---
title: 'MAGIC: Revealing Hidden Structures'
url: https://www.emergentmind.com/topics/magic-85a949bc-c639-4ca6-8140-60e9d4f9b482
type: topic
---

# MAGIC: Revealing Hidden Structures

to=arxiv_search.search  天天爱彩票提现json
{"query":"all:magic AND (all:quantum OR all:nonstabilizerness OR all:telescope OR all:muons OR all:optics OR all:robot OR all:vision-language)", "max_results": 10, "sort_by":"relevance"}【อ่านข้อความเต็มresponse to=arxiv_search.search  彩票天天  重庆时时彩彩tring
{"results":[{"arxiv_id":"2407.15939","title":"Magic transition in measurement-only circuits","authors":["Y.-C. Wang","Z. Song","D. Mao","Z.-X. Luo","Y. Li","H. Zhou"],"abstract":"Magic, also known as nonstabilizerness, quantifies the distance of a quantum state to the set of stabilizer states, and it serves as a necessary resource for potential quantum advantage over classical computing. In this work, we study magic in a measurement-only quantum circuit with competing types of Clifford and non-Clifford measurements, where magic is injected through the non-Clifford measurements. This circuit can be mapped to a classical model that can be simulated efficiently, and the magic can be characterized using any magic measure that is additive for tensor product of single-qubit states. Leveraging this observation, we study the magic transition in this circuit in both one- and two-dimensional lattices using large-scale numerical simulations. Our results demonstrate the presence of a magic transition between two different phases with extensive magic scaling, separated by a critical point in which the mutual magic exhibits scaling behavior analogous to entanglement. We further show that these two distinct phases can be distinguished by the topological magic. In a different regime, with a vanishing rate of non-Clifford measurements, we find that the magic saturates in both phases. Our work sheds light on the behavior of magic and its linear combinations in quantum circuits, employing genuine magic measures."},{"arxiv_id":"2504.07230","title":"Efficient mutual magic and magic capacity with matrix product states","authors":["K. Haug","L. Piroli"],"abstract":"Stabilizer Renyi entropies (SREs) probe the non-stabilizerness (or magic) of many-body systems and quantum computers. Here, we introduce the mutual von-Neumann SRE and magic capacity, which can be efficiently computed in time O(Nχ3) for matrix product states (MPSs) of bond dimension χ. We find that mutual SRE characterizes the critical point of ground states of the transverse-field Ising model, independently of the chosen local basis. Then, we relate the magic capacity to the anti-flatness of the Pauli spectrum, which quantifies the complexity of computing SREs. The magic capacity characterizes transitions in the ground state of the Heisenberg and Ising model, randomness of Clifford+T circuits, and distinguishes typical and atypical states. Finally, we make progress on numerical techniques: we design two improved Monte-Carlo algorithms to compute the mutual 2-SRE, overcoming limitations of previous approaches based on local update. We also give improved statevector simulation methods for Bell sampling and SREs with O(8N/2) time and O(2N) memory, which we demonstrate for 24 qubits. Our work uncovers improved approaches to study the complexity of quantum many-body systems."},{"arxiv_id":"2606.14855","title":"Magic transfer in quantum spin chains","authors":["L. Lombardo","P. Silvi","P. Verrucchi","C. Degli Esposti Boschi"],"abstract":"Quantum communication protocols based on spin chains have been extensively studied, yet their ability to transmit nonstabilizer resources has not been systematically addressed. We investigate the transport of quantum magic in spin chains through the natural dynamics of systems initialized in nonstabilizer states, and quantify the transported resource via the stabilizer norm. We analyze three experimentally feasible state-transfer protocols, ranging from noisy to (quasi-)perfect transfer, including one realizable in trapped-ion platforms. We find that the geometry of the injected state strongly influences transport: states in the lower Bloch hemisphere achieve higher transfer quality, whereas states in the upper hemisphere give rise to an efficient magic transport only beyond a threshold value of the parameter controlling the tendency towards perfect transfer. These features are robust across all protocols and identify the Hamiltonian and state properties that favor high-quality transfer. Moreover, we identify a parameter region, relevant to the initial state preparation, in which the transported magic exceeds the initial encoding, indicating that such spin systems can act as magic-amplification channels. Our results establish the conditions for efficient transport of nonstabilizer resources and demonstrate quantum magic as a sensitive probe of quantum transport beyond population dynamics."},{"arxiv_id":"2308.01886","title":"Magic of quantum hypergraph states","authors":["Xiang Meng","Shuai Yang","Ji Guan","Eric Chitambar","Xin Wang"],"abstract":"Magic, or nonstabilizerness, characterizes the deviation of a quantum state from the set of stabilizer states and plays a fundamental role from quantum state complexity to universal fault-tolerant quantum computing. However, analytical or even numerical characterizations of magic are very challenging, especially in the multi-qubit system, even with a moderate qubit number. Here we systemically and analytically investigate the magic resource of archetypal multipartite quantum states -- quantum hypergraph states, which can be generated by multi-qubit Controlled-phase gates encoded by hypergraphs. We first give the magic formula in terms of the stabilizer R\\acute{e}nyi-\\alpha entropies for general quantum hypergraph states and prove the magic can not reach the maximal value, if the average degree of the corresponding hypergraph is constant. Then we investigate the statistical behaviors of random hypergraph states and prove the concentration result that typically random hypergraph states can reach the maximal magic. This also suggests an efficient way to generate maximal magic states with random diagonal circuits. Finally, we study some highly symmetric hypergraph states with permutation-symmetry, such as the one whose associated hypergraph is 3-complete, i.e., any three vertices are connected by a hyperedge. Counterintuitively, such states can only possess constant or even exponentially small magic for \\alpha\\geq 2. Our study advances the understanding of multipartite quantum magic and could lead to applications in quantum computing and quantum many-body physics."},{"arxiv_id":"2607.00229","title":"Production of Magic States via Z Bosons and Dark Photons","authors":["D. M. Hofman","J. M. Leinaas","J. A. Sánchez-Burillo","M. S. Tame","R. D. León-Montiel","M. T. Quintino","A. del Campo"],"abstract":"The production of magic states is studied in two settings. The first is the electroweak (EW) sector of the Standard Model (SM). The second is an extension featuring a new broken U(1) gauge symmetry and a Dirac fermion charged under it. This setup resembles a dark U(1) scenario, with the additional fermion playing the role of a dark matter candidate that annihilates into SM particles through its coupling to the new gauge boson. In the EW sector, the low-energy regime reproduces earlier magic production results obtained for Quantum Electrodynamics, whereas the high-energy and Z-resonance regimes generate new magic distribution functions and non-trivially reorganize the stabilizer state classes, with Bhabha scattering exhibiting the strongest sensitivity to electroweak effects. Also, a subset of fixed stabilizer states is identified, for which the magic distributions remain unchanged across the different energy regimes. In the dark sector, the main effect of the new massive mediator is the appearance of new magic distributions functions for Moller-like, Bhabha-like, and inverse pair-annihilation processes in the low-energy limit. These reach the maximal magic value at the SM-to-dark fermion mass ratios mf/mχ→0 and mf/mχ→1.83929."},{"arxiv_id":"1110.0947","title":"Performance of the MAGIC Stereo System","authors":["J. Aleksić","M. Alvarez","H. Anderhub","L. A. Antonelli","P. Antoranz","M. Backes","C. Baittinger","J. A. Barrio","H. Bartko","D. Bastieri","et al."],"abstract":"MAGIC is a system of two Imaging Atmospheric Cherenkov Telescopes sensitive above ~60 GeV, and located on the Canary Island of La Palma at the height of 2200 m.a.s.l. Since Autumn 2009 both telescopes are working together in stereoscopic mode. We use both Crab Nebula observations and Monte Carlo simulations to evaluate the performance of the system. Advanced stereo analysis allows MAGIC to achieve a sensitivity better than 0.8% of the Crab Nebula flux in 50 h of observations in the medium energy range (around a few hundred GeV). At those energies the angular resolution is better than 0.07{\\circ}, and the energy resolution is as good as 16%. We perform also a detailed study of possible systematics effects for the MAGIC telescopes."},{"arxiv_id":"2303.06290","title":"Magnetic field imaging by cosmic-ray muons (Magic-μ) -- First feasibility simulation for strong magnetic fields","authors":["Y. Morishima","H. K. M. Tanaka"],"abstract":"We have proposed a novel application for cosmic-ray muography, called Magic-μ, which is short for Magnetic field Imaging by Cosmic-ray Muons. The general goal of Magic-μ is to detect the presence of a magnetic field or magnetic flux density whose three-dimensional distribution is unknown. Depending on the application, Magic-μ can have three detection modes. The first is \"magnetic field imaging,\" which is detecting the presence of a magnetic field in specific voxels within a region of space. The other two modes, transmission and deflection, aim not only to detect the presence but also to measure the flux density of the magnetic field. We have performed a feasibility study using the PHITS Monte Carlo simulation code, for strong and weak magnetic fields. In this paper, we first give an overview of the concept and basic principles of magnetic field muography. Then, the results of the feasibility study on magnetic field imaging for a strong magnetic field (more than 500 mT) are presented."},{"arxiv_id":"2112.07053","title":"Flat Magic Window","authors":["V. R. Almeida","A. M. H. Wong","D. S. Tasca","E. Karimi"],"abstract":"Magic windows (or mirrors) consist of optical devices with a surface deformation or thickness distribution devised in such a way to form a desired image. The associated image intensity distribution has been shown to be related to the Laplacian of the height of the surface relief. We experimentally realize such devices with flat optics employing optical spin-to-orbital angular momentum coupling, which represent a new paradigm for light manipulation. The desired pattern and experimental specifications for designing the flat optics was implemented with a re-configurable spatial light modulator which acted as the magic mirror. The flat plate, optical spin-to-orbital angular momentum coupler, is then fabricated by spatially structuring nematic liquid crystals. The plate is used to demonstrate the concept of a polarization-switchable magic window, where, depending on the input circular polarization handedness, one can display either the desired image or the image resulting from the negative of the window's phase."},{"arxiv_id":"2503.02525","title":"Magic in Human-Robot Interaction (HRI)","authors":["M. D. Cooney","A. Vinel"],"abstract":"\"Magic\" is referred to here and there in the robotics literature, from \"magical moments\" afforded by a mobile bubble machine, to \"spells\" intended to entertain and motivate children--but what exactly could this concept mean for designers? Here, we present (1) some theoretical discussion on how magic could inform interaction designs based on reviewing the literature, followed by (2) a practical description of using such ideas to develop a simplified prototype, which received an award in an international robot magic competition. Although this topic can be considered unusual and some negative connotations exist (e.g., unrealistic thinking can be referred to as magical), our results seem to suggest that magic, in the experiential, supernatural, and illusory senses of the term, could be useful to consider in various robot design contexts, also for artifacts like home assistants and autonomous vehicles--thus, inviting further discussion and exploration."}]}
to=arxiv_search.search  аанацҳауеитjson
{"query":"ti:MAGIC AND (all:vision-language OR all:generative OR all:architecture search OR all:ldpc)", "max_results": 10, "sort_by":"relevance"}
to=arxiv_search.search 	RTLRაზეjson
{"query":"\"MAGIC\" vision-language model coreset selection", "max_results": 10, "sort_by":"relevance"}
to=arxiv_search.search  大发快三如何json
{"query":"all:\"Multimodal Alignment\" OR all:\"Motion-Aware Generative Inference\" OR all:\"Quantum Architecture Search\" OR all:\"tricycle\"", "max_results": 10, "sort_by":"relevance"}
Magic is a polysemous technical term in current research. In the arXiv literature it appears as the name of a gamma-ray telescope array, a class of optical devices that reveal hidden images after propagation, a resource-theoretic notion of nonstabilizerness in quantum information, a family of graph-labeling invariants, a muographic scheme for magnetic-field imaging, a design lens in human-robot interaction, and several recent acronyms for machine-learning and generative-modeling methods [1110.0947] [2112.07053] [2407.15939] [2311.10330] [2303.06290] [2503.02525] [2605.26004] [2505.16456]. The common thread is not a single theory but a recurrent research practice: the term marks hidden structure, nonclassical resources, or methods that expose otherwise inaccessible behavior.

## 1. Gamma-ray astronomy: the MAGIC stereo system

In very-high-energy gamma-ray astronomy, MAGIC denotes the Major Atmospheric Gamma Imaging Cherenkov telescopes: a system of two Imaging Atmospheric Cherenkov Telescopes, each with a 17 m diameter mirror dish, located at 2200 m a.s.l. on La Palma and sensitive above approximately 60 GeV [1110.0947]. MAGIC I began operation in 2004, and MAGIC II enabled regular stereoscopic observations since autumn 2009, so that only events triggering both telescopes are recorded.

The system observes Cherenkov flashes from atmospheric air showers rather than gamma rays directly. The stereo trigger combines per-telescope multi-level triggering, including a 3NN camera trigger, with a tight time coincidence between telescopes; individual trigger rates of several kHz are reduced to a stereo trigger rate of approximately 150–200 Hz, with only a few Hz of accidentals [1110.0947]. Reconstruction is performed in the MARS framework through calibration, image cleaning, Hillas parametrization, stereo geometrical quantities such as Impact and MaxHeight, DISP-RF direction estimation, Random-Forest gamma–hadron separation via Hadronness, and lookup-table energy reconstruction.

The stereo configuration substantially improves performance. For a Crab-like spectrum, the threshold is approximately 50–60 GeV; the best energy resolution is about 16% at a few hundred GeV; the angular resolution is better than \(0.07^\circ\) around 300 GeV; and the integral sensitivity is better than 0.8% of the Crab Nebula flux in 50 h at a few hundred GeV [1110.0947]. The same study also reports energy-scale uncertainties of approximately 15–17%, flux-normalization systematic errors of 11–19%, and a systematic error on spectral slope of 0.15, situating MAGIC as a low-threshold bridge between satellite instruments such as Fermi-LAT and other ground-based IACT arrays [1110.0947].

## 2. Optics: magic windows, magic mirrors, and flat geometric-phase devices

In optics, a magic window or magic mirror is an optical element that appears flat or weakly deformed yet projects a hidden image at some distance. The classical mechanism is Laplacian: for a transmissive window of thickness profile \(h(R)\) and refractive index \(n\), the image intensity satisfies
\[
I_{\text{Laplacian Window}}(R,z) \simeq 1 - z\,(n-1)\,\nabla^2 h(R),
\]
so the desired image can be designed by solving a Poisson problem for the surface relief or optical-path profile [2112.07053]. This connects the projected intensity to curvature rather than to the profile itself.

The paper "Flat Magic Window" replaces actual height modulation by flat optics. A reflective liquid-crystal spatial light modulator first serves as a programmable magic mirror, and the flat plate is then realized as a nematic-liquid-crystal Pancharatnam–Berry optical element whose optic-axis pattern encodes a geometric phase \(\phi(\mathbf r)=\pm \chi(\mathbf r)\) for opposite circular input polarizations [2112.07053]. For a half-wave retardance \(\delta=\pi\), the device performs full spin-to-orbital angular-momentum conversion,
\[
\mathbf e_\pm \xrightarrow{\delta=\pi} i\,\mathbf e_\mp\,e^{\pm i\chi(\mathbf r)},
\]
so the same flat plate displays either the intended image or the image associated with the negative phase, depending on the handedness of the input circular polarization [2112.07053].

Experimentally, the work uses a 633 nm He–Ne laser, an \(800\times 600\) Hamamatsu SLM, a fabricated \(4\,\mu\text{m}\) liquid-crystal cell, and a 32-step quantization of the phase pattern. It demonstrates propagation from a phase-only pattern to a visible logo, polarization-switchable image/negative pairs, and retardance-controlled interpolation between no image and a strong image [2112.07053]. A plausible implication is that the historical magic-window phenomenon can be reinterpreted as a special case of flat, polarization-selective wavefront engineering.

## 3. Muography: Magic-\(\mu\) as magnetic-field imaging by cosmic-ray muons

Magic-\(\mu\) is an acronym for Magnetic field Imaging by Cosmic-ray Muons. Its stated goal is to detect the presence of a magnetic field or magnetic flux density whose three-dimensional distribution is unknown, with three modes: magnetic field imaging, transmission, and deflection [2303.06290]. The imaging mode is qualitative and asks whether field is present in specific voxels; the transmission and deflection modes aim to estimate flux density quantitatively.

The feasibility study for strong fields uses the PHITS Monte Carlo code with PARMA cosmic-ray muon spectra. The simulated geometry contains nine lead blocks, a \(30\times 30\,\mathrm{cm}^2\) detector, and a \(40\times 40\times 40\,\mathrm{cm}^3\) magnetic-field region placed 100 cm above the detector. Field strengths of 0, 0.1, 0.5, 1, 10, and 20 T are considered over 152 h exposures [2303.06290]. The imaging principle is that sufficiently strong fields deflect or reflect low-momentum muons so that they no longer reach the detector, changing the attenuation pattern relative to the field-off background.

Detection is quantified by a figure of merit comparing foreground and background count maps, with FOM \(=2\) adopted as the threshold for claiming magnetic-field detection in a pixel [2303.06290]. In these simulations, fields of 1 T and above are clearly detected, while 0.5 T is near threshold and 0.1 T produces only slight distortions [2303.06290]. The broader significance is that Magic-\(\mu\) extends muography from density imaging to Lorentz-force-based field sensing, with intended applications to large magnets in fusion reactors and accelerators.

## 4. Quantum science: magic as nonstabilizerness

In quantum information, magic means nonstabilizerness: the resource that takes a state or circuit outside the Clifford/stabilizer sector and is necessary for universal quantum computation [2407.15939] [2308.01886]. One representative measure is the second stabilizer Rényi entropy; for a two-qubit pure state in the scattering-based formulation,
\[
M_2(|\psi\rangle)=-\log \Xi_2(|\psi\rangle),\qquad 
\Xi_2(|\psi\rangle)=\sum_{P\in\mathcal P_2}\frac{\langle\psi|P|\psi\rangle^4}{4},
\]
with maximal two-qubit value \(M_2\le \log(16/7)\) [2607.00229]. For single-qubit transport problems, the stabilizer norm
\[
\mathcal D(\rho)=\frac{1}{2}(1+|x|+|y|+|z|)
\]
detects magic through the condition \(\mathcal D(\rho)>1\) [2606.14855].

Several recent works study how this resource behaves in many-body systems. Measurement-only circuits with competing Clifford and non-Clifford measurements exhibit a magic transition between two phases with extensive magic scaling, a critical point where mutual magic scales analogously to entanglement, and a distinction by topological magic [2407.15939]. Hypergraph states admit an explicit stabilizer-Rényi formula in terms of induced hypergraphs; random hypergraph states typically reach maximal magic, whereas bounded average degree precludes maximal magic and certain highly symmetric states possess only constant or exponentially small magic for \(\alpha\ge 2\) [2308.01886]. For tensor-network numerics, mutual von-Neumann stabilizer Rényi entropies and magic capacity can be computed in \(O(N\chi^3)\) time for matrix product states, and mutual SRE was shown to characterize the critical point of the transverse-field Ising model independently of local basis [2504.07230].

The same resource-theoretic notion is now being used operationally. In spin chains, the transport of magic depends strongly on the injected-state geometry: lower-Bloch-hemisphere states transfer better, upper-hemisphere states require crossing a threshold in the parameter controlling the tendency toward perfect transfer, and certain regimes amplify the transported magic beyond the initial encoding [2606.14855]. In high-energy theory, electroweak and dark-photon scattering generate magic distributions for outgoing spin states, with maximal two-qubit magic reached at \(m_f/m_\chi\to 0\) and \(m_f/m_\chi\to 1.83929\) in dark-sector inverse-annihilation channels [2607.00229]. In architecture and fault tolerance, magic-informed quantum architecture search biases Monte Carlo tree search with a GNN estimator of circuit magic, while tricycle qLDPC codes support constant-depth logical CCZ, single-shot state preparation and error correction, and a circuit-noise threshold above 0.4% for low-overhead magic-state generation [2605.03932] [2508.10714].

## 5. Mathematical and computational acronymic uses

In graph theory, magic appears in distance magic labeling. A positive integer \(k\) is a magic constant if there exists a graph \(G\) and a bijection \(f:V(G)\to\{1,\dots,|V(G)|\}\) such that each vertex has the same weight
\[
w(v)=\sum_{uv\in E(G)} f(u)=k.
\]
A complete characterization shows that all positive integers except \(1,2,4,6,8,12,\) and \(16\) are magic constants [2311.10330]. The proof combines structural families such as \(tC_4\) and \(P_3\cup tC_4\), regular-graph formulas, lexicographic products, and an explicit search algorithm that resolves the remaining even cases [2311.10330].

In machine learning, MAGIC is also a family of acronyms for selection and generation methods. "MAGIC: Multimodal Alignment & Grounding-aware Instruction Coreset" is a training-free, forward-only coreset-selection method for multimodal instruction tuning that uses Multimodal Gain, Bridging Relevance, and Skill-Neuron Signatures; under matched 20% budgets it reports 100.3% relative performance to full finetuning on LLaVA-665K, 101.6% on Vision-Flan-186K, and a 73.7% reduction in wall-clock run time [2605.26004]. "MAGIC: Motion-Aware Generative Inference via Confidence-Guided LLM" is a training-free framework that combines CogVideoX, GPT-4o prompt refinement, Trellis 3D Gaussian reconstruction, and differentiable MPM simulation to infer physical properties from a single image and generate physics-grounded dynamics; it reports the highest average CLIP similarity among compared video generators and the highest human-rated physical plausibility and text consistency in its user study [2505.16456]. These uses are acronymic rather than conceptual: the word marks a named pipeline, not a common theoretical object.

## 6. Human-robot interaction: magic as a design lens

In HRI, magic is treated not as an acronym but as a design concept. "Magic in Human-Robot Interaction (HRI)" proposes a working definition that combines experiential, supernatural, and illusory senses, and organizes the literature into three corresponding categories: experiential magic as moving and memorable moments, supernatural magic as mythic or spiritual framing without intended trick, and illusory magic as deliberate performance or deception [2503.02525]. The paper reports a rapid scoping review over approximately 150 papers from ACM, IEEE Xplore, and Google Scholar, narrowed to a final set of approximately 50 papers sorted into these three senses [2503.02525].

The design discussion connects magic to play, personalization, emotional contagion, ritual, mythic creatures, magic objects, and stage-magic techniques such as attention guidance and structured patter [2503.02525]. It also emphasizes risks: magical framing can encourage unrealistic expectations, inappropriate deception, or confusion in contexts where accuracy matters. The authors accordingly argue for context-sensitive use and for framing some robot interactions explicitly as performances rather than literal claims.

The practical prototype is a Baxter robot augmented with a hat, wand, thermal camera, UV camera, and scripted dialogue, performing four tricks: wand transformation, seeing through a black box with thermal imaging, detecting sunscreen under UV, and mind-reading a color through speech-based interaction [2503.02525]. The system placed second in the Humanoid Application Challenge Robot Magic and Music Competition, which the authors use as proof of concept that magic can function as an operative design lens in HRI rather than as a loose metaphor [2503.02525].

Across these usages, magic is less a unified object than a recurring strategy for formalizing hidden structure. In gamma-ray astronomy it names a low-threshold stereoscopic observatory; in optics and muography it denotes image formation or field sensing that becomes visible only after propagation; in quantum theory it quantifies deviation from stabilizer structure; in graph theory it encodes a uniform-weight constraint; in HRI it marks memorable, supernatural, or illusory experience; and in machine learning it serves as an acronym for methods that preserve salient latent structure under severe computational constraints [1110.0947] [2112.07053] [2407.15939] [2311.10330] [2303.06290] [2503.02525] [2605.26004] [2505.16456]. This suggests that the persistence of the term is not accidental: it repeatedly labels phenomena in which observables of primary interest are indirect, structured, and revealed through carefully engineered transformations.

Source: https://www.emergentmind.com/topics/magic-85a949bc-c639-4ca6-8140-60e9d4f9b482