Papers

Quantum circuit cutting enables the execution of large circuits on devices with a limited number of qubits by partitioning circuits into independent subcircuits. However, this introduces a sampling overhead, which grows exponentially with the number of cuts, rendering the choice of cut placements critical for practical circuit cutting. Determining optimal cut placements remains computationally challenging, particularly as circuits grow in size. Additionally, existing circuit cutting approaches typically treat gate and wire cuts independently. Those combining both cutting approaches, however, do not take advantage of joint cutting, i.e., identifying common gate groups and cutting them jointly for a reduced overhead. This work presents a unified framework that combines gate and wire cutting within a single partitioning strategy, enabling more efficient circuit decompositions. Moreover, our approach incorporates joint cutting via a novel gate grouping technique, further reducing sampling overhead. By formulating the cut placement problem as a scalable graph partitioning task, our method efficiently identifies near-optimal cut placements for large circuits, also providing diagnostic feedback on whether circuits are suitable for cutting.

We determine the relative entropy of entanglement of a bipartite mixed state $\rho_{AB}$ obtained by tracing out one subsystem of a tripartite Haar-random pure state $|\psi\rangle_{ABC}$, finding $E_R(\rho_{AB})=\log\frac{d_Ad_B}{\max(d_A,d_B,d_C)}+O(1)$. Equivalently, the relative entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(\rho_{AB})$ and the mutual information $I(A:B)$. The upper bound is achieved by an explicit separable state obtained through one-sided Schmidt dephasing, which is therefore approximately closest.

Bell experiments rule out local common-cause explanations of quantum correlations, yet they do not exclude hidden influences that travel faster than light while still having a finite speed in a preferred frame. Multipartite spacetime arrangements turn this possibility into a constraint: two late parties that are outside each other's hidden-influence cones must remain Bell-local once the earlier events are fixed. Here, we formulate this constraint as a projected-polytope separation problem for cluster-state correlations, using only marginal data containing at most one late party. From linear cluster states, we construct a four-qubit witness with the bound $S_4\le 6$ and quantum value $4+2\sqrt2$, and a five-qubit witness with $S_5\le 10$ and quantum value $6+4\sqrt2$. We certify that the exposed faces are facets of the corresponding projected hidden-influence polytopes. These results identify linear-cluster graph states as certifiable and experimentally friendly resources for finite-speed hidden-influence tests.

Classical waves in dispersive media naturally exhibit distinct phase and group velocities. Whether an analogous separation of velocities can emerge in matter waves under strong many-body interactions has remained experimentally unexplored. Here, we demonstrate the emergence of a velocity hierarchy in a strongly interacting lattice gas. Using quench spectroscopy together with time-resolved correlation measurements, we independently determine the sound, group, and phase velocities across the superfluid-to-Mott-insulator transition. These velocities are nearly degenerate close to the transition, but progressively separate as the Mott gap opens and the quasiparticle dispersion acquires a massive relativistic-like form. Strikingly, phase-coherence fronts propagate faster than the Lieb-Robinson velocity scale while remaining fully consistent with locality. The measured velocities satisfy a relativistic-like invariance relation in the insulating regime. Our results establish propagation-velocity hierarchies as emergent signatures of strongly correlated quantum dynamics.

One-bit post-training quantization represents each weight using only its sign, requiring all deployment contexts to share the same binary weight matrix even when their activation statistics favor different sign patterns. We study this shared-sign constraint and introduce Quantum Random Access Quantization (QRAQ). This framework encodes context-dependent signs in a quantum random-access code and retrieves them via context-matched Pauli measurements. Under an explicit fresh-copy logical readout model, QRAQ produces an unbiased, context-specific binary surrogate with a tractable shot-noise penalty. We prove a row-wise separation from shared-sign one-bit PTQ with signed per-row scales. When the optimal context-wise signs are incompatible, QRAQ achieves a strictly lower ideal reconstruction risk. We also derive finite-shot and calibrated-noise conditions under which this separation is retained. Fixed-readout quantum schemes are classically simulable, so the relevant resource in this model is measurement incompatibility rather than quantization alone. Finally, we characterize the role of scale granularity, provide finite-sample certificates, and evaluate the predicted ideal, finite-shot, noisy, and multi-context regimes in simulator experiments.

Quantum processors have crossed the one-hundred-qubit mark, but noise continues to limit circuit performance, while full quantum error correction remains too costly for routine use. Error suppression and mitigation therefore play an important role in extracting value from current hardware, yet independent comparisons of commercial solutions on identical workloads and devices remain scarce. We benchmark IBM Qiskit Runtime, Q-CTRL Performance Management, and Qedma QESEM on IBM Pittsburgh, a 156-qubit IBM Quantum Heron r3 processor. For Sampler workloads, we run Bernstein-Vazirani, quantum phase estimation, GHZ-state preparation, and randomized mirror circuits with up to 100 measured qubits, comparing raw execution, IBM measurement twirling, and Q-CTRL. For Estimator workloads, we measure chain-averaged magnetization and correlation observables of an eight-layer transverse-field Ising circuit at 25, 50, and 75 qubits against an exact matrix-product-state reference, comparing IBM raw execution, IBM TREX plus twirling, Q-CTRL, and QESEM. Q-CTRL produced the best results on the three structured Sampler workloads while keeping reported QPU times within the same order as the IBM configurations. Across six Ising observable and system-size cases, aggregate mean absolute error was 0.0883 for IBM raw execution, 0.0807 for IBM TREX plus twirling, 0.0285 for Q-CTRL, and 0.0188 for QESEM. Relative to raw execution, Q-CTRL and QESEM reduced aggregate error by factors of 3.10 and 4.70, respectively, while QESEM used 7.5 to 11.1 times the reported QPU time of Q-CTRL. These results show that managed error suppression and mitigation can substantially improve current hardware performance, but with distinct accuracy and execution-time tradeoffs.

Distributing entanglement between distant qubits is a crucial element of scalable quantum computing. Here, we describe a scalable quantum interconnect that generates remote entanglement at rates approaching those compatible with two-qubit gates of current neutral-atom quantum processors. The proposed approach exploits the strong dipole-dipole interactions between atomic Rydberg states to generate entanglement between stationary qubits and propagating photons, without the need for an optical cavity. We provide a thorough description of the optimal conditions for the developed entanglement-generation protocol for realistic experimental parameters and demonstrate that entanglement-generation rates $\gtrsim 3\times 10^5$ s$^{-1}$ can be achieved using Rydberg states of ytterbium atoms. Given the inherent scalability and design flexibility of the proposed interconnect, our results suggest a promising approach towards distributed networks based on neutral-atom quantum architectures.

Non-Abelian anyons arise as exotic excitations in fractional quantum Hall (FQH) matter and have proved very elusive to realize in conventional platforms. In this work, we show that on a programmable quantum hardware platform, the more exotic FQH excitations are the less costly ones to prepare: clustered non-Abelian FQH states admit parallel quantum preparation circuits whose two-qubit depth is independent of system size, while constructing the more common Abelian Laughlin state requires a sequential circuit chain with linear depth. The centerpiece of this work is our new systematic framework for cataloging possible FQH states and preparing them on quantum circuits at unprecedented scale and variety. Our prepared parafermionic Read–Rezayi $\mathbb{Z}_3$ state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read–Rezayi $\mathbb{Z}_4$ state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian $e/4$ quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.

Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth $\Omega(N)$ in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.

The quantum approximate optimization algorithm (QAOA) tackles combinatorial problems by tuning a quantum circuit in a classical loop, often guided by gradients. We show that the gradient used to tune the circuit's final parameter is bounded by imaginarity, which weights phase relationships between candidate solutions by how strongly the circuit connects them and how differently the problem scores them. Imaginarity is necessary but not sufficient for a nonzero gradient. We extend the bound to three common noise models and compare it numerically with the gradient in Max-Cut simulations.

Perfect prepare-and-measure games exhibit an all-or-nothing quantum advantage: a quantum system of dimension $d$ satisfies every prescribed winning constraint, whereas a classical $d$-level message cannot. We establish three structural results for such forbidden-output support constraints. First, every binary-output support game reduces exactly to a conflict graph: perfect classical realization with a $d$-level message is equivalent to $d$-colorability, perfect $d$-dimensional quantum realization is equivalent to a $d$-dimensional orthogonal representation, and the minimum number of Bob inputs realizing a fixed conflict graph is its edge biclique-cover number. Second, for an arbitrary finite output alphabet, every perfect qubit strategy admits a perfect classical-bit realization. Third, with at most two Bob inputs every perfect qutrit strategy admits a perfect classical-trit realization. An explicit seven-preparation qutrit game with three Bob inputs satisfies $C_3=20<Q_3=S=21$, so three Bob inputs are necessary and sufficient in dimension three. Conversely, a two-input, six-output game in dimension five satisfies $C_5=39<Q_5=S=40$. Thus the smallest dimension admitting a two-input perfect same-dimensional separation is either four or five; the four-dimensional case remains open. As a flagship binary application, the $13$-ray qutrit graph yields a compressed game $(X,Y,B)=(13,8,2)$ with $C_3=39<Q_3=S=40$, and eight Bob inputs are minimal among all binary-output realizations of that graph. Graph extensions demonstrate the mechanism in every dimension, while Torpedo and antidistinguishability games illustrate the genuinely nonbinary regime. These results connect exact communication, graph coloring, contextuality, state exclusion, and zero-error information theory.

Exceptional points (EP's) are a hallmark of non-Hermitian quantum systems. We show that momentum-space deformation provides a general design principle for creating and controlling EP's in quadratic many-body Hamiltonians. We identify universal criteria for the momentum sectors to host EP's and the corresponding critical deformation strengths, while revealing that a single momentum-sector EP induces quite remarkably an exponential proliferation of many-body eigenvector coalescences. We further establish EP's as a universal mechanism for purifying arbitrary mixed quantum states, uncovering distinct purification regimes and a fundamental odd-even system-size dichotomy in the thermodynamic limit. Our framework also provides a systematic reverse-engineering protocol for generating short- and long-range, reciprocal and nonreciprocal non-Hermitian quantum matter, together with an explicit Lindblad embedding. These results thus establish momentum-space deformation as a unified route to exceptional-point engineering and controlled design of many-body non-Hermitian quantum systems.

Liouvillian eigenvalues determine decay rates and oscillation frequencies, but not how the corresponding modes are excited, propagated, and detected in a chosen protocol. We develop an operational spectral theory based on matched left and right eigenoperators. Left eigenoperators determine excitation by an input or source; right eigenoperators determine the propagated density deformation and readout overlap; their product is a gauge-invariant modal weight. For bosonic systems, coherent preparations turn left eigenoperators into phase-space excitation maps whose zeros identify mode-selective suppression, while right eigenoperators yield the corresponding Wigner deformations. Resolved slow subspaces define operational coordinates and, when positivity and Markov-admissibility hold, a projected routing generator. In driven Kerr resonators, the framework identifies preparations that suppress a switching mode, separates symmetry-resolved relaxation channels, and reveals bias-induced crossovers in projected multichannel routing while the coherent-preparation partition continues to deform. Preparation geometry and slow-sector propagation thus provide complementary operational information beyond Liouvillian eigenvalues alone.

Understanding the effectiveness of quantum compilation techniques requires visibility into the entire transpilation process, not just the final circuit metrics. This demonstration presents an MLflow-inspired autologging framework for Qiskit that automatically captures compiler provenance, including transpilation stages, pass-level execution data, backend characteristics, compiler configuration, and execution results. The framework extends the QProv provenance model with compiler-specific information and stores the collected data in an MLflow Tracking Server for analysis and visualization. By eliminating manual instrumentation, the proposed approach improves compiler observability and supports reproducible evaluation of quantum compilation workflows.

We analyze a temporal-mode extension of the two-way LM05 quantum communication primitive, in which a message block is encoded into a fixed-weight binary occupation vector (the support) alongside classical ordering information. We demonstrate that applying an independent-slot recovery model to this correlated source is fundamentally inconsistent. For an ideal erasure channel, we derive the exact maximum-a-posteriori (MAP) recovery probability, showing that source-aware decoding outperforms independent guessing by orders of magnitude. We extend this analysis to a realistic threshold-detector model, quantifying the degradation caused by dark counts and inefficiency. Furthermore, we clarify the quantum-classical information split: in the ideal single-photon limit, preparation averaging renders Eve's state independent of the support, yielding zero Holevo information. We establish conditional security bounds using entropic uncertainty relations and identify photon-number-splitting as the primary practical vulnerability. These results provide a rigorous source-aware recovery benchmark and define the physical conditions under which the quantum layer offers a key-consumption advantage over classical constant-weight coding.

Neutral atom quantum computing utilizes laser-trapped neutral atoms as qubits and realizes quantum logic gate operations through Rydberg-state interactions. In recent years, it has become one of the most vibrant directions in quantum computing hardware. This paper systematically reviews the working principles of neutral-atom quantum computers, including qubit encoding, atom trapping and manipulation, Rydberg states and interactions, the Rydberg blockade quantum gate mechanism, and atom rearrangement with reconfigurable architectures. The mainstream technical routes are surveyed, represented by optical tweezer arrays combined with Rydberg interactions, optical lattice schemes, and dipole trap arrays. A panoramic review is provided of domestic and international research progress from theoretical foundations in 2000 to the latest achievements in 2026, including thousand-qubit-scale systems, logical qubits, and quantum error correction experiments. Key breakthroughs are highlighted, such as the 6100-atom qubit array, continuous operation of a 3000-qubit system, quantum simulation of the Kitaev honeycomb model, toric code error correction demonstrations, encoding rates exceeding 1/2, and fault-tolerant architectures. The core bottlenecks are analyzed in depth, including the scalability–fidelity trade-off, engineering implementation of quantum error correction, atom loss and mid-circuit replenishment, laser system industrialization, control electronics scalability, and long-distance quantum interconnection. This paper aims to provide a systematic reference for academic research and technological development in this field.

Multiport interferometers with $N$ ports are basic devices in both classical and quantum photonics. Ideally, they implement a linear unitary transformation between the input and output electric field vectors with $N$ components, each associated with a spatial mode of classical coherent light or a single photon. Standard designs for a fully reconfigurable universal multiport interferometer are given by the Reck or the Clements schemes. In this work, we introduce routing schemes to implement a generic unitary transformation on classical coherent light or single photons using linear or tree geometries via multiple projective measurements on a single detector with the minimum number of components. Then, we generalize this result to the case of any multi-photon state for scattershot boson sampling experiments with multi-routing schemes. Finally, we test the robustness of routing schemes compared to universal schemes with respect to losses and phase noise.

Bergemann and Morris (2016) show that one information structure is more informative than another exactly when it induces a smaller set of Bayes correlated equilibrium outcomes in every game. We build the quantum analogue. An information structure becomes a family of density operators indexed by the payoff state, which the mediator observes. We show that obedience is equivalent to a Loewner domination between operators on one player's subsystem. The equilibrium set is then a nonempty compact spectrahedron computable by semidefinite programming, classical structures embed exactly, and under quantum individual sufficiency more information shrinks the equilibrium set in every game.

Fast preparation of quantum error-correcting codes is essential for scalable quantum memories, but geometric locality and $U(1)$ charge conservation impose an unavoidable transport constraint. We combine exact complementary-channel geometry, charge-sector Haar analysis, and a gate-resolved connected-moment expansion to study one-dimensional covariant encoders under flagged erasure. Charge-Haar codes attain the universal adjacent-charge lower bound up to exponentially small corrections, yielding an exact $n^{-1/2}$ extensive-erasure law and a sharp half-erasure transition. For local number-conserving brickwork circuits, diffusion of the logical charge enforces an $\Omega(n^2)$ encoding-time lower bound; we also prove an $O(n^3)$ mixing bound for the classical component and reduce the remaining full-channel upper bound to a source-restricted low-support operator-spreading problem. These results identify diffusion as an operational limit on symmetry-constrained quantum coding and establish a route to its exact formation time.

We determine the sharp modulus of continuity, in trace distance, of the optimized Petz and sandwiched Rényi conditional entropies for every order $\alpha\in[\frac12,1)$. If two bipartite states are within trace distance $\delta$, then both conditional entropies differ by at most $\frac{1}{1-\alpha} \log[(1-\varepsilon)^{\alpha} +(D-1)^{1-\alpha}\varepsilon^{\alpha}]$, where $\varepsilon := \min\{\delta,1-1/D\}$ and $D$ is the effective dimension, given by the dimension of the first subsystem times the largest possible Schmidt rank. For every distance constraint $\delta\in[0,1]$, the bound is attained by an isotropic pair with a maximally entangled anchor. Taking $\alpha\uparrow1$ recovers the recent sharp continuity bound of quantum conditional entropy by Berta et al. [arXiv:2607.24687]. The proof linearizes the relevant concave Rényi functional at a comparison point dictated by the isotropic equality family. Schmidt-rank domination extends the equality geometry to an arbitrary anchor state, after which trace-distance duality and a noncommutative calibration estimate control the perturbation and anchor term without weakening the sharp constant. The latter estimate requires matrix analysis and is assisted by ChatGPT 5.6 Sol.

Quantum computing is a deep technology whose progress cannot be driven effectively from one direction alone. While the field has developed a growing catalogue of mathematically grounded algorithmic speedups, industrial impact will depend just as much on starting from real industrial decision contexts and working downward to what must be computed, validated and integrated. In this Perspective, I argue that sustained progress requires treating these two directions: bottom-up development from physics, hardware and algorithms, and top-down development from industrial needs and constraints. Equally primary and continuously coupled. This dual-viewpoint is not a matter of balance for its own sake. Quantum computers cannot solve arbitrary problems, so engagement with industry must remain anchored in algorithmic tractability. Yet tractable computations are rarely valuable unless they connect to decision points in established workflows such as candidate selection in drug discovery or the design of a new aircraft shape with improved aerodynamics. I analyse how historical narratives and structural separations of expertise slowed the formation of this coupling and outline what it takes to build it: explicit interfaces between technical teams and domain context and intermediate layers that translate quantum outputs into decision-relevant observables without suffocating foundational innovation. Framed this way, quantum computing's opportunity is clearest where deep physical modelling meets high-value decisions. Provided the field co-designs both sides from the outset.

Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.

Quantum superresolution reveals that the vanishing of separation sensitivity in conventional imaging below the Rayleigh limit does not necessarily indicate a fundamental loss of information in the optical field. However, the quantum limit for estimating the physical distance between two incoherent point sources in three-dimensional imaging systems and its dependence on the spatial structure of the point-spread function remains largely unknown. In this work, we derive the quantum-limited precision for estimating the full distance between two incoherent point sources with arbitrary intensity imbalance in a three-dimensional spatially invariant imaging system. We show that the distance information remains finite in the sub-Rayleigh regime and is governed by the second-order displacement-response tensor of the point-spread function. The eigensystem of this tensor determines the optimal relative orientation between the two sources, and reflection symmetries of the point-spread function can further provide a simplified means of identifying the optimal orientation. This geometric structure is coordinate invariant and provides a direct strategy for improving resolution by physically rotating an anisotropic imaging system to align its optimal principal response direction with the source displacement. For a general three-dimensional Gaussian point-spread function, the response tensor is proportional to the inverse spatial covariance, establishing a direct connection between quantum-limited distance precision and the geometry of Gaussian distribution.

Qualification of quantum states judges which of two sets of quantum states an unknown state lies in, where the two sets are labeled by two distinct parameter regions. We formulate this problem as a composite quantum hypothesis test and uncover universal scaling laws for the minimum error probability for $N$ copies. Taking polarization-direction qualification and purity qualification as examples, we show that the $N$-copy permutation symmetry and the geometric symmetries of the parameter regions identify the optimal measurements and the "worst pairwise states". The minimum error probability scales as $N^{-3/2}\exp(-N\xi)$ for disjoint regions and as $(NF)^{-1/2}$ for adjacent regions, where $\xi$ and $F$ are the quantum Chernoff divergence and quantum Fisher information associated with the "worst pairwise states", respectively. With the minimum error probability serving as an order parameter, the transition between the scaling behaviors becomes a second-order phase transition as $N\to\infty$. Our approach determines whether a quantum state belongs to a given set without full state tomography, thereby enabling qualification of large ensembles using finite samples.

The recently proposed spontaneous disentanglement hypothesis is formulated using a modified Schrödinger equation having an added nonlinear term. The hypothesis is motivated by some outstanding issues in the foundations of quantum mechanics, including the problem of quantum measurement. Spontaneous disentanglement is explored in the current study for the macroscopic limit. This is done using some many–body models having known exact solutions. For the under–study models, it is found that non–local entanglement becomes unstable in the macroscopic limit. On the other hand, stability in the macroscopic limit of local entanglement is not excluded. These findings demonstrate that the spontaneous disentanglement hypothesis can bridge between the quantumness of the microscopic realm, and the classicalness of the macroscopic one.

Although Arnoldi reduction of a generally non-Hermitian Hamiltonian yields an upper Hessenberg matrix rather than the tridiagonal form of Hermitian Lanczos theory, we show that a closed Toda sector survives in its diagonal and subdiagonal coefficients. For a fixed finite-dimensional Hamiltonian and a cyclic state vector deformed holomorphically, the Krylov Gram determinants are $\tau$ functions of the finite two-dimensional Toda lattice, whose Flaschka variables coincide exactly with these Arnoldi coefficients. The Toda dynamics therefore closes on this sector without determining the remaining upper Hessenberg entries. The subdiagonal part of the same sector also has a direct geometric meaning: the squared subdiagonal coefficients determine both the Fubini–Study metric and the Berry curvature of holomorphic Krylov subspaces, whereas the geometric quantities associated with subspaces lost at Arnoldi breakdown cease to be defined. Along a smooth real path in the cyclic region, the Arnoldi-frame connection further provides a Hermitian tridiagonal generator of exact isospectral transport. When added to the Arnoldi matrix, this generator cancels transitions between instantaneous eigenspaces and realizes counterdiabatic driving whenever the matrix is diagonalizable with a nondegenerate spectrum.

We study the dynamics of a single quantum particle on a finite-size square lattice with a fractal structure resembling the Sierpiński carpet, and compare it to the dynamics on a uniform lattice of the same size. For a particle initially localized at a corner of the lattice, we monitor the probability of finding it near the initial and opposite corners using zone-integrated probabilities, allowing a consistent comparison across fractal orders. While on the uniform lattice the particle reaches the opposite corner ballistically, in a time proportional to the lattice size, on the Sierpiński lattice it becomes increasingly confined to the vicinity of its initial position. We show that this trapping builds up self-similarly across the whole hierarchy of corner zones of the lattice.

All realistic quantum systems are inevitably in contact with the environment. Suppressing theimpact of environmental noise is a critical challenge in cutting-edge quantum technologies. In thiswork, we introduce and systematically analyze a scheme for the protection of quantum states againstamplitude-damping (AD) noise based on the circuit structure called the quantum filter. Filtrationcircuits employing single- and multi-control qubits are examined, and their capability to enhance stateprotection fidelity while preserving a high success probability is discussed. Moreover, for many-bodyqubit states, those with a fixed quantum Hamming weight can be perfectly protected against ADnoise, whereas states with the largest Hamming weight difference set a lower bound on the achievableprotection fidelity. Our work provides a resource-efficient route for quantum state protection withoutrequiring full quantum error correction.

Rydberg entangling gates in optical-tweezer arrays are commonly executed with the trapping light switched off, so every gate contains a release–and–recapture cycle that heats the atomic motion and can ultimately limit circuit depth. We develop a motional refocusing protocol that exactly removes this heating in the harmonic approximation using only programmable intensity switching of the trapping light. The protocol closes the release–and–recapture cycle for every matched harmonic mode, returning arbitrary motional populations and coherences exactly up to ordinary evolution under the static trap. We derive the recovery sequence in closed form for arbitrary catch depth and prove that, within the experimentally relevant regime, it is the unique globally time-optimal solution under bounded trap intensity. The harmonic theory is then extended in two directions. First, we construct exact common-intensity recovery sequences that simultaneously refocus several nondegenerate harmonic modes, including radial–axial and fully anisotropic three-dimensional traps. Second, we derive a composite sequence that suppresses the leading anharmonic correction of weakly anharmonic traps by canceling all first-order motional transitions induced by the quartic anharmonicity, changing the residual heating law from $U_0^{-2}$ to $U_0^{-4}$. Wave-packet simulations in realistic Gaussian tweezers validate the analytic theory and quantify the residual effects of anharmonicity, finite switching ramps, trap ellipticity, and control errors. Applied to representative cesium Rydberg gates, the protocol suppresses the dominant recapture heating to the anharmonic floor and prevents the associated motional Doppler contribution from increasing with circuit depth. The resulting framework provides a practical route toward heating-free trap-off neutral-atom gates using only trap-intensity modulation.

The tin-vacancy (SnV) center in diamond is a promising spin-photon interface for quantum networks, combining favorable optical properties with spin coherence above 1K. Unfolding the full potential requires cavity enhancement to increase photon-emitter coupling efficiency. Here, we demonstrate cavity-enhanced light-matter coupling of SnV centers in a fully tunable Fabry-Pérot microcavity operating at temperatures down to 1K with in-situ magnetic field control. We access the diamond-like regime of hybrid cavity modes through integration of low-roughness diamond membranes, where the field is concentrated inside the diamond and Purcell enhancement is maximized. Diamond-like modes deliver a more than two-fold increase in the effective Purcell factor over air-like modes, reaching $C_0 = 4.1(1)$ compared to $C_0 = 1.85(5)$ in the air-like case, while simultaneously relaxing mechanical stability requirements. Resonant probing reveals coherent cavity-emitter coupling with 96% extinction contrast and a coherent cooperativity of $C = 4.0(14)$. By applying a magnetic field, we further achieve spin-resolved cavity extinction, observing spin-selective optical transitions with a contrast of ${\cal C}_{\rm spin} = 0.91$. These results establish SnV centers in diamond coupled to open Fabry-Pérot microcavities as a promising platform for efficient spin-photon interfaces.