Papers

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.

We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally imposed randomness. Within the theory of moving manifolds, we establish a curvature-noise correspondence: fluctuations are governed by the inverse curvature tensor, while entropy production is controlled by curvature deformation. The invariant continuity law on a moving hypersurface yields a geometric Fokker-Planck equation, and curvature-velocity coupling generates a quadratic Onsager-Machlup functional determining path weights. The resulting entropy functional satisfies a curvature-driven monotonicity law, providing a geometric derivation of the Second Law. In two dimensions, the curvature invariant reduces to Gaussian curvature and encodes topology, so topological transitions produce discrete entropy jumps. When the ambient space carries a Minkowskian signature, the same curvature-kinetic quadratic form that generates dissipative thermal weights produces oscillatory phase weights, and the Laplace-Beltrami operator governing entropy evolution acquires a Schrödinger-type structure. This provides a geometric resolution of the apparent distinction between classical stochastic behaviour and quantum dynamics. These results show that stochastic behaviour, thermodynamic irreversibility, and quantum transition amplitudes are unified within the moving manifold framework. Geometry does not merely accommodate stochasticity; stochastic behaviour arises as a consequence of deterministic geometric evolution. The theory predicts curvature-controlled anisotropic diffusion, entropy jumps at topology-changing events, and a geometric thermal-quantum crossover in which classical stochastic weights and quantum amplitudes are generated by the same curvature-kinetic action.

In this work, we construct small sets of bipartite orthogonal pure states that cannot be perfectly distinguished by local operations and classical communication (LOCC). We mention that not all the states within the constructed sets are necessarily entangled. However, such a set contains at least one entangled state which cannot be conclusively identified by LOCC (with nonzero probability). Then, we show that the states of any such set can be perfectly distinguished by LOCC using a minimal-dimensional entangled resource state. Clearly, here the entangled resource state provides an advantage irrespective of the dimension of the given set. Using this result, we also prove that any pure entangled state is useful as a resource to distinguish the states of any present set unambiguously with nonzero probability under LOCC. These sets exist in all two-qudit Hilbert spaces. Furthermore, it is possible to decrease the average entanglement content of such a set or to increase the cardinality of the set without changing certain properties of the same.

Understanding whether the features of open quantum dynamics are genuinely quantum remains a central challenge in quantum dynamics. Even though the non-Markovian behavior of quantum dynamics has been widely investigated across different settings, there is still no consensus on which properties of a dynamics reflect genuine quantum features and which arise from classical or non-genuine quantum sources. In this review, we provide detailed information on recent developments in characterizing quantum non-Markovianity based on information backflow and the nature of its origin. We also present a survey on how various approaches separate classical and quantum contributions, as well as how they define operational tasks that reveal genuine quantum non-Markovianity. We analyze several frameworks, including state-distinguishability -based, channel-based (“CP-divisibility”), and process-tensor methods. For each framework, we outline the underlying physical motivation, the criteria proposed to distinguish genuine quantum non-Markovianity from practical or apparent memory effects. We further compare different approaches and their strengths and limitations. The review aims to clarify the conceptual and operational aspects of quantum non-Markovian processes based on their nature and to provide a foundation for future research on quantum non-Markovianity and its role in advancing quantum information science and technology.

Polar molecules represent a promising platform for quantum simulation and computation protocols. Highly controllable arrays of optical tweezers are now accessible in experiments, allowing for unprecedented control of individual molecules. Motional dephasing is typically seen as an obstacle in quantum computing scenarios. Here, we instead consider using the trap structure as a resource for implementing efficient quantum gates. By numerically solving the two-body problem of dipoles trapped in separate tweezers, we identify trap-induced resonances that can serve as the mechanism for achieving state-dependent dynamics and can be further utilized for quantum sensing.

The 2D $\mathbb{Z}_2$ toric code admits a global symmetry exchanging electric and magnetic quasiparticles, known as electromagnetic duality. Known realizations include lattice translation symmetry, an exact $\mathbb{Z}_4$ symmetry generated by a Clifford circuit, and an exact $\mathbb{Z}_2$ symmetry generated by a non-Clifford circuit. We show that a Clifford electromagnetic duality cannot realize an exact internal $\mathbb{Z}_2$ symmetry. This is proved rigorously for symmetries with coarse translation invariance by $l$ lattice units for generic odd $l$. Therefore an exact internal $\mathbb{Z}_2$ electromagnetic duality must be non-Clifford, whereas generic internal Clifford realization necessarily has $\mathbb{Z}_{2^m}$ algebra with $m\ge 2$. Our result suggests an unexpected connection between the algebra of exact electromagnetic duality and Clifford hierarchy of circuits.

We propose a general framework, termed the imaginary gauge phase imprint (IGPI), which enables engineering arbitrarily configurable wavefunctions with exact solutions and self-organization dynamics in any-dimensional non-Hermitian lattices under imaginary gauge fields. Using this method, we uncover a novel phase with exact critical wavefunctions, dubbed the skin critical phase (SCP), which is marked by unconventional localization, topological-skin, and dynamical characteristics. Furthermore, we validate the IGPI by imprinting and visualizing complex fractal states with Sierpinski-carpet and Koch-snowflake profiles, as well as exotic super-moire and 3D-moire states in regular lattices. Our work not only offers fresh insights into non-Hermitian critical and fractal physics, but also provides a rigorous paradigm for controlling and visualizing wavefunction patterns using the IGPI in engineered non-Hermitian systems.

Frustrated spin-ice systems support emergent gauge fields and fractionalized quasiparticles that act as magnetic monopoles. Although artificial platforms have enabled their direct visualization, access to their quantum-coherent dynamics has remained limited. Here we realize a programmable dipolar square spin-ice model using a superconducting-qubit quantum annealer, providing access to a previously unexplored quantum-coherent regime of artificial spin ice. By implementing a direct one-to-one mapping between lattice spins and physical qubits, together with engineered extended couplings, we realize effective dipolar interactions on frustrated lattices comprising more than 400 vertices. Tuning transverse-field fluctuations enables us to probe the real-time dynamics of Dirac-string defects and interacting monopole plasmas. We observe super-diffusive monopole transport, with scaling exponents intermediate between classical diffusion and ballistic motion, indicating dynamics beyond classical stochastic relaxation and consistent with coherent propagation within an emergent gauge manifold. These results establish programmable quantum spin ice as a scalable platform for investigating fractionalized excitations and emergent gauge dynamics in engineered quantum matter.

Integrating quantum circuits into deep learning pipelines remains challenging due to heuristic design limitations. We propose Q-DIVER, a hybrid framework combining a large-scale pretrained EEG encoder (DIVER-1) with a differentiable quantum classifier. Unlike fixed-ansatz approaches, we employ Differentiable Quantum Architecture Search to autonomously discover task-optimal circuit topologies during end-to-end fine-tuning. On the PhysioNet Motor Imagery dataset, our quantum classifier achieves predictive performance comparable to classical multi-layer perceptrons (Test F1: 63.49%) while using approximately \textbf{50$\times$ fewer task-specific head parameters} (2.10M vs. 105.02M). These results validate quantum transfer learning as a parameter-efficient strategy for high-dimensional biological signal processing.

Device-independent quantum key distribution (DIQKD) provides a model of quantum key distribution with minimal assumptions and highly abstract theoretical building blocks. Although DIQKD frees us from detailed discussions of specific device models and associated error parameters, it replaces them with fundamental assumptions about the validity of quantum experiments. In this work, we propose a way to lift a protocol based on DIQKD-style assumptions to a device-dependent QKD protocol by performing local self-tests in the laboratories of the two key-generating parties. In particular, we consider routed Bell-test setups as a means of self-testing the local parties in earnest and develop a rigorous mathematical framework showing that the underlying optimization problems can indeed be transferred to the device-dependent QKD setting. As an application, we illustrate many of the relevant techniques through the case study of a routed BB84 protocol.

We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing high-order time-averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high-order three-photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three-photon state $\ket{g,3}$ and the qubit excited state $\ket{e,0}$ in the squeezed picture. Numerical simulation results confirm the high fidelity and robustness of the proposed protocol. Our method provides a practical pathway for generating complex non-Gaussian entangled states, which are of significant value for fault-tolerant quantum computation and quantum metrology beyond the standard quantum limit.

Quantum-enhanced Markov chain Monte Carlo, a hybrid quantum-classical algorithm in which configurations are proposed by a quantum proposer and accepted or rejected by a classical algorithm, has been introduced as a possible method for robust quantum speedup. Previous work has identified competing factors that limit the algorithm's performance: the quantum dynamics should delocalize the system across a range of classical states to propose configurations beyond the reach of simple classical updates, whereas excessive delocalization produces configurations unlikely to be accepted, slowing the chain's convergence. Here, we show that controlling the degree of delocalization by adiabatically dressing the quench protocol can significantly enhance the Markov gap in paradigmatic spin-glass models.

We present an analytic flat-spacetime accelerating boundary analog of Hawking-type emission that possesses infinite asymptotic acceleration (and radial acceleration in the black hole analog) but finite total radiated energy (and zero surface gravity in the black hole analog). We perform a unified study of its scattering symmetry, horizon formation, asymptotically extreme acceleration, finite total radiated energy, and the distinction between local energy flux and global particle production within a single closed-form model. The particle spectrum, energy spectrum, and equivalent spacetime metric are derived, revealing an interesting mix of normal and extremal black hole properties.

The model of light-matter interaction in quantum electrodynamics typically relies on the Markovian approximation, which assumes that the system's future evolution depends solely on its current state, effectively treating it as a “memoryless" process. However, this approximation is not valid in scenarios when retardation effects are significant. These memory and retardation effects have the potential to improve existing quantum technologies (e.g., large-scale quantum networks, quantum information processing) and unlock new phenomena for future applications. In this work, we show theory and experiments of a time-delayed coherent feedback system using a transmon artificial atom (treated as a qubit) embedded in a superconducting circuit waveguide, in both linear and nonlinear excitation regimes. By using a feedback loop with a delay time comparable to the qubit relaxation time, pronounced non-Markovian effects appear in the dynamics of the qubit evolution. We also show how the resonance fluorescence spectrum, including elastic and inelastic scattering (such as the well-known Mollow triplet), can be significantly modified through the interaction between the qubit and feedback loop to show genuine non-Markovian and quantum nonlinear phenomena that cannot be explained with instantaneous coupling parameters. This work presents the first experimental report of Mollow triplets in the non-Markovian regime.

Achieving both broad solar-spectrum absorption and strong redox capability is critical for semiconductor photocatalysts in environmental remediation and energy conversion. Herein, an S-scheme heterojunction photocatalyst is constructed by coupling TiO2(B) nanorods with g-C3N4 nanosheets. Its well-matched band structure extends light absorption from the UV to the visible region and enables efficient charge separation. Under simulated sunlight irradiation, the 40 wt% g-C3N4/TiO2(B) heterojunction delivers a H2 evolution rate of 1.98 mmol g-1 h-1 for water reduction with methanol as the sacrificial agent, which is 1.5 and 2.0 times higher than those of pure g-C3N4 and TiO2(B), respectively. When exposed to amoxicillin wastewater instead of methanol solution, the heterojunction degrades 98.2% of amoxicillin and produces 20.70 umol g-1 of H2 within 90 min. Moreover, the heterojunction shows excellent photodegradation activity toward various organic antibiotics and dyes, owing to the S-scheme charge separation mechanism. This work highlights the promising potential of S-scheme heterojunctions for photocatalytic H2 production coupled with organic wastewater treatment.

We introduce a spin $z$-component ($S_{z}$) conserving symmetry-preserving ansatz and a shallow quantum phase estimation (QPE) routine of spin $x$ ($S_x$), and combine them into a spin-filtering variational quantum deflation (sfVQD) scheme for noisy intermediate-scale quantum (NISQ) computing era excited state calculations. The scheme encodes the spin information into a small ancilla register through controlled rotations under $\mathrm{exp} (i\theta\hat{S}_{x})$ with only modest circuit overhead. The encoded information is then utilized to suppress spin contamination by screening, avoiding costly explicit evaluation on the total spin $\langle\hat{S}^{2}\rangle$. Because the screening module operates independently of the variational ansatz, it can also be employed with other excited-state calculation schemes based on variational quantum eigensolvers. As a demonstration, we apply sfVQD to LiH and BeH$_2$ with varying geometries to show markedly improved separation of singlet and triplet manifolds over conventional VQD without QPE-derived screening. These results suggest that ancilla-assisted symmetry screening provides a modular and NISQ-compatible route to securing excited state calculations of physically meaningful properties. We discuss how our scheme may naturally be extended to computing other conserved quantities.

Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model–referred to as a noncontextual model–making it crucial to identify which features prevents such models from reproducing the corresponding quantum measurements. In this work, we theoretically demonstrate contextual features inherent in the structure of quantum non-demolition measurements. These features not only reveal the nonclassicality of unambiguous state discrimination, but also extend to sequential unambiguous discrimination and probabilistic quantum cloning, both of which involve post-measurement states. Moreover, our analysis extends to noisy scenarios, highlighting its potential relevance for practical implementations. We believe that our results broaden the scope of observing nonclassicality in quantum systems and ultimately contribute to the advancement of various quantum technologies.

We present a quantum-mechanical treatment of positron channeling radiation in a planar harmonic potential that explicitly accounts for interference between transition amplitudes from different transverse energy levels. Because the planar channel potential for positrons in diamond~(110) is well approximated by a parabola, the transverse spectrum is equidistant, $\varepsilon_n = \Omega(n+\tfrac{1}{2})$, and all $n \to n{-}j$ transitions radiate at the same Doppler-shifted frequency. The sudden-approximation entry of the positron into the crystal produces a Glauber coherent state~\cite{Glauber1963} with Poisson-distributed level populations $|c_n|^2 = e^{-n_0}n_0^n/n!$ and mean occupation $n_0 \propto \theta_{\rm in}^2$. Phase synchronization between the $c_n$ and the dipole matrix elements ensures constructive interference of all contributing amplitudes. Three exact scaling laws follow: (i)~$I_{\rm incoh}\propto n_0\propto\theta_{\rm in}^2$; (ii)~$I_{\rm coh}\propto n_0^2\propto\theta_{\rm in}^4$; (iii)~$\mathcal{G}\equiv I_{\rm coh}/I_{\rm incoh}\approx n_0 \propto\theta_{\rm in}^2$. Numerically, $\mathcal{G} = 12\text{--}31$ for positron energies of $4\text{--}14$~GeV in diamond~(110) at $\theta_{\rm in}=31\;\mu$rad, in agreement with the experimental first-harmonic peak positions of Avakyan et al.~\cite{Avakyan1982} to within 15%. The transition from $N$- to $N^2$-scaling of radiated intensity, driven by quantum coherence, opens a route toward high-intensity monochromatic gamma-ray sources.

Current quantum computers present significant noise, especially as circuit depth and qubit count increase. Prior work has demonstrated that erroneous outcomes exhibit some behavior in Hamming space, enabling improvements in the output distributions of NISQ-era computers. We present HAMMR-L: a principled post-processing technique for improving the fidelity of output distributions by applying Richardson-Lucy image deconvolution on a state graph of measurement results connected by Hamming distance. We show that this preliminary implementation of HAMMR-L outperforms existing cutting-edge Hamming-based post-processors such as QBEEP while being circuit and hardware agnostic, which QBEEP is not. HAMMR-L also demonstrates clear potential for future improvements and we discuss how such improvements might be realized while highlighting the strengths, limitations, and generality of the underlying concept.

The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also capturing thermodynamic evolution – entropy production – within a canonical Hamiltonian framework. Heat transfer at constant volume is analyzed, and the derived thermal conductance matches the universal quantum of heat conductance $G_{Q}$ in the quantum limit. Having a Hamiltonian scheme interpretable in thermodynamic terms, a Schrödinger-like wave equation is formulated whose wavefunction solutions contain the information about the entropy evolution. The results show exact agreement with 'classical' results for non abrupt changes. Finally, comparisons with a pure quantum mechanical treatment of the wave function in an expanding box confirm consistency in quasi-static regimes and reveal adiabaticity breakdown under far-from-equilibrium conditions.

This paper aims to extend the understanding of the mechanism of photo-electrical detection of magnetic resonance (PDMR) in nitrogen-vacancy (NV) centres. This technique is particularly important for development of solid-state quantum computing platforms. In particular, we report on the new insight in the photocurrent (PC) generation and charge cycling in the single NV centre, which is related to PDMR contrast reaching 50% and above. We develop a technique to locate PC related features. We find that electrons generated at the NV centre are stored in interface trap levels and establish that the interface states serve as an amplifier that can be driven by introducing a second laser into our confocal setup. We show that controlling these interface states allows one to significantly enhance the PDMR contrast. We develop a model that consistently explains observed amplification effects even without the application of a bias voltage.

In this paper, we demonstrate an approach to quantum robust control based on the tools of geometric optimal control. The central objects of interest are the sensitivity functions defined as the coefficients in the Taylor expansion of the trajectory with respect to the (unknown, small) parameters which describe the deviation of the actual model from nominal one. In terms of these quantities, we formalize an optimal control problem where one searches for the optimal nominal trajectory which minimizes the size of the sensitivity while taking into account other aspects of the control design such as the energy of the control field. We consider in detail the case of a single qubit with a dephasing Hamiltonian term, and the optimal control problem of obtaining a state transfer by minimizing the weighted sum of the energy of the controlling field and the first order sensitivity. At the limit of a very large weight on the sensitivity, we obtain the optimal control which zeros the sensitivity and minimizes the control field energy. This problem has a rich mathematical structure which enables its solution in terms of elliptic integrals. For this problem, we obtain an explicit solution which is particularly simple and also smooth, avoiding discontinuities which are present in other approaches. We extend the results to the robust control of two quantum bits minimizing cross-talk contamination, as we show that such a problem decouples in two independent one qubit problems.

Optically addressable molecular triplet spins provide a chemically tunable platform for quantum application, but their coherence is often limited by interactions with surrounding spin baths. Here we demonstrate controlled suppression of nuclear-bath-induced decoherence in photoexcited triplet spins of pentacene co-crystallized in high-purity naphthalene single crystals. By hyperpolarizing the proton spin bath through triplet dynamic nuclear polarization (triplet-DNP), magnetic noise generated by the nuclear spins is suppressed, leading to an extension of the electron spin transverse coherence time. Experimentally, we observe a 25% enhancement of the spin-echo decay time with $60\%$ polarization of the proton spin bath. The measured scaling of the spin-echo decay time ($T_2$) with nuclear polarization quantitatively follows the predicted dependence derived from the polarization-controlled nuclear second moment. Both the enhancement and the absolute value of the coherence time are quantitatively reproduced by cluster correlation expansion (CCE) simulations. These results establish nuclear spin hyperpolarization as a general and actively tunable approach to engineering coherence in molecular qubits. This work provides a broadly applicable design framework for high-coherence molecular and solid-state spin systems.

Phase kickback is a fundamental primitive that is used in many quantum algorithms, such as quantum phase estimation. Here we observe that by using information about the controlled unitary, we can replace the controlled unitary with an uncontrolled one at the cost of introducing controlled state preparations. We then show how this modified phase kickback can be used as part of the quantum phase estimation algorithm when the goal is to estimate the phase of an eigenstate whose preparation procedure is known. We prove that this yields an exponential reduction in the number of two-qubit gates for an m-bit phase estimation in the relevant limit. Examples of applications are also presented. Naturally, this can be adapted to any algorithm that uses the phase kickback phenomenon and satisfies the assumptions.

Embedding high-dimensional data into resource-limited quantum devices remains a significant challenge for practical quantum machine learning. In multimodal face anti-spoofing, while linear compression methods such as principal component analysis can reduce dimensionality to accommodate limited quantum budgets, such approaches often lose critical high-order cross-modal correlations due to the loss of structural information. To this end, we propose a hybrid Matrix Product State (MPS)-Variational Quantum Circuit (VQC) framework, where the MPS serves as a structured, differentiable pre-quantum compression and fusion module, and the VQC acts as the quantum classifier. Built upon the low-rank structure controlled by the virtual bond dimension and integrated with a configurable nonlinear enhancement mechanism, this MPS module explicitly models long-range cross-modal correlations while compressing multimodal data into a compact representation matching the quantum budget and improving numerical stability under extreme compression. Experiments on the CASIA-SURF benchmark demonstrate that MPS-VQC achieves accuracy comparable to strong classical neural network baselines with fewer than 0.25M parameters, highlighting the parameter efficiency of tensor-network representations for high-dimensional multimodal data under tight resource budgets. Leveraging the intrinsic compatibility between MPS structures and quantum circuit topology, this framework not only provides a viable technological pathway for efficient multimodal anti-spoofing on NISQ devices but also serves as a stepping stone toward fully quantum implementations of such tasks in the future.

Large language models have recently shown potential in bridging the gap between classical machine learning and quantum machine learning. However, the lack of standardized, high-quality datasets and robust translation frameworks limits progress in this domain. We introduce Q-Bridge, an LLM-guided code translation framework that systematically converts CML implementations into executable QML variants. Our approach builds on a self-involving pipeline that iteratively expands a verified seed codebase into a large-scale dataset, CML-2-QML, integrating verifiable and unverifiable code pairs. The Q-Bridge model is fine-tuned using supervised LoRA adaptation for scalable and memory-efficient training, achieving faithful and interpretable quantum code generation across diverse architectures. Empirical analysis confirms the feasibility of direct CML-to-QML translation and reveals consistent structural alignment between classical and quantum paradigms. Case studies further demonstrate that Q-Bridge can maintain deterministic correctness and also enable creative architectural exploration. This work establishes the first reproducible framework and dataset for LLM-driven quantum code translation, offering a foundation for scalable quantum AI development.

We study nonequilibrium mode selection in dissipative exciton-polariton condensates incoherently pumped through an excitonic reservoir in the presence of pure energy relaxation. For a confined system in which a vortex mode is selected at threshold, we show that energy relaxation qualitatively changes the condensation scenario: as the pump increases, the asymptotic state evolves from a vortex condensate to a rotating mixed state and then to a ground-state condensate. Pure energy relaxation thus destabilizes condensation into excited states and promotes ground-state selection.

The interplay between interlayer coupling and quantum fluctuations governs charge ordering and defect dynamics in Kagome systems, yet these parameters are intrinsically entangled in existing Kagome metals and artificial spin-ice platforms, preventing their independent control. Here we realize a bilayer Kagome frustrated-magnet simulator comprising 1,536 connected spins on D-Wave quantum annealer, in which the effective quantum drive, $\Gamma_{\rm eff}$, and interlayer exchange, $J_{\perp}$, are independently programmable. We observe an interlayer-driven transition from ferroelectric to antiferroelectric Ice-II charge order at a critical coupling $(J_\perp/J_1)^*\approx0.04$, a phenomenon absent in single-layer geometries. Monte Carlo calculations show the transition persists in the classical limit, allowing the experimentally observed critical coupling to quantify the quantum renormalization induced by fluctuations. Applying resulting phase diagram to Kagome charge-density-wave materials places KV$_3$Sb$_5$ and RbV$_3$Sb$_5$ deep within the ordered antiferroelectric regime, while locating CsV$_3$Sb$_5$ near the phase boundary, providing a natural explanation for its metastable $2\times2\times4$ stacking order. We further show that restricting charge-correlation measurements to ice-rule configurations resolves a systematic underestimation of ordering in conventional analyses, enabling direct reinterpretation of resonant X-ray, XMCD, STM and anomalous Hall experiments. Finally, we demonstrate that the same charge-sector reorganization framework explains near-degenerate plateau states in the metallic Kagome spin-ice HoAgGe and yields experimentally testable predictions for nanomagnetic, Kagome-metal and van der Waals frustrated systems. These results establish programmable quantum annealers as scalable simulators of emergent charge order and monopole physics in frustrated quantum matter.

Wave–particle duality is a cornerstone of quantum mechanics, traditionally formulated under definite causal order. We investigate how complementarity is modified when the temporal order of operations is coherently superposed, as in the quantum switch. We show that no universal, state-independent, linear additive complementarity relation exists that combines spatial coherence, path distinguishability, and causal coherence within a common unit-normalized bound. This result follows from explicit extremal constructions in the quantum-switch family: although the three quantities are derived from the same global switch state, the standard spatial duality relation can be saturated while the reduced control coherence is simultaneously maximal. Tracing out the order qubit recovers the standard duality relation at the level of the reduced quanton–detector state, while coherence associated with alternative causal orders remains inaccessible in this reduced description. To characterize this contribution, we introduce causal coherence, defined as the coherence of the reduced order qubit in the causal-order basis. We further show that complementarity admits a state-dependent entropic formulation based on incompatible measurements on the causal degree of freedom, which arises from a universal uncertainty principle and provides a canonical operationally meaningful description. These results show that operational formulations of complementarity can depend on causal structure and cannot, in general, be fully characterized at the level of reduced quantum states alone.

This paper presents classical benchmark simulations of a practical hybrid decoding scheme for parity-encoded spin systems, which is well-suited to the development of quantum annealing devices based on on-chip superconducting technology. We compared the performance of finding the optimal solution using two embedding schemes for emulating all-to-all connectivity from local interactions: the SLHZ scheme, proposed by Sourlas, Lechner, Hauke, and Zoller, and the commonly used minor embedding (ME) scheme. We found that the SLHZ scheme is more efficient than the ME scheme when combined with postreadout classical decoding based on the classical bit-flipping algorithm, although the SLHZ scheme itself is substantially less efficient than the ME scheme.