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Jingbo Wang

Publications and source records attributed to Jingbo Wang.

At least 37 records · Page 2Linked to original sources
arXiv2026

An Exactness Barrier for ZX-Calculus Optimization of Synthesized Clifford+T Circuits

Gate synthesis and circuit optimization are usually studied separately, and evidence on their interaction is contradictory: ZX-calculus rewriting removes a stable fraction of Solovay-Kitaev circuits, yet almost nothing from number-theoretically synthesized circuits. We show both behaviours follow from a single bound. For any optimizer that preserves the implemented element exactly--including all sound ZX rewriting with extraction--the achievable T-count is bounded below by the denominator exponent of the synthesized ring element. This exactness barrier is computable per instance and separates exact post-processing from approximation-aware resynthesis by a certified factor reaching 101x at recursion depth five. The two behaviours are then the barrier operating at different distances from the floor. For Solovay-Kitaev circuits we prove that the local ZX simplification layer (spider fusion and identity removal) computes exactly the free-product normal form of Z_2 * Z_8, giving exact per-instance compression and, under a calibrated ergodicity hypothesis, a depth-independent limit law confirmed on two independently constructed nets. For number-theoretically synthesized circuits the floor is already saturated: on single-qubit words automated ZX simplification attains it exactly, via a closed-form formula for minimal T-count in terms of phase linkage through the Z-axis normalizer. At two qubits and beyond the same valuation yields unconditional rigidity certificates, which on the quantum-Shannon-decomposition plus gridsynth pipeline certify 99.4-99.9% of the synthesized T-count as incompressible, with rigidity strengthening as accuracy tightens. This explains, and predicts the size of, the near-null optimization recently reported for that pipeline.

quant-ph↗
arXiv2026

Numerical Evaluation of ZX Calculus Optimization for Solovay Kitaev Quantum Circuit Synthesis

Fault-tolerant architectures implement non-Clifford T gates through magic-state distillation, so the T-count of a synthesized circuit dominates its physical cost. The Solovay-Kitaev algorithm approximates any single-qubit unitary from a finite gate set with a sequence length that grows only polylogarithmically in the inverse target error, but it optimizes for numerical convergence rather than circuit economy, and its output carries structural redundancy that a gate-level compiler cannot see. We report a measurement of what diagrammatic post-processing recovers from that redundancy. Twelve hundred random single-qubit targets, spanning the three Pauli rotation families and the general gate U(theta, phi, lambda), are synthesized over Clifford+T at three recursion depths, translated into graph-like ZX-diagrams, simplified by automated rewriting, and extracted back to circuits. Post-processing removes 26.6-30.1% of the total gate count and 18.5-22.2% of the T-count. The absolute saving grows with recursion depth, from about 60 to about 1600 gates, while the fractional saving does not: it rises slightly from the shallowest setting and is then flat across a twenty-five-fold change in circuit length, and by the deepest setting the four target families are no longer distinguishable from one another. Because the rewrite rules preserve the implemented linear map, the approximation error is unchanged. The compile-time cost of the rewriting layer, by contrast, grows sharply with depth and comes to dominate the synthesis itself.

quant-ph↗
arXiv2026

Analyzing and Mitigating Cross-Lingual Degradation in Multilingual Medical VQA

Medical visual question answering (VQA) is a crucial task in clinical AI, yet its evaluation has so far centered almost exclusively on English, limiting its relevance to linguistically diverse patients and clinicians. Recent multilingual medical VQA benchmarks show that large vision-language models (LVLMs) degrade in non-English languages, but lack a fine-grained analysis of how cross-lingual variation affects the distinct capabilities that medical VQA requires. To this end, we construct a multilingual medical VQA benchmark over eight languages, organized into four representative scenarios that isolate the core capabilities medical VQA requires. Evaluating five open- and closed-source LVLMs, we find that cross-lingual degradation is not uniform but highly scenario-dependent. We therefore propose MedVL-XLRepE, a training-free scenario-aware representation engineering method, leveraging LVLMs' superior English medical VQA capability to steer non-English representations toward their English counterparts at inference time. Across three LVLMs and eight languages, MedVL-XLRepE consistently mitigates cross-lingual degradation, with gains of up to 6.33\%.

cs.AI↗
arXiv2026

Towards Professional Tennis Styles for Humanoid Robots with Adaptive Motion Planning and Tracking

Humanoid robots have recently demonstrated promising capabilities in real-world ball sports. However, achieving professional motion styles while maintaining strong task performance remains challenging. In this work, we propose AdaPT, an Adaptive Motion Planning and Tracking framework that learns professional tennis serving and rally styles directly from broadcast videos. This hierarchical design is motivated by the key insight that the planner generates stylistic kinematic motions, while the tracker executes them with minimal interference with planning. Despite its effectiveness in simulation, a substantial sim-to-real gap emerges: tracking performance inevitably degrades on real robots, and this degradation is partially overlooked by autoregressive planning and further compounded by noisy perception. To address these issues, our adaptation mechanism improves tracking robustness by learning to track randomized execution speeds, while conditioning the planner on a learned motion-speed adapter to mitigate compounding errors. Real-world experiments on the Unitree G1 demonstrate the effectiveness of our adaptation mechanism in bridging the sim-to-real gap. We further deploy AdaPT policies on the full-size Dobot Atom humanoid robot (1.7m) and demonstrate in-the-wild serving without motion capture. Beyond these results, our real-world experiments reveal both algorithmic and engineering insights for future humanoid ball-sports systems. Videos and code are available on our \href{https://humanoidtennis.github.io/AdaPT/}{project website}.

cs.RO↗
arXiv2026

Fusion-Aware Direct 3D Gaussian Generation with Structured Patch Latent Flows

Class-guided 3D object generation is important for intelligent content creation, virtual environments, and digital asset design. Although 3D Gaussian Splatting (3DGS) offers an explicit and render-efficient representation, directly generating 3D Gaussian objects is difficult because Gaussian primitives are unordered, variable-sized, locally dense, and highly sensitive to rendering. Existing 3DGS generation methods usually depend on multi-view synthesis, reconstruction, or lifted 2D priors, fusing information mainly from observed views rather than modeling the intrinsic structural distribution of 3D Gaussian objects. This paper proposes a fusion-aware hierarchical Gaussian patch representation for direct class-guided 3DGS generation with rectified flow. Irregular Gaussian sets are decomposed into canonical local patches and encoded as structured tokens. The resulting hierarchical latent space fuses global class semantics, patch-level geometry and appearance, spatial correspondence, and rendering-sensitive cues. On this basis, we design a structure-aware rectified flow model with patch-position conditioning, global-local coupled velocity prediction, and density-aware velocity weighting, enabling direct latent generation of class-conditioned 3DGS objects within seconds. A render-feedback fusion strategy further aligns latent flow learning with decoded multi-view rendering quality. Experiments show that the proposed method generates 3D Gaussian objects with more coherent geometry, sharper local details, and better multi-view consistency than baseline latent generative models. Ablation studies confirm the contributions of hierarchical information fusion, global-local coupling, density-aware supervision, and render-feedback learning while preserving practical sampling efficiency overall.

cs.CV↗
arXiv2026

Task-Prototype Guided Flow Matching for Few-Shot Generalization in Vision-Language Robot Manipulation

Vision-language robot manipulation policies can follow semantic instructions, but adapting them to a new procedure from only a few demonstrations remains difficult because language underspecifies contact timing, motion phases, corrective behavior, and execution style. This paper presents Task-Prototype Guided Flow Matching (TP-Flow), a few-shot manipulation framework that converts support demonstrations into structured task-prototype tokens and uses them to guide both the initial flow prior and the velocity field. TP-Flow employs symmetric cross-attention with learnable queries to extract phase-level prototypes, parameterizes a task-adaptive initial distribution, and injects prototype information through gated adaptive normalization. It is trained with an episodic support-query objective and prototype contrastive regularization, so few-shot adaptation is simulated during training while nuisance information is suppressed. On the LEROBOT-ARM-SO101 platform, TP-Flow achieves 66.8\%, 79.6\%, and 82.1\% success rates under 1-, 4-, and 6-shot settings, with a 75.5\% few-shot AUC. At 1-shot, it improves over CFM, Pooled-Demo CFM, and In-Context Flow by 29.8, 14.5, and 9.9 percentage points. It also improves held-out target-group generalization across novel-object transfer, goal recombination, long-horizon composition, and contact/correction tasks. TP-Flow maintains real-time execution with six online prototype tokens, 54.3 ms latency, 3.9 GB peak memory, and a 10 Hz control rate, while reducing the noisy-support success drop to 6.2\%. Theoretical diagnostics show that prototype distance aligns with action-distribution distance, the adaptive prior reduces transport cost, and gated modulation keeps measured trajectory deviations below the derived ODE bound. The code repository is omitted for anonymous review.

cs.RO↗
arXiv2026

Beyond Similarity Matching: Structured Reasoning for Open-Vocabulary Referring Segmentation in 3DGS

Open-vocabulary referring segmentation in 3D Gaussian Splatting (3DGS) requires a neural model to select Gaussian primitives according to free-form language expressions. Existing 3DGS-based methods usually rely on global text-region similarity, which is weak for queries involving attributes, reference objects, spatial relations, and fine-grained parts. This often causes target-reference confusion, granularity mismatch, part-whole leakage, and relation violations. We propose QAGaussian, a query-adaptive neural reasoning framework for language-guided Gaussian primitive selection. QAGaussian first learns query-conditioned multi-scale Gaussian slots as differentiable candidates whose receptive fields are shaped by the input expression. It then builds a relation-aware slot graph with language-conditioned edge weighting to propagate target-reference, attribute, part-whole, and contextual evidence. A granularity-adaptive router softly combines region-level, object-level, part-level, attribute-aware, and relation-aware mask branches, followed by relation-constrained refinement for spatial, part-whole, attribute, and geometric consistency. QAGaussian is pretrained only on Mosaic3D-5.6M for Gaussian-text alignment and evaluated on independent benchmarks without target-dataset fine-tuning. It achieves 47.2 Avg. mIoU and 63.2 Avg. F1, outperforming the strongest 3DGS referring baseline by 2.7 mIoU points and 2.9 F1 points. It also improves Part-mIoU from 38.6 to 43.4, Rel-mIoU from 44.4 to 50.8, and reduces target-reference confusion from 10.8 to 7.4. These results demonstrate that query-conditioned slot learning, relation-aware graph reasoning, and adaptive routing provide an effective neural modeling strategy for open-vocabulary referring segmentation in 3DGS. The code is available at https://github.com/zqeslwyz/QAGaussian.

cs.CV↗
arXiv2026

RoboStriker: Latent-Space Strategic Games for Autonomous Humanoid Boxing

Achieving human-level competitive intelligence and physical agility in humanoid robots remains a profound challenge, particularly in contact-rich and highly dynamic tasks such as boxing. While Multi-Agent Reinforcement Learning offers a principled framework for strategic interaction, its direct application to unstructured raw motor spaces inevitably leads to joint-level physical collapse, preventing the emergence of any viable combat tactics. To resolve this fundamental conflict between strategic exploration and physical feasibility, we formulate the humanoid combat task as a novel two-player latent-space zero-sum Markov game. Under standard regularity and approximate best-response assumptions, we show that the latent formulation induces an equivalent game over the decoder-reachable action manifold, providing an approximate-Nash interpretation of the resulting self-play dynamics. To instantiate this theoretical formulation, we propose RoboStriker, a hierarchical framework that decouples high-level reasoning from low-level execution. It first distills the tracking expertise of predefined boxing motions into a topologically bounded latent manifold. This structured latent foundation subsequently drives multi-agent co-evolution via Latent-Space Neural Fictitious Self-Play. Extensive experimental results demonstrate that gaming within this structured latent space substantially outperforms direct exploration. By constraining strategic exploration through a pretrained motion decoder, RoboStriker substantially reduces the catastrophic balance failures observed in raw action-space methods and achieves superior tactical performance in both competitive win rates and striking efficiency. Finally, we successfully deploy and validate our learned combat policies on real-world humanoid robots. Our code and video and supplementary materials are available at RoboStriker.

cs.RO↗
arXiv2026

Conflict Extraction in Probabilistic Datalog Analyses

Probabilistic extensions of Datalog enable static analyses such as pointer analysis, data race detection, and side-channel analysis to rank alarms by likelihood, but this added expressiveness also introduces a new challenge absent from deterministic analyses: the final output may contain alarms that are individually plausible yet mutually inconsistent, because marginal probabilities do not guarantee joint satisfiability. As a result, developers may spend effort investigating combinations of alarms that can never co-occur in any possible world. We address this problem by formalizing such inconsistencies as minimal unsatisfiable subsets (MUSes) and introducing PPProbe, a conflict extractor specialized for probabilistic Datalog analyses. Rather than improving MUS enumeration in general, PPProbe exploits the structure of Datalog derivation graphs to guide the search toward likely conflicts and prune the search space through bottom-up UNSAT inference. We evaluate PPProbe on 70 benchmarks from power side-channel analysis, data race detection, semantic diffing, and Bayesian-network inference. The results show that PPProbe achieves 2.5 to 24 times higher throughput than state-of-the-art MUS enumerators, and that the conflicts it identifies yield a conservative estimate of false-positive reduction, filtering out an average of 47.7% of mutually inconsistent alarms.

cs.SE↗
arXiv2026

DFM-VLA: Iterative Action Refinement for Robot Manipulation via Discrete Flow Matching

Vision-Language-Action (VLA) models that encode actions using a discrete tokenization scheme have been widely adopted for robotic manipulation, but existing decoding paradigms remain fundamentally limited. Whether actions are decoded sequentially by autoregressive VLAs or in parallel by discrete diffusion VLAs, once a token is generated, it is typically fixed and cannot be revised in subsequent iterations. Consequently, early token errors cannot be effectively corrected later. We propose DFM-VLA, a discrete flow matching VLA that iteratively refines action tokens. DFM-VLA models a token-level probability velocity field that dynamically updates the full action sequence across refinement iterations. We investigate two approaches to constructing the velocity field: an auxiliary velocity-head formulation and an embedding-guided formulation. To further improve prediction accuracy, we introduce a metric-aligned action tokenizer (MAAT) tailored to the coarse-to-fine nature of DFM, together with a two-stage decoding strategy. Extensive experiments on CALVIN, LIBERO, LIBERO-Plus, and real-world manipulation tasks demonstrate the effectiveness of our approach. Our project is available at https://chris1220313648.github.io/DFM-VLA/.

cs.RO↗
arXiv2026

Möbius-Guided Diagonal-Gate Compilation with Native Multiqubit Controlled-Phase Gates on Neutral-Atom Processors

Diagonal gates are ubiquitous primitives in quantum algorithms, from phase oracles, hypergraph-state preparation, and multi-control logic to Hamiltonian simulation of spin models and digitized lattice field theories, where Ising interactions and local potential terms are diagonal in the encoded basis. Standard compilers, however, often lower diagonal structure into one- and two-qubit gates before neutral-atom hardware can exploit native Rydberg-mediated multiqubit controlled-phase operations. We propose a Möbius-guided compiler that maps a diagonal phase function to a phase hypergraph via subset-lattice Möbius inversion. The hypergraph retains the support and angle of each many-body phase term, allowing sparse or local high-order structure to be routed as native multiqubit controlled-phase candidates when feasible and decomposed otherwise. The neutral-atom scheduler accounts for atom motion, interaction-zone constraints, blockade feasibility, and error costs, enabling a direct comparison between native high-order execution and decomposed alternatives. Benchmarks against routed ZAP and ZX-calculus baselines show improved estimated success for algorithmic instances with exploitable three- and four-body phase terms, and comparable performance on predominantly two-body instances. These results provide a feasible compilation strategy for more fully exploiting the native capabilities of neutral-atom hardware, using atom reconfigurability and Rydberg-mediated multiqubit phase operations as practical resources for more efficient quantum computation.

quant-ph↗
arXiv2026

ABot-AgentOS: A General Robotic Agent OS with Lifelong Multi-modal Memory

Recent VLM and VLA systems have improved robotic perception and action prediction, yet long-horizon embodied agents still require a general runtime layer for reasoning, memory, tool use, verification, and cross-embodiment execution. We present ABot-AgentOS, a general robotic Agent Operating System that sits above low-level controllers and provides a deliberative agent layer for scene-conditioned planning, context-isolated skill execution, multi-stage verification, multi-modal memory, and edge-cloud collaboration. To evaluate such systems, we introduce EmbodiedWorldBench, an executable benchmark with 16 indoor, outdoor, and hybrid scenes, four difficulty levels, and over 200 tasks involving navigation, object search, NPC dialogue, dynamic events, and trace-grounded scoring. ABot-AgentOS further introduces Universal Multi-modal Graph Memory, a persistent source-grounded substrate that converts dialogue, visual observations, spatial context, temporal relations, and task traces into typed nodes and edges. A failure-driven self-evolution loop converts diagnosed memory failures into gated runtime evo-assets that are promoted only to later evaluation splits, preventing current-split ground-truth leakage while enabling continual improvement. On an initial EmbodiedWorldBench subset, ABot-AgentOS improves over a single-controller baseline in both task success and goal completion. Across memory benchmarks, ABot-AgentOS Static achieves 87.5 on LoCoMo, 59.9 on OpenEQA EM-EQA, 88.6 on Mem-Gallery, and 76.5 Acc@All on NExT-QA; self-evolution further improves LoCoMo to 88.7, OpenEQA to 60.4, and Mem-Gallery to 89.0. These results suggest that a general Agent OS layer can improve long-horizon embodied execution while providing persistent, auditable memory for continual interaction.

cs.AI↗
arXiv2026

Scaling Behavior Foundation Model for Humanoid Robots

Humanoid control requires natural whole-body coordination, precise real-time responses to control signals, and robust generalization across diverse environmental contexts, making it a cornerstone for generalist embodied agents. Behavior Foundation Models (BFMs) have recently emerged as a promising solution to address these challenges by leveraging large-scale behavioral data to achieve superior expressiveness, versatility and generalization. However, despite growing interest in scaling BFMs to further improve their capabilities, it remains unclear how key factors, including the learning paradigm, behavioral data and model architecture should be coordinated to enable effective scaling. In this work, we revisit the scaling recipe for BFMs and demonstrate that substantial performance gains can be achieved through the coordination of three core components: 1) the learning paradigm of motion tracking that reformulates diverse humanoid control problems as the reproduction of integrated whole-body behaviors in the global frame; 2) the strategic synergy between on-policy rollout quantity and reference motion diversity; and 3) the expressive and scalable model architecture termed Humanoid Transformer that facilitates the natural emergence of structured behavioral representations. Through extensive experiments in both simulation and real-world deployment, we demonstrate that our approach yields significant improvements in control fidelity and task generalization, reducing Mean Per-Keypoint Position Error (MPKPE) on the test set by over 10% in local mode and 82% in global mode compared with existing humanoid controllers. These results establish BFM as a principled and effective foundation for scalable and general-purpose humanoid control.

cs.RO↗
arXiv2026

Optimal-Agent-Selection: State-Aware Routing Framework for Efficient Multi-Agent Collaboration

The emergence of multi-agent systems powered by large language models (LLMs) has unlocked new frontiers in complex task-solving, enabling diverse agents to integrate unique expertise, collaborate flexibly, and address challenges unattainable for individual models. However, the full potential of such systems is hindered by rigid agent scheduling and inefficient coordination strategies that fail to adapt to evolving task requirements. In this paper, we propose STRMAC, a state-aware routing framework designed for efficient collaboration in multi-agent systems. Our method separately encodes interaction history and agent knowledge to power the router, which adaptively selects the most suitable single agent at each step for efficient and effective collaboration. Furthermore, we introduce a self-evolving data generation approach that accelerates the collection of high-quality execution paths for efficient system training. Experiments on challenging collaborative reasoning benchmarks demonstrate that our method achieves state-of-the-art performance, achieving up to 23.8% improvement over baselines and reducing data collection overhead by up to 90.1% compared to exhaustive search.

cs.AI↗
arXiv2026

Lazy-Move Compilation for Neutral-Atom Quantum Computers via a Buffer-Relay Fabric

Neutral atom quantum computing offers strong scalability and flexible qubit connectivity, but most existing compilation flows rely on reconfigurable atom arrays that physically shuttle qubit atoms during execution. Although this approach improves connectivity, it also introduces handoff errors, motional heating, and atom-loss risks that can degrade overall fidelity. We present BRIDGE, a Buffer-Relay Interconnect for Data-stable Gate Execution that co-designs a static, compiler-managed buffer-relay fabric with a lazy-move compiler that exploits it. BRIDGE targets an optimized, dual-species 2D interleaved atom array, using non-encoding ``buffer atoms'' to mediate long-range interactions in the fixed baseline and introducing limited data motion only for selected hotspots. By using calibrated heteronuclear and homonuclear Rydberg channels, BRIDGE realizes a static routing backbone in which data-buffer and buffer-buffer interactions are enabled while residual data-data crosstalk is suppressed. Across a 22-circuit matched benchmark suite re-estimated under a single shared error model, BRIDGE attains a geometric-mean $\sim$10$\times$ higher total fidelity than ZAP and $\sim$16$\times$ than Enola, together with $\sim$540$\times$ and $\sim$1000$\times$ lower circuit execution time, respectively, while reducing data-atom movement from thousands of transport events to zero.

quant-ph↗
arXiv2026

Assessing Cost Hamiltonian Reliability in Quantum Protein Structure Prediction

In variational quantum algorithms, QAOA, and quantum annealing, the cost Hamiltonian defines the optimization landscape explored by the quantum hardware; however, in many application-driven formulations, this Hamiltonian is a simplified proxy for the true task-level objective. Using lattice-based quantum protein structure prediction as a case study, we investigate whether the contact-energy cost Hamiltonian commonly used in this setting is sufficiently aligned with structural accuracy, as measured by RMSD against experimentally determined structures. Through this specific problem, we show the importance of studying the reliability of the cost Hamiltonian independently from the quantum approach used. This work shows that, for small peptides and on average, the energy landscape of the considered cost Hamiltonian is not correlated well enough to the actual error to provide meaningful predictions. Moreover, this correlation was estimated through Monte-Carlo sampling for larger instances. It shows an increase of said correlation for larger problem instances and when more interaction shells are considered. This investigation illustrates the meaningfulness of investigating cost Hamiltonian relevance independently from the quantum algorithm used.

quant-ph↗
arXiv2026

RoboNaldo: Accurate, Stable and Powerful Humanoid Soccer Shooting via Motion-Guided Curriculum Reinforcement Learning

Elite humanoid soccer shooting requires whole-body stability, high-impulse whole-body interactions, and accuracy to targets. Motion tracking-driven reinforcement learning (RL) provides stability in whole-body movement coordination, but a fixed reference makes it hard to adapt to varied ball positions and strike timings; in contrast, task reward-driven RL struggles to explore and discover valid kicks from scratch. We therefore introduce RoboNaldo, a three-stage motion-guided curriculum RL framework for high-impulse humanoid interaction. A single human-kick reference is used as a scaffold and progressively shifts optimization towards shooting performance. The curriculum first learns a stable whole-body kicking prior, then adapts the kick to free-kick settings where the ball is stationary at random positions, and finally extends it to moving-ball shooting through a locomotion-command and kick-trigger interface. A high-level heuristic planner controls this interface during training, while alternative high-level controllers can drive the same low-level policy at inference. In simulation, RoboNaldo demonstrates free-kick shot error 48.6% lower and shoot velocity 2.96x than prior work baselines. In real world on a Unitree G1 with onboard perception, RoboNaldo attains 0.73 m and 0.86 m average target shooting error from 3 m away in free-kick and moving-ball cases, accordingly. And the post-contact ball velocity reaches 13.10 m/s, which is 59-71% of reported professional open-play shot speed. Project page: https://opendrivelab.com/RoboNaldo.

cs.RO↗
arXiv2026

Quantum walk-based optimisation for capacitated vehicle routing with homogeneous and heterogeneous fleets

The capacitated vehicle routing problem (CVRP) is an appealing candidate for quantum optimisation due to its combinatorial complexity and practical importance. However, the problem's constrained search space poses a challenge for such quantum algorithms. We introduce a quantum walk-based optimisation algorithm (QWOA) for the CVRP with homogeneous or heterogeneous vehicle fleets, addressing this challenge through a continuous-time quantum walk over a product space that coincides with combinatorial structures intrinsic to the CVRP solution space. Relative to the prior QWOA-based formulation, this approach reduces the per-layer gate complexity from $\mathcal{O}(n^{3}\log n)$ to $\mathcal{O}(n^{2}\log n)$ and supports a circuit parameterisation schedule generated by a fixed number of classical parameters. Exact state-vector simulation on instances with up to $n=8$ customers and $K=3$ vehicles demonstrates improved convergence to low-cost solutions using markedly fewer objective function evaluations, with the advantage broadening as problem size increases. These results identify structured product-space walks as a promising tool for optimisation over constrained combinatorial spaces.

quant-ph↗