theory, simulation and experiment, these results establish coupling-phase engineering as a key principle for accurately modeling and designing multimode cavity magnonics devices.

Engineering the photonic environment using lattices of coupled resonators, which we refer to as lattice quantum electrodynamics (QED), provides a route to control both the spontaneous emission of individual quantum emitters and the photon-mediated interactions between them. Here we introduce an optical lattice QED platform based on individual dibenzoterrylene (DBT) molecules embedded in anthracene crystals and coupled to lattices of open optical microcavities. This hybrid architecture benefits from narrow-linewidth molecular emitters, site-resolved optical access, engineered coupled-resonator bands, and compatibility with established molecular frequency-tuning techniques. As a proof-of-principle demonstration, we observe emitter-photon bound states formed when the optical transition of a single molecule is tuned to the band gap of a Su-Schrieffer-Heeger (SSH) cavity lattice. These in-gap states display directional localization and photon emission on a single sublattice, inherited from the vacancy-induced topological edge modes of the underlying SSH lattice. Our results establish open-cavity lattices coupled to DBT molecules as a versatile architecture for engineering many-emitter quantum optical systems with controllable photon-mediated interactions.

While combinatorial optimization problems are central to many scientific and engineering applications, their solution remains challenging due to exponentially large search spaces. Variational quantum algorithms offer a promising route for tackling such problems, yet their practical performance is limited by repeated quantum circuit evaluations and classical parameter updates. In this work, we introduce DQAOA-GPT, a hybrid framework that integrates the distributed quantum approximate optimization algorithm (DQAOA), which decomposes a large optimization problem into smaller sub-problems, with GPT-based quantum circuit generation for solving those sub-problems. Rather than relying on iterative variational optimization, the proposed approach uses a trained generative model to directly generate high-quality quantum circuits for the decomposed sub-problems. As a benchmark, we evaluate DQAOA-GPT against conventional DQAOA on dense HUBO optimization problems with up to 100 decision variables. The results demonstrate that DQAOA-GPT significantly reduces computational cost while maintaining competitive solution quality, with larger acceleration observed for larger sub-problem sizes. Although this work focuses on benchmark-scale validation, the framework provides a promising foundation for larger-scale combinatorial optimization in hybrid HPC-QC environments through increased GPU resources and parallel computing capability.

We study redundancy and effectiveness of Variational Quantum Circuits via algebraic and geometric views of Lie groups. Considering unitary transformations acting on Hermitian observables, a stabilizer group decomposition is given. Subsequently, we identify the Hermitian orbit with a quotient space of a symmetric space. Through this connection, we characterize the effective circuit degrees of freedom. Our approach of spectral decompositions and homogeneous spaces yields tractable calculation criteria, which are verified by numerical experiments.