Papers

The recent development of small-scale quantum networks poses the question of which network-level mechanisms could enable quantum communication to operate at scale in a future Quantum Internet. The question can be answered within a well-established framework where a quantum network is mapped into a classical weighted graph, and communication reliability is assessed using methods from network theory. Previous work relied on this framework to determine sufficient conditions for viable network-wide communication only on special network topologies, such as regular lattices, and to devise communication protocols applicable only to small- and moderate-sized real networks. Here, we overcome both limitations by introducing a family of quantum communication protocols that scale to networks with hundreds of millions of nodes. We show that the competition between increasing communication distance and path redundancy determines their large-scale behavior, and that degree heterogeneity can provide sufficient redundancy to sustain communication in small-world networks. These conclusions are supported by a systematic analysis of both real network topologies and synthetic networks, and an analytical treatment in the limit of infinitely large random scale-free graphs.

We show that the standard power-series method described in many textbooks of quantum-mechanics and quantum-chemistry is simpler and more powerful than the wavefunction approach proposed by Ikhdair and Sever [Cent. Eur. J. Phys. 6, 697 (2008)]. As illustrative examples we choose the pseudoharmonic and Kratzer-Fues potentials already treated by those authors.

Quantum reinforcement learning (QRL) is a promising approach to learn effective decision strategies across several applications with stochastic environments. Instead of directly modeling the random variables that govern these environments, existing QRL architectures indirectly approximate environment behavior by estimating expected outcomes, which limits their expressive power and adaptive potential. Overcoming such challenges requires a novel QRL approach that exploits the distributional nature of quantum computers to directly model environment random variables as quantum state distributions. Hence, in this paper, a novel framework dubbed quantum-native reinforcement learning (QnRL) is proposed. QnRL is a distributional RL framework that learns conditional distributions naturally in Hilbert space via superimposed and entangled quantum states. Thus, QnRL can directly model the behavior of stochastic learning environments via the natural properties of quantum systems. QnRL accomplishes this via a novel, proposed quantum amplitude kickback (QuAK) algorithm that enables comparing the $n$-th power of the $m$-th moment of multiple superimposed distributions. It is theoretically proven that a conditional action policy distribution is distilled from the moments of a quantum generative model entirely within Hilbert space via QuAK, and optimized via QnRL. This complex distribution composition is also shown to provide extra dimensions for expressing environment correlations that are unknown to purely classical and classically-sampled quantum distributional models. Experimental results across diverse environments show that QnRL achieves up to $82.9\%$ higher evaluation scores, with up to $94.3\%$ fewer parameters on average, more accurately estimates the expected return for unseen observations, and better adapts to varying stochastic conditions compared to the baseline.

A well-known model in game theory, the Volunteer's Dilemma describes a group of $n$ players who decide whether to volunteer for a collective benefit at a personal cost, or to abstain and risk forfeiting the benefit altogether. A quantum version of this dilemma, developed within the Eisert-Wilkens-Lewenstein framework, allows each player to manipulate one qubit of a shared entangled state, leading to symmetric Nash equilibria with higher expected payoffs than in the classical game. Existing analyses, however, assume maximal entanglement, which is experimentally demanding for hardware-constrained quantum systems. Within the same framework, we introduce a generalized Quantum Volunteer's Dilemma with a tunable entanglement parameter $\gamma$ and study the extent to which equilibrium behavior depends on the level of entanglement. We derive explicit conditions relating $\gamma$, the number of players, and the players' strategies under which symmetric Nash equilibria exist, focusing on two canonical strategy profiles: one for $2\leq n\leq 9$, and one for even $n$. We find that maximal entanglement is not required to sustain symmetric equilibria. Instead, equilibrium behavior persists above a threshold value, which we compute analytically in both cases. We also demonstrate that the threshold value directly depends on system size.

In this paper the Clifford groups of general multipartite quantum systems with configuration space $\mathbb{Z}_{n_1}\oplus\cdots\oplus\mathbb{Z}_{n_k}$, $k\geq 1$ are studied. It is known that the Clifford group is a natural semidirect product provided the dimension $N=n_1\cdots n_k$ of the corresponding Hilbert space is an odd number. For even $N$ special results on the Clifford groups are scattered in the mathematical literature, but they do not concern the semidirect product structure. Using the relation of generators of the associated symplectic group $\mathrm{Sp}_{[n_1,\dots,n_k]}$ we prove that for even $N=n_1\cdots n_k$ both Clifford group and the projective Clifford group are natural semidirect products if and only if $N$ is not divisible by four.

We prove that every rank-2 bipartite entangled state is already steerable with projective measurements, closing the first possible gap between entanglement and Einstein-Podolsky-Rosen (EPR) steering. In arbitrary finite local dimensions, any rank-2 entangled state is projectively steerable in at least one direction; when the effective dimensions are equal, steering is two-way. The argument is geometric: a rank obstruction forces some projective outcome on the larger local system to reach the boundary of the trusted-state space. From this boundary contact, a neighboring measurement produces a linear displacement that cannot be reproduced by a local-hidden-state model, because positivity only permits a quadratic filling into a kernel direction. This same block witnesses partial-transpose entanglement. If the contact is degenerate, a Schur complement removes one product layer and reduces the problem to a lower-rank entangled residual; each such reduction lowers the rank, so the recursion terminates. More broadly, we derive a directional rank criterion: if an $m\otimes n$ entangled state $\rho$ satisfies $\rank\rho\le 1+\lfloor(m-1)/(n-1)\rfloor$, then it is projectively steerable from $A$ to $B$. Since counterexamples already occur at rank three, rank two is the unique mixed rank for which entanglement guarantees projective steering, and the proof provides an operational certificate based solely on the support and kernel of the density matrix.

This paper investigates the Markovian dynamics of open two-state quantum systems defined over the real numbers (rebits). Two main objectives are pursued. First, we present a comprehensive classification of Markovian rebit quantum channels, i.e. one-parameter semigroups of completely positive, trace-preserving (CPTP) maps acting on the rebit state space. We show that a full characterisation of their action can be achieved and that describing these channels as solutions of the GKSL equation allows us to explicitly identify the associated Lindblad generators and conditions for complete positivity. Second, we present an original application of this classification to colour perception. Using a recent model in which perceived colours arise from Lüders measurements on the rebit state space, we show how chromatic distortion induced by a non-neutral illuminant can be modelled by a Markovian rebit channel that progressively diminishes colour distinguishability. Other types of channels could be used to study colour vision deficiencies. These phenomena are illustrated by simulations on digital images, highlighting the relevance of rebit Markovian dynamics in modelling colour vision.

We analytically evaluate the efficiency of continuous dynamical decoupling (CDD) to curb decoherence in generic qubit setups where diverse sources of noise can be present. Previous theoretical approaches to CDD have mainly focused on its potential to cope with longitudinal fluctuations. Here, the basic scenario tackled with CDD is generalized. Apart from dealing with pure dephasing induced by diagonal noise, we consider the impact of transverse fluctuations, usually present in the practical arrangements. In particular, the implications of anisotropic noisy inputs are studied. Additionally, we analyze the role of the fluctuations in the dressing of the qubit by the CDD field of control: since the driving field is usually switched on through linear ramps of its characteristic parameters, the associated dressing of the original states can be described in terms of noisy Landau-Zener transitions. In our approach, based on a sequence of unitary transformations, the noise entering the system is cast into effective stochastic terms whose spectral characteristics are dependent on the driving parameters. This description allows the design of strategies to mitigate the impact of the fluctuations using controlled changes in the effective-noise properties. Significant robustness of CDD against the generalization of the basic scenario can be achieved through an appropriate choice of the parameters of control.

We study a disorder-free variant of the Sachdev-Ye-Kitaev (SYK) model with dissipation within the Gorini-Kossakowski-Sudarshan-Lindblad formalism. By utilizing the integrability of the clean SYK model, we derive an exact solution in a spectrum-resolved form, i.e., the eigenvalues and corresponding projection superoperators of the Liouvillian for arbitrary system size $N$. We determine the scaling of the gap that governs the long-time decay of the two-point correlation functions. Importantly, the gap does not vanish in the dissipationless limit when the thermodynamic limit is taken first, despite the integrability of the model. This phenomenon, known as anomalous relaxation, suggests a possible connection with chaotic dynamics and quantum Ruelle-Pollicott resonances. We also find several spectral features, such as transitions in the Liouvillian spectrum from complex to real eigenvalues with increasing dissipation strength, as well as the convergence of the dissipative form factor to the spectral form factor in the dissipationless limit. These findings indicate that the present model offers a useful platform for exploring nontrivial open dynamics of many-body quantum systems.

In this work, we propose an operator-splitting variational quantum algorithm, termed Dirac-sVQA, for simulating the nonlinear Dirac equation (NLDE). The main difficulty arises from the state-dependent nonlinear interaction, its time-discrete update depends explicitly on the intermediate spinor state and, in general, cannot be implemented as a fixed state-independent unitary circuit. To address this difficulty, we decompose the NLDE evolution into a structured linear Dirac substep and a nonlinear variational correction. The linear substep is implemented by a spinor-Fourier Dirac propagator on a joint position-spin register, preserving the spin-momentum coupling and mass-induced spin evolution of the Dirac operator. The nonlinear correction is reformulated as a measurement-based variational update through a small set of overlap, self-channel, and cross-channel observables. We provide the corresponding quantum circuits and derive measurement-aware resource and complexity estimates. Numerical experiments in several nonlinear regimes show that Dirac-sVQA accurately captures both the total density and the componentwise spinor dynamics, agrees well with classical Fourier pseudospectral splitting solutions, and exhibits stable error behavior over time. These results provide numerical evidence for the feasibility of operator-splitting variational quantum simulation for nonlinear relativistic wave equations.

Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

Electrical transport and magnetic measurements have been made on UTe2 under pressure P up to approximately 16 GPa to determine the superconducting transition temperature Tc vs P phase diagram in the high-pressure tetragonal phase. Superconductivity emerges near 5 GPa, coincident with the orthorhombic to tetragonal phase transition; in the tetragonal phase, Tc reaches a maximum value of approximately 4 K at 6 GPa and then decreases with P and appears to vanish near 18 GPa. Tetragonal UTe2 has a relatively small upper critical field Hc2(0) $\approx$ 1.2 T at 5.3 GPa, smaller than the Pauli paramagnetic limit, and is orbitally limited with a coherence length $\xi$tetra $\approx$ 16.5 nm. This small value of Hc2(0) favors more conventional superconductivity; in contrast, the large values of Hc2(T) for orthorhombic UTe2 exceed the Pauli paramagnetic limit in all three crystallographic directions and have been attributed to unconventional superconductivity, widely believed to involve spin-triplet pairing. The temperature-pressure phase diagram of UTe2 shows a striking dichotomy: a narrow, fragile, unconventional superconducting region in the orthorhombic phase vs a broad, robust, and more conventional superconducting dome in the tetragonal phase. This dichotomy is consistent with the proposal that U-dimers, present (absent) in the orthorhombic (tetragonal) phase, may play a role in spin-triplet superconductivity of orthorhombic UTe2. In the tetragonal phase, the normal-state electrical resistivity $\rho$(T) exhibits metallic behavior with a knee between 200 and 240 K that depends weakly on P and most likely marks the onset of a transition to a magnetically ordered phase that coexists with superconductivity.

Negatively charged boron vacancy ($V_B^-$) centers in hexagonal boron nitride ($h$-BN) have attracted wide-range interests owing to their van der Waals lattice and their potentials for $in$-$situ$ quantum sensing. Here we propose and experimentally demonstrate an all-optical strategy for wide-field magnetometry based on $V_B^-$ centers. This strategy exploits the magnetically sensitive ground-state level anti-crossing (GSLAC) of $V_B^-$ centers, which induces a strong electron spin transition between $m_S = 0$ and $m_S = -1$ states, enabling microwave-free magnetic field measurement. By monitoring the shift of GSLAC feature, the external magnetic field can be precisely determined. Using this technique, we demonstrate all-optical wide-field imaging of near-field DC magnetic field distribution from current-carrying circuits over an area of around 42 $\times$ 21 $\mu$m$^2$. An estimated photon shot-noise-limited sensitivity of 67.1 $\mu$T/$\sqrt{\text{Hz}}$ is achieved for a single pixel, which is an approximately threefold improvement over the ODMR method, along with a spatial resolution of about 1 $\mu$m per pixel. Our approach expands the applicability of $V_B^-$ centers in quantum sensing, paving the way for robust and convenient magnetometry under extreme conditions.

We extend the classical ideas of the Partial Information Decomposition (PID) to the quantum domain and quantify unique, redundant, and synergistic quantum information. We show that unique information plays the central role in quantum error correction codes: any erasure-correctable subset of encoding qubits must contain zero unique information. Synergistic information between two disjoint subsets of encoding qubits appears when a logical operation is supported on the whole set but not on the subsets separately. In a different application of our PID, we show that redundant quantum information is the crucial feature of the decoherence mechanism proposed by Zurek et al. to explain how the classical world emerges out of the quantum world.

Unambiguous state discrimination (USD) measurements are attractive because outcomes are either marked as conclusive (i.e., error free) or inconclusive (i.e., erased). We study affine filtering measurements, a structured variant of USD for decoding classical linear codes over pure-state classical-quantum channels, where a conclusive outcome identifies an affine subspace containing the transmitted codeword and an inconclusive outcome is treated as an erasure. For a group-covariant indexing of pure-state codewords, we show that the optimal design of affine filtering measurements is a semidefinite program that can be reduced to a linear program via character-based diagonalization. We use the resulting measurement to build a quantum decoding framework for local codes, and we demonstrate (via simulations on regular LDPC codes from Gallager ensembles using single parity check local constraints) that affine filtering based decoding can outperform symbol-wise USD and symbol-wise pretty good measurement based decoding methods on i.i.d. pure-state channels. In an independent and concurrent work, Buzet and Chailloux study similar fine-grained USD measurements for symmetric families of states. Their focus is on the code-agnostic setting whereas our focus is on code-aware constructions and decoding.

Many-body GW-Bethe-Salpeter equation calculations are essential for accurate simulations of electronic structure and optical properties in modern low-dimensional nanomaterials. However, these methods are computationally demanding and can exhibit localized numerical instabilities or convergence failures that are difficult to detect within high-throughput workflows. We introduce an agent-guided multi-fidelity framework for correcting GW-Bethe-Salpeter excited-state landscapes in strained MoS2-WS2 bilayers. Across stacking registries, strain branches and reciprocal-space samplings, the workflow identifies spike-like excursions, near-zero-gap collapse and cross-fidelity inconsistencies associated with fragile long-wavelength dielectric screening. A structural agent evaluates calculations by assigning confidence weights and selectively using a small number of high-accuracy reference points. Machine learning models then transfer information across related systems and apply Gaussian process corrections to recover improved quasiparticle gaps and exciton binding energies, with calibrated uncertainty estimates. The approach corrects numerically induced artifacts without erasing physical strain dependence and substantially improves agreement with higher-fidelity references relative to a no-agent baseline. These results show that reliable surrogate learning for excited-state materials requires explicit diagnosis of numerical fragility, not direct interpolation of raw first-principles data points. The proposed framework is readily transferable to other optoelectronic nanomaterials characterized by strong quantum confinement, such as quantum dots, nanoribbons, layered two-dimensional semiconductors, and hybrid perovskite nanostructures.

Von Neumann's Hilbert-space formalism of quantum mechanics constitutes a logico-physical theory of observed or measured reality. Imposing the logical constraint of Booleanity, essential for objectively shareable descriptions among observers, reveals the physical meaning of classicality inherently embedded within the formalism itself. Starting from this consideration, the present work reformulates the quantum-classical transition via Hilbert-space classical mechanics (HCM), grounding classicality not in the dynamical limit ($\hbar \to 0$), but in the logical constraint of Booleanity (i.e., the mutual commutativity of preparable states). Within this state-centric framework, applying the Einstein-Podolsky-Rosen (EPR) criterion alongside locality and measurement independence reduces standard quantum mechanics to the HCM model. Thus, the EPR argument reveals not quantum incompleteness, but the implicit classical boundaries of its own premises. To resolve this impasse, we articulate a nuanced quantum ontology grounded in a fundamental structural bipartition between the observational environment and the observed object, which accommodates three categorical distinctions: ontic, processional, and tropos-existential. Building on this, we propose a criterion of objective reality wherein descriptive objectivity is treated as merely a sufficient condition for physical reality. This addresses the historical Bohr-Einstein ambiguity, enabling the quantum formalism to ontologically unify objective measured phenomena and non-objective observed interference within a context-dependent framework.

Deep learning offers a powerful approach to quantum many-body problems via neural network wavefunctions, but their optimization remains a severe bottleneck. Existing optimization methods, including natural gradient descent and stochastic reconfiguration, suffer from spectral gap-dependent convergence that limits their effectiveness on systems fraught with competing orders and nearly degenerate ground states, such as frustrated magnets and strongly correlated electron materials. Here, we introduce Projected Inverse Iteration (PII) by re-framing the ground-state search as an eigenvalue problem. PII achieves rapid, gap-insensitive convergence while preserving the favorable polynomial computational scaling of stochastic reconfiguration. Demonstrated on challenging two-dimensional spin systems, including the highly frustrated $J_1$-$J_2$ model, PII outperforms standard optimization techniques and presents a promising algorithmic strategy for discovering complex quantum states in the presence of small spectral gaps. More broadly, PII can be interpreted as a novel natural gradient method tailored for eigenvalue problems, opening up its application to related challenges within deep learning.

Every Ising energy is a known linear function of measured spin features, yet the standard QAOA estimator discards this structure. We introduce Hamiltonian-Guided Leverage Embedding (HGLE), which projects Hamiltonian coefficients onto the leading subspace of a measured feature matrix. The fraction of coefficient norm outside this subspace yields a deterministic, same-batch certificate bounding how much compression distorts the objective. This certificate is minimax-tight - no linear estimator on the same subspace achieves smaller worst-case error. We establish four results beyond the pointwise certificate. First, a held-out pilot projector with summable failure allocation gives population-distortion intervals valid over an unbounded adaptive sequence. Second, coefficient projection strictly reduces estimator variance, with the reduction equal to the variance of the discarded component. Third, one SVD basis simultaneously certifies Kobservables, defeating the rank-1 degeneracy of single-Hamiltonian compression. Fourth, the compression quality is governed by graph topology through the expected Gram matrix.

Coupling identical quantum emitters to a photonic integrated circuit (PIC) is a key step for scaling up emitter-photon interfaces for quantum science and information processing. Neutral atoms are attractive candidates due to their indistinguishability and controllability. However, experimental realizations of efficient atom trapping on a PIC while achieving strong single atom-photon coupling has so-far remained elusive. Here, we demonstrate near-deterministic single-atom loading on a microring resonator circuit, reaching single-atom cooperativity parameter C > 1 for strong coupling in cavity quantum electrodynamics. We utilize a precision optical conveyor belt, formed by a moving optical lattice in an optical tweezer, to steadily deliver trapped atoms onto a PIC. By continuously monitoring the transmission of probe photons through the circuit, which is sensitive to the proximity of single atoms near a microring resonator, we detect mean occupancy of 1.5 from 70 occupied lattice sites in a conveyor-belt transport of 4 nm position reproducibility. Based upon real-time feedback, we deterministically transfer the delivered atoms into a stationary trap on the microring, achieving 82% (18%) probability of single-(two-)atom transfer. Our technique can be extended to deterministic, highly efficient atom array assembly, providing a scalable route for neutral atom integration with PICs of complex functionalities.

We investigate the dynamical generation of entanglement in a system of two superconducting qubits coupled through a parametrically driven longitudinal interaction. Using Floquet theory and exact numerical simulations, we analyze the time evolution of the system initialized in a separable ground state. Our results reveal a nontrivial mechanism for entanglement generation, fundamentally distinct from the conventional resonant excitation to an entangled eigenstate. We show that this mechanism emerges when two initially separable eigenstates are mixed by the periodic driving under multiphoton resonance conditions. Since the effect cannot be captured within a standard rotating-wave approximation, we employ generalized Van Vleck near-degenerate perturbation theory to derive an effective analytical description. Within this framework, we demonstrate that the sustained entanglement originates from the hybridization of the dominant Floquet states, namely those with the largest overlap with the initial ground state. Furthermore, the degree of entanglement can be efficiently controlled through the driving amplitude. In particular, for specific amplitudes, the entanglement is fully suppressed. We term this phenomenon as coherent destruction of entanglement.

Direct evidence of exciton condensation in semiconductor heterostructures remains elusive. Here we propose charge transport of doped carriers as a probe of exciton condensation in transition-metal dichalcogenide heterostructures and identify distinct experimental signatures. First, condensation suppresses the phase space for carrier scattering, leading to a reduction in resistivity, that provides a general diagnostic of exciton condensation. Second, in heterostructures with a tunable solid-state Feshbach resonance, condensate-induced hybridization between doped carriers and trion bound states qualitatively modifies transport. In particular, near resonance, this hybridization yields a negative effective mass and a corresponding sign reversal of the Hall resistivity. These results establish charge transport as a promising route for detecting and characterizing exciton condensation in semiconductor heterostructures.

Heisenberg's uncertainty principle is a cornerstone of quantum mechanics, marking a decisive departure from classical physics. Conceived almost a century ago through a thought experiment showing that measuring an electron's position inevitably disturbs its momentum, it began as a deceptively simple idea that sparked countless studies and grew into the rich research field it is today. This review traces its development into a spectrum of mathematical formulations – known as uncertainty relations – and explores their interconnections and wide-ranging applications. We highlight its central role in quantum metrology, where it underpins strategies for extracting information from quantum systems with ever-increasing precision, and its links to multiparameter estimation and squeezed states. This review, dedicated to the centenary of the uncertainty principle, reflects on how it has deepened our understanding of quantum theory and driven practical advances, and looks ahead to a century poised for further surprising and transformative discoveries.

Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.

Producing high-fidelity magic states using the smallest possible number of physical qubits and operations stands as a very important challenge to achieve fault-tolerant quantum computation at scale. Besides emerging proposals for alternative methods such as cultivation, magic state distillation remains essential for achieving very low error rates. Known distillation protocols are usually built through quantum codes derived from triorthogonal matrices. Here, exploiting the specific noise structure present in magic state distillation protocols, we show that classical error-correcting codes offer a simpler framework for deriving these protocols. This formulation is particularly well suited to systematic numerical and analytical studies of distillation protocols involving a fixed number of qubits. Specifically, we use a SAT solver to derive a series of no-go theorems that relate key figures of merit, including the number of qubits and the factory distance. In particular, considering the standard implementation as a circuit of Z-diagonal Pauli product rotations followed by measurements, we show that no $T$-to-$T$ distillation protocol on fewer than eight qubits can exceed distance 3, and no $T$-to-$\mathrm{CC}Z$ protocol distance 2. Our results also include new such distillation protocols with the smallest number of qubits for a given distance in the literature, namely distance 4 and 5 $T$-to-$T$ protocols supported on 10 and 11 qubits, as well as distance 3 and 4 $T$-to-$\mathrm{CC}Z$ distillation protocols supported on 9 and 10 qubits. Finally, going beyond unitary circuits by recycling qubits through mid-circuit measurement and reinitialization, we obtain an implementation of the distance-5 $49T$-to-$1T$ protocol on only 5 active qubits.

Quantum combinatorial optimization offers theoretical advantages for complex financial modeling, but physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology. This study presents a hardware benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA) for a hybrid Mean Variance and Conditional Value at Risk (CVaR) portfolio objective. By implementing a novel classical quantum hybrid proxy matrix to bypass the CVaR auxiliary qubit bottleneck, we map up to 16 assets from the NIFTY 50 index onto an IBM heavy hex processor. We systematically quantify algorithmic resilience to the "SWAP tax" incurred during routing. Empirical results reveal a critical operational trade-off: WS-QAOA provides exact theoretical mapping but suffers catastrophic hardware decoherence due to exponential nonlocal gate overhead. Conversely, HE-VQNN preserves hardware coherence but lacks the mathematical expressibility to capture dense tail risk asset correlations. This study exposes the limitations of dense financial optimization on current architectures forces an nonviable choice between algorithmic inexpressibility and hardware decoherence. This is indicative of a deeper limitation as to what can and cannot be done with NISQ computers lacking in all-to-all connectivity.

Correlated longitudinal noise can be partially converted into common-mode fluctuations in an oddparity two-qubit subspace. We analyze an encoded logical qubit formed by the states in two coupled fluxonium qubits. Projecting the exchange-coupled two-qubit Hamiltonian onto this subspace yields an effective logical Hamiltonian in which the exchange interaction drives XL rotations and the qubit detuning drives ZL rotations. We model correlated two-levelsystem (TLS) noise by using longitudinal stochastic processes with finite memory time and evaluate encoded-gate performance through the average gate fidelity. Within the projected model, positive spatial noise correlation suppresses the differential fluctuation and thereby improves the fidelity of encoded logical gates. We further compare Gaussian Ornstein-Uhlenbeck, Markovian, and randomtelegraph noise models and examine the role of logical dynamical decoupling. These results identify a noise-adapted control mechanism for odd-parity encoded operations in coupled fluxonium devices and motivate future multilevel simulations including leakage and pulse-level constraints.

QBism recasts quantum theory as a normative framework for an agent's probability assignments, with the Born rule taking the form of a consistency condition known as the Urgleichung. Motivated by this perspective, qplex theories provide a broader class of probabilistic models in which the sets of valid states and measurements are constrained by QBist-inspired geometric conditions. While qplexes have been extensively studied for single systems, their implications for bipartite correlations remain largely unexplored. In this work, we investigate bipartite correlations in qplex theories by expressing joint expectation values as inner products between suitably defined $C$-vectors. This geometric formulation allows Bell-type inequalities to be studied as optimization problems over qplex-compatible probability assignments. We first analyze the CHSH scenario and show that the shared inner-product structure of the $C$-vectors restricts the maximal value to the Tsirelson bound $2\sqrt{2}$. We then turn to the three-outcome CGLMP inequality $I_{2233}$ and find that the same qplex-derived norm and inner-product constraints allow a violation of up to $\leq 2+2\sqrt(3)/3 \approx 3.1547$ versus the quantum maximum of $\approx 2.8729$, thereby exhibiting super-quantum correlations. These results show that qplex geometry captures enough structure to reproduce an important quantum bound in the two-outcome case, but not enough to recover the full set of quantum correlation constraints. The analysis therefore suggests that additional principles are needed to complete the QBist reconstruction of quantum theory.

The implementation of high-fidelity quantum gates for spin qubits requires accurate control of exchange interactions between electrons confined in quantum dots, but pulse distortions can limit this control accuracy. Although linear-dynamical distortions can be compensated for by appropriately convolving the control signal, determining the necessary convolution requires detailed knowledge of the distortion's transfer function, and therefore the calibration of numerous parameters. Alternatively, control pulses can be designed to have a net-zero time integral canceling out linear-dynamical pulse distortions. We generalize net-zero pulse designs to quasi-zero pulses allowing net-positive but reduced time integrals. Using these pulse designs, we systematically develop complete gate sets for exchange-only qubits, and study the resulting tradeoffs between pulse duration, fidelity, and the required number of tunable parameters, both in simulation and experiment. We benchmark the optimized gate pulses on Intel's Tunnel Falls six-dot device and show they achieve fidelities similar to those obtained with a full filtering approach, with identical pulse durations and fewer tuning parameters. This reduction in complexity opens the door to fast and easily automated calibration schemes compatible with large-scale commercial quantum devices.

Quantum metasurfaces comprised of subwavelength atomic arrays emerged as a promising platform for enhanced atom-photon interaction. However, realizing such a system with solid-state emitters has been considered impractical due to strong inhomogeneous broadening, which was expected to suppress the photon-mediated interactions that underpin collective emission. Here we report the observation of collective emission from subwavelength arrays of silicon-vacancy centres in diamond – solid-state emitters whose inhomogeneous broadening exceeds the natural linewidth by two orders of magnitude – demonstrating that collective effects such as resonance shifts, modified decay rates and directional coherent emission survive this disorder. A crucial enabling element is the implantation of a high density of silicon ions at each array site. This creates so-called superatoms, local ensembles that probabilistically achieve frequency matching across the array and enhance the collective response. We support our observations with a theoretical analysis explaining the mechanisms that preserve the collective effects even in the presence of inhomogeneity. These observations have direct implications for the realization of subwavelength arrays in any solid-state system, paving the way for quantum-emitter metasurfaces that are naturally integrated into nanophotonic environments.