Papers

We show that a spin-1/2 particle can behave as if it were spin-$s$, and generate $2s+1$ spots in a Stern Gerlach measurement (albeit with a smaller gyromagnetic ratio). This arises from some subtle properties of effective Hamiltonians and Hamiltonians with constraints. Examples of implications of the effect in condensed matter are discussed. We also give some simple non-perturbative bounds for a system subjected to strong constraints.

Excitation of trapped-ion hyperfine qubits with fast optical Raman pulses enables faster-than-trap-period entangling gates with qubits of long coherence time for practical quantum computation. Achieving high-fidelity fast two-qubit gates requires high-quality spin-dependent kicks (SDKs), which form their fundamental building blocks. Here, we characterize the control parameters (including Raman frequency difference, pulse arrival times, Lamb–Dicke parameter, temperature, pulse width, and SDK time) that maximize the performance of single-ion SDKs for protocols compatible with performed experiments involving a small number of fast pulses. We demonstrate through analytical methods and numerical simulations that, within the model commonly used for infidelity optimization, finite pulse duration is the dominant source of error, exceeding the contribution of secular motion by orders of magnitude for nanosecond-scale SDKs. Low infidelities – below $10^{-3}$ for schemes with $\gtrsim10$ fixed-amplitude, equispaced, picosecond pulses – are achievable in SDK times on the order of nanoseconds. These results provide quantitative design rules for achieving competitive SDK fidelities with current pulsed-laser technology, laying the foundation for sub-microsecond trapped-ion quantum entangling operations.

The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, translation-invariant and gauge-invariant quasifree states on doubly infinite fermionic chains, and give explicit formulas for a wide range of regularized Rényi divergences between such states, including $(\alpha,z)$, log-Euclidean, geometric, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and for any fixed $\alpha$, the regularized Rényi $(\alpha,z)$-divergences give different regularized values for different $z$ parameters in general. We also generalize a previous construction from [Bunth, Maróti, Mosonyi, Zimborás, Lett.~Math.~Phys.~113:(7), 2023] to the case of multiple modes per lattice site to obtain a large class of states exhibiting super-exponential decay of the discrimination error probabilities.

The rapid development of quantum computers and sensors urges for the development of a quantum Internet capable of transmitting quantum bits over long distances. Photons used for quantum data transfer are fragile over time and sensitive to their environment, so that they cannot be directly used over long distances. To remedy this problem, long distance paths are segmented into shorter links and entangled pairs of photons are distributed over these links and swapped to create end-to-end entangled pairs over long distances, eventually used for teleportation. In this paper, we develop an existing protocol taking account of fidelity and imperfect memories. We shorten the execution time and thus increase its link success probability creating the so-called Locally Heralded Distribution (LHD). It turns out that the proposed protocol outperforms some previous protocols. We benchmark through simulation the performances of protocols considered in this paper by using a blind entanglement protocol as a baseline.

Single electron spins can be used to encode and process information in semiconductor quantum devices. Progress has been hindered by materials challenges, such as the small energy splitting between low-lying valley states and hyperfine coupling to nuclear spins. Here we use density functional theory to optimize the valley splitting and spin dephasing time in realistic Si/SiGe heterostructures. Reductions in the Si quantum well width generally increase the valley splitting. However, in narrow quantum wells, a larger fraction of the electronic wavefunction resides in the SiGe buffer layers, which increases the hyperfine coupling with spinful $^{73}$Ge. Our work shows that Si/SiGe heterostructures with 3~–~4~nm wide quantum wells and $^{73}$Ge and $^{29}$Si concentrations of 50 ppm should support average valley splittings $E_{v}$~$>$~500~$\mu$eV and spin dephasing times $T_2^*$ exceeding 15~$\mu$s assuming an effective quantum dot area of 700 nm$^2$. In addition, sharper Si/SiGe interfaces in general result in larger valley splittings and longer spin dephasing times.

Quantum batteries modeled as two-qubit systems coupled to Markovian thermal reservoirs have been shown to benefit from measurement-assisted charging, where projective measurements enhance the charging rate at an infinite thermodynamic resource cost. In this work, we consider weak, continuous measurements implemented via quantum point contact detectors (QPC), which enhance the charging rate at a definite and quantifiable resource cost. We analyze three measurement configurations namely, a single QPC, two independent QPCs, and a series-coupled (coherent) two-QPC scheme, and study their effect on the steady-state charging rate, defined as the rate of energy flow from the charger qubit to the battery qubit, relative to the unmeasured baseline. We find that the charging rate enhancement is non-monotonic as a function of the temperature gradient and potential gradient required to drive the QPCs, exhibiting a plateau of near-optimal enhancement. Comparing the three configurations, the plateau of optimal enhancement contracts toward lower temperature and chemical potential for both the cases with two QPCs compared to the single QPC case. The coherent measurement further shows a lowering of the resource requirement relative to the two independent QPC case for achieving the same enhancement. The hierarchy is coherent greater than two independent QPCs which is greater than single QPC with respect to both the magnitude of the charging rate enhancement and the minimization of measurement resources.

We experimentally demonstrate a non-linear dependence of the spin noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin noise spectroscopy (SNS) near the D2 transition of rubidium, a quadratic spin noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in non-interacting ensembles. This non-linear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross-correlations due to resonant dipole-dipole interaction (DDI) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.

This work studies trainable quantum spectral models (QSMs) for solving linear partial differential equations (PDEs). Instead of learning solutions directly in physical space, QSMs learn the inverse differential operator in a spectral representation, embedding prior knowledge of the equation's natural basis. We systematically study the expressibility and trainability of several QSM architectures, ranging from near-diagonal to fully parameterized unitaries. In particular, we introduce a family of richer spectral models that interpolate between purely diagonal operators and fully mixing unitaries through a parameterized mixer controlled by $\epsilon$. Our results reveal an intermediate regime, typically around $\epsilon \approx 0.5$, where models achieve the best tradeoff between expressibility and trainability. Beyond this threshold, increased circuit complexity degrades convergence without improving accuracy. Among the architectures considered, models inspired by the inverse step of the Harrow-Hassidim-Lloyd (HHL) algorithm achieve the fastest training convergence while maintaining high solution fidelity. Numerical experiments on the (variable-coefficient) Poisson and Helmholtz equations show that trainable operations in the spectral basis outperform standard variational quantum circuits acting directly in the computational basis. These advantages appear through faster convergence, more stable gradients, and more accurate recovery of the reference solution spectrum, particularly through stronger suppression of spurious high-frequency components, even when the operator is not exactly diagonal in the chosen spectral basis. Our results identify operator-aware spectral representations as a promising route toward trainable and physically grounded quantum methods for scientific computing.

Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset.

In the presence of spin-orbit coupling and in geometrically frustrated materials, a noncollinear treatment the magnetization density is essential. However, in density functional theory most exchange–correlation functional approximations were originally developed for locally collinear magnetization. Many practical approaches to noncollinear DFT have emerged over the past decade. However, a first-principles connection between widely used semilocal collinear functionals and their noncollinear generalizations remains lacking. In this work, a locally exact relation between collinear and noncollinear exchange–correlation functionals is derived at the level of gradient expansions within a $u(2)$ matrix representation of the energy functional. Within this framework, collinear semilocal variables naturally acquire distinct dependencies on transverse and longitudinal magnetization gradient components. The widely used Scalmani–Frisch scheme emerges as a first-order approximation. The transformation of collinear functional derivatives to noncollinear space is implemented through numerically robust $SU(2)$ rotations. A consistent description of local magnetic torques is demonstrated for the prototypical spin-frustrated Cr$_3$ cluster. The approach further extends to fully nonlocal functionals and provides a direct route towards numerically stable relativistic response calculations. The influence on magnetic properties in presence of spin-orbit coupling is illustrated through calculations of hyperfine couplings in the high-spin ground states of uranium and the uranium ion.

Electrons floating in vacuum provide a clean platform for quantum information processing owing to their isolation from material defects. In particular, electrons on solid neon have emerged as a promising qubit platform because of their potentially long coherence times. Here, toward spin-qubit realization, we couple a single electron on solid neon to a magnetic-field-compatible superconducting NbTiN nanowire resonator. We realize a charge qubit and demonstrate microwave readout and coherent control, with Rabi frequencies up to 76 MHz, an order of magnitude larger than in previous studies. Under strong driving, we observe a qubit frequency shift from nonlinear interactions with the intense microwave field. Deterministic electron trapping at an intended position remains challenging due to solid neon surface roughness; we characterize the electron's position from its differential coupling to distinct electrodes. Although not trapped at an intended position, our estimates indicate that spin-qubit demonstrations remain feasible.

We study discrimination problems generated by the same basic Haar-random measurement mechanism at two observational levels. First, we derive an explicit expression for the type-II error in the task of discriminating a Haar-random measure-and-prepare channel from the identity channel $\mathbb{I}$, using a coherence-sensitive entangled tester. Second, after passing to the induced classical measurement records, we compare two random measurement models: one induced by a single collective unitary of the form $U^{\otimes (n_1+n_2)}$ with $U\in U(d)$, and another induced by independent local unitaries $U_1^{\otimes n_1}\otimes U_2^{\otimes n_2}$. For the associated Haar-averaged aggregate histogram laws, in which the block of origin of each count is not retained, we obtain closed-form formulas and quantify their discrepancy through the total variation distance. We derive asymptotic expressions in the fixed-$N$, large-$d$ regime, the fixed-$d$, large-$N$ regime, the sparse joint-scaling regime $N=o(\sqrt d)$, and the critical scaling regime $N/\sqrt d\to c$. We also identify the block-resolved pair-of-histograms law, showing that the aggregate total variation distance is a coarse-grained lower bound on the distinguishability available when block labels are retained.

While the interface between strong-field physics and quantum optics offers a unique regime for combining extreme nonlinearity with quantum optical resources, its potential for generating non-classical states of light remains largely unexplored. Standard protocols for generating optical Schrödinger cat states, such as photon subtraction from squeezed light, are inherently limited in the achievable macroscopicity of the state and its scalability. In this work, we bridge this gap by demonstrating that above-threshold ionization driven by bright squeezed light provides a strong-field analogue of photon subtraction, where photoelectron detection acts as a high-intensity heralding mechanism, enabling the generation of large amplitude optical Schrödinger cat states. We characterize the resulting non-Gaussian features and show that they can be tuned via the detected photoelectron momentum, and study their robustness against the experimental imperfections arising from finite momentum resolution at the heralding step. Despite the noise, we show that the generated states can be manipulated to violate a Bell inequality, thereby highlighting their potential for foundational and practical applications. Our results establish strong-field processes as a scalable platform for macroscopic quantum state engineering, opening a route to quantum optics in previously inaccessible regimes.

Quantum computers hold great promise for molecular simulation, but noise remains a fundamental obstacle. We introduce a Quantum Monte Carlo (QMC) pre-screening procedure that constructs compact, physically motivated Givens rotation ansätze tailored to realistic quantum hardware. By identifying the most important wavefunction contributions early in a QMC simulation, we build circuits that are shallower that conventional alternatives while preserving number symmetry. Benchmarked on Quantinuum System Model H1, QMC-prescreened circuits outperform more complex ansätze under realistic noise conditions. The method offers a practical path toward chemical accuracy on quantum devices, by providing an adjustable trade-off between expressivity and circuit depth to generate shallow circuits suited to current high-noise devices, as well as deeper, more expressive circuits that can be deployed on future lower-noise devices.

Many advancements in optics have relied on the tight-binding approximation, which simplifies the description and prediction of complex system behaviors. This approximation describes the dynamics of the total light field by examining the coupling between the guided modes of individual single-mode substructures – also known as coupled mode theory. However, the underlying assumption, that the guided modes of individual waveguides form an orthogonal basis, breaks down when waveguides are brought into close proximity or when larger arrays are considered. In this work, we systematically analyze the consequences of this non-orthogonality and show that it leads to a generalized eigenvalue problem involving an overlap matrix, causing a fundamental mismatch between the standard TB model and solutions of the paraxial wave equation. To resolve this issue, we introduce a modified TB framework based on the Löwdin orthogonalization, which constructs an orthonormal basis from the non-orthogonal guided modes while minimally altering their physical shape and preserving their symmetry properties. The resulting Löwdin-TB method restores the standard eigenvalue problem and yields excellent agreement with exact beam propagation simulations across a wide range of system sizes and waveguide separations. Furthermore, it captures important physical effects, such as enhanced long-range coupling and nontrivial hopping phases, that are absent in the standard approach.

A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent $2^n$-dimensional data using only $n$ qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.

Acute spectral sensitivity to boundary conditions and the formation of a generalized Brillouin zone associated with complex quasimomenta are features frequently attributed to systems with non-trivial non-Hermitian topology, showcasing the non-Hermitian skin effect. We show that, away from the thermodynamic limit, these features themselves are not uniquely tied to this phenomenon; they can similarly arise as parity-induced even-odd effects in non-Hermitian systems without skin effect. Despite an underlying generalized Brillouin zone description, wavefunctions remain delocalized. In addition, the effect can arise in skin-effect models as entirely separate distinguishable feature

Generating reliable random and pseudo-random sequences is important in many electronic and signal processing systems, such as secure communications, radar, spread-spectrum methods, and autonomous platforms. Although true and quantum random number generators provide stronger unpredictability, classical pseudo-random number generators, including Linear Feedback Shift Registers (LFSRs) and the Mersenne Twister (MT), are still widely used because they are efficient and easy to implement. This work introduces a user-friendly software platform for generating, analyzing, and evaluating the predictability of pseudo-random bit sequences. The software supports two main functions: generating sequences using classical PRNGs and hybrid combinations, and analyzing input sequences through statistical measures and data-driven methods. In particular, hybrid LFSR-MT structures are studied to examine how they affect sequence complexity and resistance to prediction. The platform also includes machine-learning and deep-learning tools to investigate when deterministic PRNGs may remain partially predictable, even when their structure becomes more complex. The results show that algorithmic random sequence generators have inherent limitations in terms of unpredictability, which supports the use of quantum random sequences in security-critical applications. A comparative study between classical LFSR-MT sequences and quantum random sequences shows that quantum randomness offers higher unpredictability due to its non-deterministic physical origin. The potential use of quantum random sequences in jamming applications is also discussed, highlighting their improved robustness against prediction-based attacks. Overall, the proposed software provides a practical tool for analyzing, comparing, and benchmarking random sequence generators in modern electronic, sensing, and quantum-enabled communication systems.

We evaluate deterministic higher-order product formulae for molecular ground-state energy estimation. Motivated by recent fault-tolerant architectures in which non-Clifford operations may be generated more locally and cheaply than in conventional assumptions, we re-examine such formulae as practical candidates for quantum chemistry. Using one-dimensional hydrogen chains from $\mathrm{H}_2$ to $\mathrm{H}_{15}$ as benchmarks, we estimate both the total gate count and the depth of $R_Z$-rotation layers required to reach a target energy error. To make this comparison feasible at larger system sizes, we use a perturbative method to estimate the eigenvalue error induced by each product formula and thereby evaluate the cost of the corresponding phase-estimation procedure. Among the previously considered formulae, the eighth-order construction introduced by Morales et al. [M. E. S. Morales et al., "Greatly improved higher-order product formulae for quantum simulation," arXiv:2210.15817v2 (2024)] minimizes both cost metrics in the benchmark at a chemically relevant target error. We also find that increasing the formal order does not automatically reduce the total cost: near chemical accuracy, the tenth-order formula introduced in the same work can be less efficient than the eighth-order one. Motivated by this observation, we construct a new fourth-order formula; it achieves the lowest total gate count among the formulae considered for all H-chain instances near chemical accuracy and over much of the 0.1-10 mHa target-error window for most instances, while also reducing the $R_Z$-layer depth. These results clarify how deterministic higher-order product formulae should be selected for molecular ground-state energy estimation.

We use boson sampling as part of a gradient-free variational algorithm (the Binary Bosonic Solver) to solve a minimum dominating set problem and compare these results to a number of exact and heuristic classical algorithms. The boson sampling has been performed on the physical PT-2 time-bin interferometer from ORCA Computing. The PT-2 device has been tested here using both a single- and double-loop configuration and the results are compared based on the best found solution and the overall run time. With the parameters used in this experiment, the boson sampler is outperformed by the classical methods, but we hypothesise that this is due to insufficient samples and iterations. We classically simulate boson sampling in a single-loop configuration to break down the runtime for individual algorithmic components, allowing for estimates of when boson sampling may outperform classical methods. This study recommends a watching brief on boson sampling as the complexity of the interferometer is improved and the loss in the hardware is reduced allowing for better performance from the associated algorithms.

Using the operator method and properties of $O(2,1)$ algebra, the integral representation for the two-dimensional Green's function of an electron in the field of a magnetic monopole is found. This representation is valid in all complex plane of the electron energy.

Roaming reactions occur when a molecule enters a near-dissociation region, avoids immediate separation, and later forms products by a pathway not controlled by the conventional tight transition-state bottleneck. Classical studies have shown that roaming is best understood in phase space: inner and outer transition-state structures, together with their invariant manifolds, organize trapping, return, and dissociation. The corresponding quantum question is less settled. Can a single quantum resonance carry a recognizable signature of the classical roaming region? We address this question in Chesnavich's two-degree-of-freedom model for the ion–molecule reaction $\mathrm{CH}_4^+\rightarrow\mathrm{CH}_3^+ + \mathrm{H}$. Resonance states are computed with a complex absorbing potential and analyzed using diagnostics designed to mirror the classical phase-space picture: radial probability weights derived from the tight and outer transition-state structures, radial Husimi projections, angular-momentum channel weights, and coherent-state probes of the classical periodic orbits. One resonance is distinguished from the rest of the computed resonance ensemble. Its wavefunction is concentrated in the projected region between the inner and outer transition-state structures, its radial phase-space distribution is centered at intermediate radius with nearly zero radial momentum, and its angular structure is consistent with a standing rather than a directed rotating component. We interpret this state as a phase-space-localized quantum analogue of classical roaming. The result provides a controlled example in which quantum roaming is identified directly from a resonance wavefunction and its phase-space diagnostics, rather than only from product-state or scattering signatures.

Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an a priori diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.

Harnessing dissipation in the presence of strong symmetries has recently emerged as a promising route for generating entanglement in atomic clocks. However, previous proposals relied on regimes where cavity photons can be adiabatically eliminated, significantly limiting their applicability to experimentally relevant cavity-QED regimes that lie in or near the resolved vacuum Rabi splitting regime. Here we show that symmetry-protected dissipative spin squeezing can be realized even when cavity photons actively participate in the dynamics, extending the experimental relevance of the protocol. We study a three-level ensemble of $^{87}\mathrm{Sr}$ atoms coupled to an optical cavity in the resolved vacuum Rabi splitting regime and demonstrate that, with smooth ramps of the drive amplitude and detunings, the driven-dissipative dynamics enters a stable low-photon regime in which nonadiabatic cavity excitations and sector-resolving photon leakage can be controlled. Within this low-photon operating window, sector-resolving photon leakage is suppressed and the sector-dependent geometric phase realizes effective one-axis twisting. At the end of the protocol the entanglement can also be efficiently transferred directly onto the long-lived clock states by turning the drive off. For experimentally realistic parameters, we theoretically show that more than $25\,\mathrm{dB}$ of squeezing can be generated for $10^5$ atoms, closely saturating the ideal one-axis twisting scaling $\xi_{\min}^2 \propto N^{-2/3}$. At fixed cooperativity, the optimized squeezing remains broadly comparable to the unresolved-regime implementation, while the resolved-regime implementation reaches comparable squeezing on a substantially shorter physical timescale. These results establish symmetry-protected dissipative dynamics as a practical route to beyond the standard-quantum-limit performance in optical-clock platforms.

The eigenstate thermalization hypothesis (ETH) posits that energy eigenstates encode local properties of the microcanonical ensemble. Motivated by recent interest in the physics of non-commuting conserved charges and the non-Abelian ETH, we study chaotic eigenstates in the presence of symmetries described by general compact Lie groups, such as SU(2). By applying non-Abelian symmetry resolution, we develop a non-Abelian microcanonical entropy and relate this entropy to the entanglement entropy of chaotic eigenstates. We find that microcanonical entropy is closely related to the symmetry-resolved entanglement entropy, which differs from conventional entanglement entropy by a universal logarithmic correction. Our results depend on the global Casimir charge, e.g. total spin. At finite charge density, we find a logarithmic enhancement to conventional entanglement entropy. At zero density, we find no such correction to entanglement entropy, but a logarithmic reduction to microcanonical entropy and symmetry-resolved entanglement entropy. We discuss the implications of our approach for non-Abelian eigenstate thermalization.

Achieving uniform critical current across Josephson junctions is essential for the large-scale integration of superconducting quantum circuits. In this work, we statistically analyzed the variation of the critical current of Al/AlO${\rm _x}$/Al junctions using room-temperature tunnel resistance statistics, and identified the dominant contribution among the modeled sources of the variation based on their dependence on geometry and deposition conditions of junctions. Our model-based analysis reveals that fluctuations in the Al film thickness play the dominant role among the modeled contributing factors. Based on this analysis, we found that, in Dolan-bridge double-angle deposition, adopting a deposition angle of 30-degree for bilayer junctions significantly improves uniformity, yielding a relative standard deviation of 1.2% (0.5%) across a 9.75 mm (1.5 mm) square region.

Quantum error correction (QEC) is transitioning from physical feasibility demonstrations to systems engineering challenges. Google has achieved below-threshold performance on distance-5/7 surface codes, while Riverlane and Rigetti have demonstrated hardware-integrated low-latency feedback loops. These milestones indicate that the core challenge of real-time decoding has shifted from algorithmic capability to system-level engineering. However, a substantial engineering gap remains between laboratory demonstrations and scalable fault-tolerant quantum computing (FTQC). This white paper addresses three questions: (1) Where are the real bottlenecks in real-time QEC: beyond average decoder speed, the constraints lie in QEC round time, tail latency, and end-to-end data path coordination; (2) How mature are mainstream decoder algorithms: we benchmark the major decoders for both surface codes and quantum low-density parity-check (qLDPC) codes, evaluating their real-time readiness; (3) What system stack do we propose: a six-layer reference architecture from syndrome acquisition to logical operations, with interface definitions and latency budget models. Our results quantify the gap between current decoder performance and real-time requirements, and identify the architectural choices needed to close it.

The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. 92 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent $z\approx 2$. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.

While quantum position verification aims to certify a prover's location using quantum information, existing security definitions only guarantee that part of the successful adversarial party is in the claimed location. This leaves open the possibility that a distributed team of adversaries can jointly simulate a prover in a way that defeats the intended meaning of `being at a location' in position-based cryptography. We introduce stronger notions of position verification that we call quantum localization, which requires that there is a specified, unclonable state at the verified spacetime point-and that this state can be found nowhere else. We show that quantum localization leads naturally to a meaningful notion of trajectory verification, in which quantum information is verifiably tracked through space and time. We construct quantum localization and trajectory verification protocols using quantum anchor states, which generalize coset states from unclonable cryptography. The security of our schemes is proven in the classical oracle (i.e. ideal obfuscation) model, which can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation. We also introduce and instantiate the concept of functionality localization, which guarantees that the adversary has the ability to compute a secret function at the verified spacetime point, and this function cannot be computed anywhere else. This raises the intriguing possibility of localizing computational capabilities in space and time. More broadly, we believe our notions of quantum localization and subsequent feasibility results provide stronger foundations for position-based cryptography. At a conceptual level, our results also explore the tight link between two fundamental notions in physics-location and information-thus serving as a natural foundation for cryptographic capabilities tied to physical spacetime.

We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial.