Papers

The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to improve the decoder's accuracy often lead to unacceptable increases in decoding time and hardware complexity, while attempts to accelerate decoding result in a significant degradation in logical error rate. To overcome this challenge, we propose a novel framework, decoder switching, which balances these competing demands by combining a faster, soft-output decoder ("weak decoder") with a slower, high-accuracy decoder ("strong decoder"). In usual rounds, the weak decoder processes error syndromes and simultaneously evaluates its reliability via soft information. Only when encountering a decoding window with low reliability do we switch to the strong decoder to achieve more accurate decoding. Numerical simulations suggest that this framework can achieve accuracy comparable to, or even surpassing, that of the strong decoder, while maintaining an average decoding time on par with the weak decoder. We also develop an online decoding scheme tailored to our framework, named double window decoding, and elucidate the criteria for preventing an exponential slowdown of quantum computation. These findings break the long-standing speed-accuracy trade-off, paving the way for scalable real-time decoding devices.

We propose an architecture, called NVQLink, for connecting high-performance computing (HPC) resources to the control system of a quantum processing unit (QPU) to accelerate workloads necessary to the operation of the QPU. We aim to support every physical modality of QPU and every type of QPU system controller (QSC). The HPC resource is optimized for real-time (latency-bounded) processing on tasks with latency tolerances of tens of microseconds. The network connecting the HPC and QSC is implemented on commercially available Ethernet and can be adopted relatively easily by QPU and QSC builders, and we report a round-trip latency measurement of 3.96 microseconds (max) with prospects of further optimization. We describe an extension to the CUDA-Q programming model and runtime architecture to support real-time callbacks and data marshaling between the HPC and QSC. By doing so, NVQLink extends heterogeneous, kernel-based programming to the QSC, allowing the programmer to address CPU, GPU, and FPGA subsystems in the QSC, all in the same C++ program, avoiding the use of a performance-limiting HTTP interface. We provide a pattern for QSC builders to integrate with this architecture by making use of multi-level intermediate representation dialects and progressive lowering to encapsulate QSC code.

The continuous miniaturisation of metal-oxide-semiconductor field-effect transistors (MOSFETs) from long- to short-channel architectures has advanced beyond the predictions of Moore's Law. Continued advances in semiconductor electronics, even near current scaling and performance boundaries under cryogenic conditions, are driving the development of innovative device paradigms that enable ultra-low-power and high-speed functionality. Among emerging candidates, the Josephson Junction Field-Effect Transistor (JJFET or JoFET) provides an alternative by integrating superconducting source and drain electrodes for efficient, phase-coherent operation at ultra-low temperatures. These hybrid devices have the potential to bridge conventional semiconductor electronics with cryogenic logic and quantum circuits, enabling energy-efficient and high-coherence signal processing across temperature domains. This review traces the evolution from Josephson junctions to field-effect transistors, emphasising the structural and functional innovations that underpin modern device scalability. The performance and material compatibility of JJFETs fabricated on Si, GaAs, and InGaAs substrates are analysed, alongside an assessment of their switching dynamics and material compatibility. Particular attention is given to superconductor-silicon-superconductor Josephson junctions as the active core of JJFET architectures. By unfolding more than four decades of experimental progress, this work highlights the promise of JJFETs as foundational building blocks for next-generation cryogenic logic and quantum electronic systems.

Superconducting qubits have motivated the exploration of Josephson-junction technologies beyond quantum computing, with emerging applications in low-energy photon and phonon detection for astrophysics and dark matter searches. Achieving sensitivity at the THz (meV) scale requires materials with smaller superconducting gaps than those of conventional aluminum or niobium-based devices. Here, we report the fabrication and characterization of hafnium (Hf)-based Josephson junctions (Hf-HfOx-Hf), demonstrating Hf as a promising low-Tc material platform for ultra-low threshold single THz photon and single-phonon detection. Structural and chemical analyses reveal crystalline films and well-defined oxide barriers, while electrical transport measurements at both room and cryogenic temperatures exhibit clear Josephson behavior, enabling extraction of key junction parameters such as critical current, superconducting gap and normal-state resistance. This work presents the first comprehensive study of Hf-based junctions and their potential for next-generation superconducting detectors and qubit architectures leveraging low superconducting gap energies.

We introduce the Phase-Coupled Caldeira-Leggett (PCL) model of quantum dissipation and develop an exact framework for its dynamics. Unlike the conventional Caldeira-Leggett model with linear system-bath coupling $H_{\mathrm{SB}}\propto\hat F$, the PCL model features an exponential interaction $H_{\mathrm{SB}}\propto e^{i\lambda \hat F}$, where $\hat F$ denotes the collective bath coordinate. This model unifies concepts from quantum Brownian motion and polaron physics, providing a general platform to study phase-mediated dissipation and decoherence beyond the linear-response regime. Despite its nonlinear system-bath coupling, the Gaussian nature of the environment allows a nonperturbative and non-Markovian treatment of PCL model within the algebra of dissipative quasiparticles. We obtain an exact closed-form equation of motion for the reduced density operator, and numerical simulations reveal distinctive dynamical behaviors that deviate markedly from those predicted by the conventional Caldeira-Leggett model.

The assumption of a deterministic local hidden variable model constrains the experimentally accessible statistics in a Bell experiment to be contained in the Bell-local polytope. But what if the outputs for only a subset of the measurements at each site are predetermined by the model? In this work, we thoroughly explore this concept of `partial determinism', allowing for arbitrary numbers of parties, inputs and outputs per site. The resulting objects form new classes of convex polytopes which recover the Bell and the no-signalling polytopes as special cases. Nontrivial equivalence classes of partially deterministic models arise, which we classify completely. In particular, the Bell polytope for any scenario can be expressed in multiple different ways in terms of local partially deterministic models. This allows us to generalise Fine's theorem, recovering the original formulation as a special case, but finding new constraints otherwise. We discuss scenarios with different physical motivations, which do not require the causal structure of the Bell scenario, and where classes of partially deterministic polytopes are relevant. Our example applications include device-independent quantum state inseparability witnesses, classes of broadcast-local polytopes, and Local Friendliness scenarios in quantum foundations. We also point out instances in previous literature where classes of related objects have been studied. In the case of correlations compatible with the Local Friendliness assumptions, we find a one-to-one correspondence between partially deterministic polytopes and sequential extended Wigner's friend scenarios so that every partially deterministic polytope has physical relevance. We discuss how the framework captures a broad class of non-classicality notions, and identify an even broader notion of `composable sets', of which partially deterministic polytopes are special cases.

We prove a generalized dynamical duality for identical particles in one dimension (1D). Namely, 1D systems with arbitrary statistics – including bosons, fermions and anyons – approach the same momentum distribution after long-time expansion from a trap, provided they share the same scattering length for short-range interactions. This momentum distribution is uniquely given by the rapidities, or quasi-momenta, of the initial trapped state. Our results can be readily detected in quasi-1D ultracold gases with tunable s- and p-wave interactions.

We quantize punctured plane, $X=\mathbb{R}^2-\{0\}$, employing Isham's group theoretic quantization procedure. After sketching out a brief review of group theoretic quantization procedure, we apply the quantization scheme to the phase space, $M=X \times \R^2$, corresponding to the punctured plane, $X$. Particularly, we find the canonical Lie group, $\mathscr{G}$, corresponding to the phase space, $M=X \times \R^2$, to be $\mathscr{G} = \R^2 \rtimes (SO(2)\times \R^+)$. We establish an algebra homomorphism between the Lie algebra corresponding to the canonical group, $\mathscr{G} = \R^2 \rtimes (SO(2)\times \R^+)$, and the smooth functions, $f\in C^{\infty}(M)$, in the phase space, $M=X \times \R^2$. Making use of this homomorphism and unitary representation of the canonical group, $\mathscr{G} = \R^2 \rtimes (SO(2)\times \R^+)$, we deduce a quantization map that maps a subspace of classical observables, $f\in C^{\infty}(M)$, to self-adjoint operators on the Hilbert space, $\mathscr{H}$, which is the space of all square integrable functions on $X=\mathbb{R}^2-\{0\}$ with respect to the measure $\dd \mu = \dd \phi\dd\rho/(2\pi\rho)$.

We report the experimental realization and optical characterization of chlorine-vacancy (ClV) color centers in 4H-SiC emitting in the fiber-optic telecom bands. These defects are created via chlorine ion implantation followed by high-temperature annealing. Photoluminescence spectroscopy reveals four distinct ClV configurations with zero-phonon lines (ZPLs) located in the O-band (1260 - 1360 nm), S-band (1460 - 1530 nm) and C-band (1530 - 1565 nm). Controlled implantation and annealing experiments confirm that the ClV centers originate specifically from chlorine incorporation into SiC and are not intrinsic to this material. We optimize the creation conditions for ClV ensembles and demonstrate negligible reduction of the ZPL intensity up to a temperature of 30 K. These results establish ClV defects as a new class of telecom-band color centers in a CMOS-compatible platform, offering strong potential for scalable quantum networks.

Quantum correlations are the singular, defining resource of quantum information science and metrology, forming the basis of every operational advantage that quantum systems hold over classical ones. Yet exact bounds on these correlations-such as the Lieb-Robinson bound on entanglement propagation and the Heisenberg limit on metrological precision-are known only in special cases and have long appeared to arise from unrelated mechanisms. Here we show that these limits share a common geometric origin. We identify a positivity invariant of the block correlation matrix, denoted $\chi$, that quantifies how far a bipartite state lies from the positivity boundary of quantum state space. For any system with a specified observable algebra and parameter-encoding map, every correlation measure determined solely by the positive correlation matrix obeys a $\chi$-dependent inequality. For systems with simple symmetry structures these inequalities take closed analytic form, reproducing the structure of the Heisenberg and Cramér-Rao limits and producing new results, including an exact entanglement floor and a universal Fisher-information ceiling even in all-to-all connected quantum networks. We thus demonstrate that positive geometry provides a unified framework for the attainable strength of quantum correlations, linking entanglement, metrological sensitivity, and dynamical causal structure through a single invariant.

Modulating the free-electron wave function with light brings new opportunities to create attosecond electron pulse trains, to probe the quantum coherence of systems with significantly improved spatial resolution, and to generate classical and non-classical states of light with wide tunability. It is therefore crucial to efficiently generate free-electron wave functions that are suitable for these applications. In this study, we theoretically investigate an efficient free-space optical modulation of free electrons with two counter-propagating Gaussian beams. We find that the Gaussian beams' Gouy phase not only plays a crucial role in the interaction, but also enables straight-forward generation of valuable free-electron states, including comb-shape spectra with similar amplitudes, and states with high degree of coherence. We also discuss the feasibility of demonstrating these Gouy phase-related effects with chirped femto-second laser pulses. Our study establishes a theoretical foundation and physical intuition about the role of the Gouy phase. It can provide guidance to efficiently shape the free-electron wave function for a wide range of quantum applications.

Rogue waves are extreme evanescent nonlinear structures that are challenging to observe in atomic gases, as their emergence requires a dynamically unstable attractive environment. Here, we report the experimental observation of vector extensions of Peregrine solitons in highly particle-imbalanced, pairwise immiscible three-component repulsive Bose-Einstein condensates. The possibility of an effectively attractive character of the minority components is established by constructing a generalized reduction scheme for an imbalanced N -component setup with arbitrary interaction signs. These components are subject to intra- and inter-component modulation instability, which along with the presence of an attractive potential well induces the dynamical formation of highly reproducible vector rogue waves. Exploiting different Rb hyperfine states, it is possible to flexibly tune the effective interactions stimulating the realization of a plethora of vector rogue waves, including single and double Peregrine-like wave peaks. The experimental findings are in quantitative agreement with suitable three-dimensional mean-field simulations, while quasi-one-dimensional analysis of the non-polynomial Schroedinger model provides additional insights into the rogue wave characteristics.

We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed ground state with short-time quantum evolution of product states sampled from it. The resulting quantum samples define an effective subspace of the Hilbert space, onto which the Hamiltonian is projected to enable efficient classical simulation of long-time dynamics. This subspace-based approach achieves high-resolution spectral reconstruction using shallow circuits and few samples. Benchmarks on molecular systems show excellent agreement with exact diagonalization and demonstrate access to dynamical timescales beyond the reach of purely classical methods, highlighting its suitability for near-term and early fault-tolerant quantum hardware.

Monogamy of entanglement, which limits how entanglement can be shared among multiple parties, is a fundamental feature underpinning the privacy of quantum communication. In this work, we introduce a novel operational framework to quantify the unshareability or unextendibility of entanglement via a virtual state-extension task. The virtual extension cost is defined as the minimum simulation cost of a randomized protocol that reproduces the marginals of a $k$-extension. For the important family of isotropic states, we derive an exact closed-form expression for this cost. Our central result establishes a tight connection: the virtual extension cost of a maximally entangled state equals the optimal simulation cost of universal virtual quantum broadcasting. Using the algebra of partially transposed permutation matrices, we obtain an analytical formula and construct an explicit quantum circuit for the optimal broadcasting protocol, thereby resolving an open question in quantum broadcasting. We further relate the virtual extension cost to the absolute robustness of unextendibility, providing it with a clear operational meaning, and show that the virtual extension cost is an entanglement measure that bounds distillable entanglement and connects to logarithmic negativity.

Reversing unitary operations is a key task in quantum computing and quantum control. In this work, we introduce and develop the framework of shadow unitary inversion, a relaxed variant of unitary inversion in which the goal is to reproduce the action of the inverse unitary only at the level of the expectation value of a fixed observable. This task captures an operational setting in which only shadow information is required and allows query complexities significantly below those of full unitary inversion. We establish a dimension-dependent lower bound showing that any $t$-query scheme requires $t$ to scale at least linearly with the system dimension, with the constant determined by the spectral properties of the target observable. In the qubit case, we construct a deterministic three-query sequential protocol that achieves exact shadow inversion, and we provide a complete characterization of all admissible qubit channels satisfying the shadow constraint. Numerical evidence suggests that three queries are optimal. For higher-dimensional systems, we develop a semidefinite-programming formulation for optimizing shadow-inversion combs and introduce a representation-theoretic symmetry reduction that decomposes the problem into invariant blocks, substantially reducing the problem size. These results provide the first systematic study for shadow unitary inversion and establish its resource requirements and symmetry structure across dimensions.

Quantum simulators hold great promise for studying real-time (Minkowski) dynamics of quantum field theories. Nonetheless, preparing non-trivial initial states remains a major obstacle. Euclidean-time Monte-Carlo methods yield ground-state spectra and static correlation functions that can, in principle, guide state preparation. In this work, we exploit this classical information to bridge Euclidean and Minkowski descriptions for a (1+1)-dimensional interacting scalar field theory. We propose variational ansatz families which achieve comparable ground-state energies, yet exhibit distinct correlations and local non-Gaussianity. By optimizing selected wavefunction moments with Monte-Carlo data, we obtain ansatzes that can be efficiently translated into quantum circuits. Our algorithmic cost analysis shows these circuits' gate complexity scales polynomially in system size. Our work paves the way for systematically leveraging classically-computed information to prepare initial states in quantum field theories of interest in nature.

Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin-glass models provide a natural framework to explore this connection, as their energy landscapes are governed by competing interactions and constrained topologies. We investigate the non-exponential relaxation behavior of spin glasses on network architectures relevant to quantum annealing hardware – such as finite size Chimera, Pegasus, and Zephyr graphs – where embedding constraints and finite connectivity strongly modulate the distribution of barriers and metastable states. This slow relaxation arises from the combined effects of frustration and disorder, which persist even beyond the conventional spin-glass transition. Within the Fortuin-Kasteleyn-Coniglio-Klein (FKCK) cluster formalism, the appearance of unfrustrated cluster regions gives rise to multiple relaxation scales, as distinct domains follow different dynamical pathways across a rugged energy landscape. This framework enables a more comprehensive characterization of spin-glass energy landscapes and offers valuable insight into how topological constraints and disorder jointly govern relaxation dynamics, providing quantitative benchmarks for evaluating the performance and limitations of quantum annealing architectures.

Investigating the robustness of non-reciprocity in the presence of competing interactions is central to understanding non-reciprocal quantum matter. In this work, we use reservoir engineering to induce non-reciprocal hopping and pairing in the fermionic Kitaev chain, and reveal the emergence of a pairing-induced phase transition. The two phases appear in the spectrum of the non-Hermitian Kitaev Hamiltonian describing the dynamics of correlations, separated by an exceptional point. In the non-reciprocal phase, dynamics are characterized by directionality and slow relaxation, and the steady state supports non-reciprocal density and spatial correlations. At strong pairing, we uncover an unexpected density wave phase, featuring short relaxation times, a modulation in particle occupation and strikingly different correlation spreading depending on pairing non-reciprocity. Our work highlights the non-trivial breakdown of non-reciprocity due to superconducting pairing and invites experimental investigation of non-reciprocal fermionic systems.

We study frustration-free control, a measurement-feedback protocol for quantum state preparation that extends the concept of frustration-free Hamiltonians to stochastic dynamics. The protocol drives many-body systems into highly entangled target states, common dark states of all measurement projectors, through minimal local unitary corrections that realize an absorbing-state dynamics without post-selection. We show that relaxation to the target state is governed by emergent transport of nonlocal charges, such as singlet excitations in SU$(2)$-symmetric dynamics. While measurement-feedback annihilates compatible charge configurations, both measurement and scrambling unitaries induce charge transport and thus determine the convergence time. Mapping a baseline model of SU$(N)$ SWAP measurements with local corrections to a solvable absorbing random walk yields a runtime scaling $t \sim L^z$ with transport exponent $z=2$. Simulations of Motzkin and Fredkin chains reveal subdiffusive scaling $z \ge \tfrac{8}{3}$, confirming the transport picture and suggesting strategies for controlled entangled-state preparation and charge-transport probing in monitored quantum dynamics.

The dynamical evolution of neutrino flavor in supernovae can be modeled by an all-to-all spin Hamiltonian with random couplings. Simulating such two-local Hamiltonian dynamics remains a major challenge, as methods with controllable accuracy require circuit depths that increase at least linearly with system size, exceeding the capabilities of current quantum devices. The eigenstate thermalization hypothesis predicts that these systems should thermalize, a behavior confirmed in small-scale classical simulations. Here we investigate flavor thermalization in much larger systems using random quantum circuits as an empirical tool to emulate the non-local dynamics, and demonstrate that thermal behavior can be reproduced using a depth independent of system size. By simulating systems of over one hundred qubits, we find that the thermalization time grows approximately as the square root of the system size, consistent with predictions from semi-classical methods. Our study also illustrates that near-term quantum devices are useful tools to test and validate empirical classical methods, and highlights an application of random circuits in physics.

The construction of parent Hamiltonians that possess a given state as their ground state is a well-studied problem. In this work, we generalize this notion by considering simple quantum states and examining the local Hamiltonians that have these states as exact eigenstates. These states often correspond to Quantum Many-Body Scars (QMBS) of their respective parent Hamiltonians. Motivated by earlier works on Hamiltonians with QMBS, in this work we formalize the differences between three distinct types of parent Hamiltonians, which differ in their decompositions into strictly local terms with the same eigenstates. We illustrate this classification using the $W$ state as the primary example, for which we rigorously derive the complete set of local parent Hamiltonians, which also allows us to establish general results such as the existence of asymptotic QMBS, and distinct dynamical signatures associated with the different parent Hamiltonian types. Finally, we derive more general results on the parent Hamiltonian types that allow us to obtain some immediate results for simple quantum states such as product states, where only a single type exists, and for short-range-entangled states, for which we identify constraints on the admissible types. Altogether, our work opens the door to classifying the rich structures and dynamical properties of parent Hamiltonians that arise from the interplay between locality and QMBS.

We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-André potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasi-degenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.

A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum algorithm on superconducting quantum hardware. Compared to sequential generation, it has been shown that the RG-based protocol asymptotically prepares short-range correlated MPS with an exponentially shallower circuit depth (when scaling system size), but it is not yet clear for which system sizes it starts to convey an advantage. We thus apply this algorithm to prepare a class of MPS exhibiting a phase transition between a symmetry-protected topological (SPT) and a trivial phase for systems of up to 80 qubits. We find that the reduced depth of the RG-based circuits makes them more resilient to noise, and that they generally outperform the sequential circuits for large systems, as we showcase by measuring string-order-like local expectation values and energy densities. We thus demonstrate that the RG-based protocol enables large-scale preparation of MPS and, in particular, SPT-ordered states beyond the fixed point.

Using an ultracold gas of $^{87}$Rb$^{133}$Cs molecules, we perform hyperfine-resolved spectroscopy of transitions from the vibronic ground state to the lowest rovibrational states of the electronic state $\mathrm{b}\,^3\Pi_0$, as a function of magnetic field. These transitions are spin forbidden, resulting in narrow linewidths, and feature near-diagonal Franck-Condon factors. We develop a model of the hyperfine and Zeeman structure that includes coupling between the $0^+$ and $0^-$ components of $\mathrm{b}\,^3\Pi_0$. We fit the spectra to obtain rotational and hyperfine coupling constants. We measure transition dipole moments associated with specific transitions by directly observing Rabi oscillations as a function of a resonant laser pulse duration. Using resonant $\pi$ pulses, we prepare molecules in the electronically excited state and directly measure the spontaneous emission rate.

Quantum Mpemba effect occurs when a quantum system, residing far away from the steady state, relaxes faster than a relatively nearer state. We look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a non-trace preserving map, the trace distance of an operator is not a monotonically decaying function of time, unlike its quantum state counterpart. Consequently, the trace distance can not serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a dressed distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. Applying the formalism to various open quantum system settings, we find that, interestingly, in the single qubit case, only accelerated relaxation of operators is possible, while genuine Mpemba-like effects emerge in higher-dimensional systems such as qutrits and beyond. Furthermore, we demonstrate the existence of Mpemba-like effects in nonlocal, non-equilibrium operators, such as current, in a double-quantum-dot setup. Our results, besides offering fundamental insight about the occurrence of the Mpemba-like effect under non-trace preserving dynamics, open avenues for new experimental studies where quicker relaxation of observables could be of significant interest.

We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as a categorical analogue of statistical covariance. In the finite-dimensional setting, we obtain a complete characterization of the fields of covariances satisfying an additional continuity property in terms of a strictly positive constant $\alpha$ and a continuous function $F\colon[0,+\infty)\rightarrow(0,+\infty)$ that is operator monotone on $(0,+\infty)$. In the commutative case, our result recovers a contravariant formulation of Čencov's characterization of the Fisher–Rao metric tensor, and extends the corresponding uniqueness statement to tracial states on possibly noncommutative algebras. On faithful states, a subfamily satisfying a symmetry constraint recovers the regular Morozova–Čencov–Petz monotone metric tensors. More generally, the covariance fields induce positive contravariant symmetric tensors on the homogeneous manifolds of states generated by the action of the invertible elements of an arbitrary finite-dimensional $C^*$-algebra. The geometry internal to the support is determined by the positive spectrum of the modular operator, whereas support-changing directions are governed by $F(0)$. For $F(t)=(1+t)/2$, and with a suitable normalization convention, the resulting tensors recover the inverse of the Riemannian metrics induced by the Jordan product. In particular, on pure states, every $F$ induces a multiple of the inverse Fubini–Study tensor, with coefficient $2F(0)$ in our normalization, in agreement after inversion with the Petz–Sudár radial extension.

Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates. Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible with the square-grid connectivity and yields high-fidelity magic states. However, it relies on the complex grafted code, which incurs substantial spacetime overhead and complicates practical implementation. In this work, we propose an efficient cultivation-based protocol compatible with the square-grid connectivity. We reduce the spatial overhead by avoiding the grafted code and further reduce the average spacetime overhead by utilizing code expansion and enabling early rejection. Numerical simulations show that, with a color code distance of 3 and a physical error probability of $10^{-3}$, our protocol achieves a logical error probability for the resulting magic state comparable to that of magic state cultivation ($\approx 3 \times 10^{-6}$), while requiring about half the spacetime overhead. Our work provides an efficient and simple distillation protocol suitable for megaquop use cases and early fault-tolerant devices.

The ability to engineer non-Gaussian quantum resources underlies quantum technologies from communication and metrology to universal computation. However, while a number of canonical works have set no-go limits for attaining such resources from Gaussian operations, it is widely assumed that such resources can be tuned freely by non-Gaussian Hamiltonian dynamics. Here we prove a general no-go theorem for such resource shaping: no smooth Hamiltonian dynamics can modify higher-order statistical moments of a continuous-variable state without simultaneously changing its mean and covariance. This analytic constraint implies a rigidity theorem for Hamiltonian quantum control-only quadratic (symplectic) generators preserve the Gaussian moment hierarchy, while every non-quadratic term necessarily couples the Gaussian and non-Gaussian sectors. The theorem identifies the symplectic algebra as the unique invariant subalgebra whose differential representations terminate at finite (second) order within the otherwise infinite Hamiltonian algebra. It thereby defines the analytic boundary between classically simulable Gaussian dynamics and the fully universal non-Gaussian regime-the continuous-variable analogue of the Gottesman-Knill frontier.

For any element $g$ of compact reductive group $G$ we investigate the asymptotic behavior of its normalized irreducible character in the high-dimension limit, $\frac{\chi_\lambda(g)}{d_\lambda}$. We show that when $G$ is simple the limit vanishes besides identity element. For semisimple groups one gets the same results under the additional assumption that dimensions of irreducible representations of all simple components are going to infinity. Using the notion of approximate $t$-designs we connect this observations with bounds on the production of quantum randomness in large quantum systems.

For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic limit, examining them is beneficial for a sharper understanding of how the limit is attained. We contrast a classical and a quantum model of particle-wall correlations within the canonical ensemble.