Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.00229

Production of Magic States via ZZZ Bosons and Dark Photons

Carlos Alvarado, Alfredo Aranda, César Bonilla, Yahir Lua, Ethan Rodríguez-Martínez

hep-phquant-phSubmitted Jun 30, 2026• Announced Jul 2, 2026• 0 citations
arXivHTMLPDF

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 $m_f/m_χ\to 0$ and $m_f/m_χ\to 1.83929$.

Comments
61 pages, 21 figures, 24 tables

Related papers

Quantum magic in quantum electrodynamics

Qiaofeng Liu, Ian Low, Zhewei Yin

In quantum computing, non-stabilizerness -- the magic -- refers to the computational advantage of certain quantum states over classical computers and is an essential ingredient for universal quantum computation. Employing the second order stabilizer R\'enyi entropy to quantify magic, we study the production of magic states in Quantum Electrodynamics (QED) via 2-to-2 scattering processes involving electrons and muons. Considering all 60 stabilizer initial states, which have zero magic, the angular dependence of magic produced in the final states is governed by only a few patterns, both in the non-relativistic and the ultra-relativistic limits. Some processes, such as the low-energy $e^-\mu^-\to e^-\mu^-$ and Bhabha scattering $e^-e^+\to e^-e^+$, do not generate magic at all. In most cases the largest magic generated is significantly less than the maximal possible value of $\log (16/7) \approx 0.827$. The only instance where QED is able to generate maximal magic is the low-energy $\mu^-\mu^+\to e^-e^+$, in the limit $m_e/m_\mu \to 0$, which is well approximated in nature. Our results suggest QED, although capable of producing maximally entangled states easily, may not be an efficient mechanism for generating quantum advantages.

arXiv:2503.03098•Physical review. D/Physical review. D.•Dec 2, 2025•11 citations

Quantum Magic in High Energy Collision

Ying-Ying Li, Ian Low, Yi-Lin Wang +1 more

Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger $T$-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.

hep-phCross-listedarXiv:2608.19095•Aug 20, 2026•0 citations

Quantum Magic and the Strong Coupling Constant

Qiaofeng Liu, Ian Low, Zhewei Yin

The three gauge couplings of the Standard Model (SM) can be parameterized as the fine structure constant $α$, the weak mixing angle $\sin^2θ_w$, and the strong coupling $α_s$. They are fundamental constants whose values remain unexplained. Previously we showed that minimizing magic production in charged-lepton scattering reproduces $\sin^2θ_w$ with great precision. Here we study magic production in the six flavor-diagonal color-singlet channels $q\bar q\to q\bar q$ at tree level, including photon, gluon, $W/Z$, and Higgs exchange. Varying only $α_s$, with all other inputs fixed at each center-of-mass energy, we find that the finite-$α_s$ magic minimum in the top channel reproduces the $\overline{\mathrm{MS}}$ value of $α_s$ to within $5\%$ from $1~$TeV to $10^9~$GeV. Higgs exchange involving the large top Yukawa coupling is essential for this agreement. All six channels produce near-minimal magic at the SM couplings, and reducing $α_s$ toward $α$ increases their magic production, potentially explaining why the strong interaction is ``strong.'' To understand why minimizing magic reproduces both $\sin^2θ_w$ and $α_s$, we conjecture that the parameters of fundamental interactions among color singlets reflect a principle of quantum computational efficiency, with the physical universe emerging from a quantum simulation subject to constrained resources.

hep-phCross-listedarXiv:2610.11121•Oct 9, 2026

A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model

Qiaofeng Liu, Ian Low, Z.W. Yin

The weak mixing angle $s_W$ is a fundamental constant in the Standard Model (SM) and measured at the $Z$ boson mass to be $\widehat{s}^2_W(m_Z) = 0.23129 \pm 0.00004$ in the $\overline{\rm MS}$ renormalization scheme, where $m_Z=91.2\ \text{GeV}$. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the $Z$ boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of $s^2_W$ in the Møller scattering $e^-e^-\to e^-e^-$, which is free of kinematic thresholds. At the centre-of-mass energy $\sqrt{s}=m_Z$, there is a unique minimum in magic production at $\mathbf{s}^{2}_W(m_Z)=0.2317$, which agrees with the measured $\widehat{s}^2_W(m_Z)$ at the sub-percent level. At higher energies, the magic-minimizing $\mathbf{s}^{2}_W$ continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.

arXiv:2509.18251•Sep 22, 2025•0 citations

Next-to-Leading-Order Electroweak Corrections to Quantum Observables in Lepton-Lepton Collisions

Spencer Chang, Thomas Driscoll, Sokratis Trifinopoulos

We study how virtual next-to-leading-order electroweak corrections affect the quantum observables of entanglement and magic in lepton--lepton collisions. Treating the outgoing particles as multi-qudit systems, $\textit{i.e.}$, qubits for spin-$\tfrac{1}{2}$ fermions and qutrits for massive vector bosons, we compute entanglement entropy and the stabilizer second Rényi entropy for the processes $\ell^+\ell^- \to τ^-τ^+,\, ZZ$ at one-loop accuracy. We show that radiative corrections coherently modify the quantum structure of the final state, shifting regions of maximal entanglement and altering the generated magic relative to leading order. Our results demonstrate that these quantum observables provide novel, precision-sensitive probes of electroweak dynamics at future lepton colliders and open a path toward their use in searches for new physics.

hep-phCross-listedarXiv:2608.27559•Aug 31, 2026•0 citations

Nonstabilizerness Mpemba Effects

Zhenyu Xiao, Hao-Kai Zhang, Shuo Liu

Quantum state preparation can be strikingly counterintuitive: the fastest route to a target state need not start from the apparently closest initial condition. We uncover such a quantum Mpemba effect in the dynamical generation of quantum magic (nonstabilizerness), quantified by the stabilizer Rényi entropy, in $\mathrm{U(1)}$-symmetric random circuits initialized from tilted product states. States with lower initial magic can generate magic faster than states with higher initial magic. The acceleration is not determined solely by the conserved-charge distribution. Two initial-state families with identical initial magic and identical charge distribution exhibit qualitatively different magic-growth dynamics, depending also on the spatial structure of the initial state within each charge sector. Analogous magic Mpemba effects in $\mathrm{SU(2)}$-symmetric circuits and under nonintegrable Hamiltonian dynamics further show that the phenomenon is tied neither to Abelian symmetry nor to random-circuit dynamics, establishing quantum magic as a distinct arena for Mpemba physics.

quant-pharXiv:2605.04155•May 7, 2026•0 citations
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)U(1)U(1) gauge symmetry and a Dirac fermion charged under it. This setup resembles a dark U(1)U(1)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 ZZZ-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→0m_f/m_χ\to 0mf​/mχ​→0 and mf/mχ→1.83929m_f/m_χ\to 1.83929mf​/mχ​→1.83929.
In quantum computing, non-stabilizerness -- the magic -- refers to the computational advantage of certain quantum states over classical computers and is an essential ingredient for universal quantum computation. Employing the second order stabilizer R\'enyi entropy to quantify magic, we study the production of magic states in Quantum Electrodynamics (QED) via 2-to-2 scattering processes involving electrons and muons. Considering all 60 stabilizer initial states, which have zero magic, the angular dependence of magic produced in the final states is governed by only a few patterns, both in the non-relativistic and the ultra-relativistic limits. Some processes, such as the low-energy e−μ−→e−μ−e^-\mu^-\to e^-\mu^-e−μ−→e−μ− and Bhabha scattering e−e+→e−e+e^-e^+\to e^-e^+e−e+→e−e+, do not generate magic at all. In most cases the largest magic generated is significantly less than the maximal possible value of log⁡(16/7)≈0.827\log (16/7) \approx 0.827log(16/7)≈0.827. The only instance where QED is able to generate maximal magic is the low-energy μ−μ+→e−e+\mu^-\mu^+\to e^-e^+μ−μ+→e−e+, in the limit me/mμ→0m_e/m_\mu \to 0me​/mμ​→0, which is well approximated in nature. Our results suggest QED, although capable of producing maximally entangled states easily, may not be an efficient mechanism for generating quantum advantages.
Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger TTT-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.
The three gauge couplings of the Standard Model (SM) can be parameterized as the fine structure constant ααα, the weak mixing angle sin⁡2θw\sin^2θ_wsin2θw​, and the strong coupling αsα_sαs​. They are fundamental constants whose values remain unexplained. Previously we showed that minimizing magic production in charged-lepton scattering reproduces sin⁡2θw\sin^2θ_wsin2θw​ with great precision. Here we study magic production in the six flavor-diagonal color-singlet channels qqˉ→qqˉq\bar q\to q\bar qqqˉ​→qqˉ​ at tree level, including photon, gluon, W/ZW/ZW/Z, and Higgs exchange. Varying only αsα_sαs​, with all other inputs fixed at each center-of-mass energy, we find that the finite-αsα_sαs​ magic minimum in the top channel reproduces the MS‾\overline{\mathrm{MS}}MS value of αsα_sαs​ to within 5%5\%5% from 1 1~1 TeV to 109 10^9~109 GeV. Higgs exchange involving the large top Yukawa coupling is essential for this agreement. All six channels produce near-minimal magic at the SM couplings, and reducing αsα_sαs​ toward ααα increases their magic production, potentially explaining why the strong interaction is ``strong.'' To understand why minimizing magic reproduces both sin⁡2θw\sin^2θ_wsin2θw​ and αsα_sαs​, we conjecture that the parameters of fundamental interactions among color singlets reflect a principle of quantum computational efficiency, with the physical universe emerging from a quantum simulation subject to constrained resources.
The weak mixing angle sWs_WsW​ is a fundamental constant in the Standard Model (SM) and measured at the ZZZ boson mass to be s^W2(mZ)=0.23129±0.00004\widehat{s}^2_W(m_Z) = 0.23129 \pm 0.00004sW2​(mZ​)=0.23129±0.00004 in the MS‾\overline{\rm MS}MS renormalization scheme, where mZ=91.2 GeVm_Z=91.2\ \text{GeV}mZ​=91.2 GeV. On the other hand, non-stabilizerness - the magic - characterizes the computational advantage of a quantum system over classical computers. We consider the production of magic from stabilizer initial states, which carry zero magic, in the 2-to-2 scattering of charged leptons in the SM at the tree level, which is mediated by the photon and the ZZZ boson. Using the second order stabilizer Rényi entropy, and averaging over all 60 initial stabilizer states and the scattering angle, we compute and minimize the magic production as a function of sW2s^2_WsW2​ in the Møller scattering e−e−→e−e−e^-e^-\to e^-e^-e−e−→e−e−, which is free of kinematic thresholds. At the centre-of-mass energy s=mZ\sqrt{s}=m_Zs​=mZ​, there is a unique minimum in magic production at sW2(mZ)=0.2317\mathbf{s}^{2}_W(m_Z)=0.2317sW2​(mZ​)=0.2317, which agrees with the measured s^W2(mZ)\widehat{s}^2_W(m_Z)sW2​(mZ​) at the sub-percent level. At higher energies, the magic-minimizing sW2\mathbf{s}^{2}_WsW2​ continues to agree with the empirical value at the percent level or better, up to 10 TeV. The finding suggests the electroweak sector of the SM tends to generate minimal quantum resources from the computational viewpoint.
We study how virtual next-to-leading-order electroweak corrections affect the quantum observables of entanglement and magic in lepton--lepton collisions. Treating the outgoing particles as multi-qudit systems, i.e.\textit{i.e.}i.e., qubits for spin-12\tfrac{1}{2}21​ fermions and qutrits for massive vector bosons, we compute entanglement entropy and the stabilizer second Rényi entropy for the processes ℓ+ℓ−→τ−τ+, ZZ\ell^+\ell^- \to τ^-τ^+,\, ZZℓ+ℓ−→τ−τ+,ZZ at one-loop accuracy. We show that radiative corrections coherently modify the quantum structure of the final state, shifting regions of maximal entanglement and altering the generated magic relative to leading order. Our results demonstrate that these quantum observables provide novel, precision-sensitive probes of electroweak dynamics at future lepton colliders and open a path toward their use in searches for new physics.
Quantum state preparation can be strikingly counterintuitive: the fastest route to a target state need not start from the apparently closest initial condition. We uncover such a quantum Mpemba effect in the dynamical generation of quantum magic (nonstabilizerness), quantified by the stabilizer Rényi entropy, in U(1)\mathrm{U(1)}U(1)-symmetric random circuits initialized from tilted product states. States with lower initial magic can generate magic faster than states with higher initial magic. The acceleration is not determined solely by the conserved-charge distribution. Two initial-state families with identical initial magic and identical charge distribution exhibit qualitatively different magic-growth dynamics, depending also on the spatial structure of the initial state within each charge sector. Analogous magic Mpemba effects in SU(2)\mathrm{SU(2)}SU(2)-symmetric circuits and under nonintegrable Hamiltonian dynamics further show that the phenomenon is tied neither to Abelian symmetry nor to random-circuit dynamics, establishing quantum magic as a distinct arena for Mpemba physics.