Can minimizing quantum magic explain the value of the strong coupling constant?

Magic is the resource Clifford circuits cannot supply

The paper's central quantity is not entanglement but magic, also called non-stabilizerness. Entanglement alone cannot explain a quantum speedup: by the Gottesman–Knill theorem, circuits built from Clifford gates acting on stabilizer states can be simulated efficiently on a classical computer even when they generate maximal entanglement. Magic is the extra resource that takes a state or process outside that efficiently simulable set.

The authors quantify it with the second stabilizer Rényi entropy, M2, for a normalized two-qubit pure state. The definition averages the fourth powers of the state's expectation values over the sixteen two-qubit Pauli strings, then takes a negative logarithm. It vanishes on stabilizer states, is invariant under Clifford transformations, and reaches a maximum of ln(16/7) ≈ 0.827 for two-qubit states. Because the outgoing spin state is normalized, an overall factor of the scattering amplitude drops out at tree level and fixed center-of-mass energy, so magic depends on the couplings only through ratios that survive in that normalized state.

Quark scattering adds the αs/α ratio

The earlier work in this program minimized magic in charged-lepton scattering and recovered the weak mixing angle sin²θw within a percent of its measured MS value near the TeV scale. In that case the normalized spin state depended on the gauge couplings only through sin²θw. Elastic quark scattering changes the problem because gluon exchange introduces a second ratio, rs ≡ gs²/e² = αs/α, into the same normalized spin state.

The paper studies the six flavor-diagonal color-singlet channels qq̄ → qq̄ at tree level, including photon, gluon, W/Z, and Higgs exchange. The s-channel gluon exchange vanishes in the color-singlet channel, so the color factors are 4/3 for t-channel gluon exchange and 1 or 3 for a colorless boson exchanged in the t- or s-channel. The scan varies only αs at each center-of-mass energy, holding all other inputs fixed, including the top Yukawa coupling, the CKM matrix, and the running masses. Couplings and Yukawa matrices are evolved with one-loop Standard Model running in the MS scheme from a starting scale of 91.188 GeV, with the renormalization scale set to the center-of-mass energy.

Only the top channel yields a sharp αs minimum

Near the TeV scale αs/α is about 11, and the light-quark channels behave almost as if only gluon exchange were present. Their magic therefore depends only weakly on αs near the Standard Model value, and their near-minimal magic does not by itself determine αs precisely. The paper reports that in the five light-flavor channels the minimum shifts by only about 0.0012 percentage points, in contrast to the top channel.

In the top channel the large top Yukawa coupling lets Higgs exchange compete with gluon exchange. That competition produces a deep, finite-αs magic minimum whose location reproduces the running MS strong coupling to within a few percent from roughly 1 TeV to 10^8 GeV, and the abstract states agreement within 5% from 1 TeV to 10^9 GeV. The minimum becomes global above approximately 1.3 TeV. Removing physical Higgs exchange destroys the agreement, which is why the authors identify Higgs exchange as essential rather than incidental. At higher energies gluon exchange becomes less dominant, with αs/α ≈ 2.5 at 10^16 GeV, yet all six diagonal channels remain close to their magic minima.

Lowering αs toward α raises magic production

The light channels answer a different question from the top channel. Their minima are too shallow to single out a value of αs, but their shape carries a qualitative message. In all five light channels magic is largest when the strong coupling is weak: it lies between 0.38 and 0.46 at αs = 0, falls to about 0.30 at αs = α, and comes within 1% of the pure-QCD value once αs exceeds about 3α.

Table II in the paper quantifies the comparison with a coupling of electromagnetic strength. Lowering αs from its Standard Model value to α increases magic by 3.6% to 5.7% in the five lighter flavors and by 14% to 38% in the top channel, at the three center-of-mass energies examined. The authors read this as a potential explanation for why the strong interaction is stronger than electromagnetism: the observed coupling sits in or near a low-magic region. This is a preference, not a determination, because within that low-magic region the curves are too shallow to select a precise αs.

Color neutrality does not guarantee near-minimal magic

The pattern is not uniform across all quark channels. Flavor-nondiagonal light singlets lie 1.2% to 9.4% above their minima, somewhat further than the diagonal ones. Among light-quark nonsinglets the excess reaches 40.7% in the cc antitriplet at 10^16 GeV, while the uu antitriplet gives 39.6%. There is no uniform ordering with color: the ud̄ octet has 0.37% at 1 TeV, 4.84% at 10^6 GeV, and 37.6% at 10^16 GeV, whereas the ds̄ octet has 15.9% at both 1 TeV and 10^6 GeV but 0.74% at 10^16 GeV.

The massive color-singlet tb̄ channel, which also admits charged-current exchange, shows an excess of 29.2% at 1 TeV, 35.7% at 10^6 GeV, and 38.2% at 10^16 GeV. At 1 TeV, removing physical Higgs exchange changes that excess by only 0.034 percentage points, whereas removing charged-current exchange reduces it to 1.00%. The authors conclude that the large excess is associated with charged-current exchange rather than simply with the presence of the top quark. The preference for αs > α found in the diagonal singlets also does not extend here: at αs = α the magic is lower than at the Standard Model point in the uc̄ singlet at every sampled energy from the starting scale to 10^16 GeV, and in the ud antitriplet even the pure electroweak amplitude produces 1% to 4% less magic than the Standard Model point at every sampled energy from 1 TeV to 10^16 GeV.

The efficiency conjecture is a conjecture, not a result

The paper is explicit that the gauge couplings are fundamental constants in the sense that their values are measured inputs, not predictions of the Standard Model. The agreement between magic minimization and both sin²θw and αs is therefore presented as something to be explained, not as a derivation. The authors' proposal is 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.

They frame this as a conjecture and list what it would require. One open question is which measure of magic is physically relevant, since different measures need not select the same coupling values, which makes the choice of measure itself empirically testable. Another is which processes enter a common resource cost, given that color neutrality alone does not ensure near-minimal magic, as the tb̄ singlet illustrates. A third is the computational prescription, including the choice of spin basis: the Lab basis gives a common encoding along the fixed beam axis, while converting to the helicity basis requires angle-dependent rotations that are generally non-Clifford and can change the magic. Applying the conjecture fully would also require relating the perturbative quark singlets studied here to physical hadronic processes.

A 5% agreement in one channel, not a derivation of αs

The paper's strongest quantitative claim is narrow and should be read that way. It is a tree-level calculation in six flavor-diagonal color-singlet channels, with αs the only varied input and all other parameters fixed at each center-of-mass energy. The 5% agreement between the top-channel magic minimum and the running MS αs applies from 1 TeV to 10^9 GeV and depends on including physical Higgs exchange with the large top Yukawa coupling. The light channels support only the qualitative preference for αs > α, and the flavor-nondiagonal and nonsinglet channels show a less uniform pattern that includes cases where αs = α produces less magic than the Standard Model point.

The practical priority the paper establishes is therefore a comparison between channels rather than a single number. The top channel is where magic minimization has discriminating power over αs; the five light diagonal channels are where it explains the direction of the hierarchy between the strong and electromagnetic couplings; and the tb̄ singlet shows that charged-current exchange, not color neutrality or the top quark alone, can drive a channel far from its magic minimum. Any extension of the efficiency conjecture has to reproduce that split before it can claim to account for the value of αs.

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