⚛️ high-energy theory

The magic of top quarks

This proceeding reviews the concept of "magic" in quantum computing and demonstrates that top quark pair production at the Large Hadron Collider naturally generates this resource, offering a novel high-energy physics platform for studying quantum computational advantage.

Original authors: Chris D. White, Martin J. White

Published 2026-02-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Chris D. White, Martin J. White

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Finding "Magic" in Particle Collisions

Imagine the Large Hadron Collider (LHC) not just as a machine that smashes particles to find new ones, but as a giant laboratory for testing the rules of the universe. For a long time, physicists have used this machine to study entanglement—a spooky connection where two particles act as one, no matter how far apart they are.

But this paper introduces a different, stranger concept called "Magic."

In the world of quantum computing, "Magic" isn't about wizards or wands. It is a specific technical term that measures how "weird" or "complex" a quantum state is. The authors, Chris White and Martin White, argue that when the LHC creates pairs of top quarks (the heaviest known particles), it naturally produces these "Magic" states. This turns the LHC into a new playground for studying the very ingredients needed to build powerful quantum computers.

The Ingredients: Bits, Qubits, and Stabilizers

To understand "Magic," we first need to understand the building blocks:

Classical Bits vs. Qubits: A normal computer uses bits (0 or 1). A quantum computer uses qubits, which can be a mix of 0 and 1 at the same time (like a spinning coin that is both heads and tails until it lands).
The "Boring" States (Stabilizers): Imagine a set of Lego instructions that are very simple and predictable. In quantum physics, there are states called Stabilizer states. These are special configurations that are easy for a regular, classical computer to simulate. Even if they are "entangled" (connected), they aren't "weird" enough to give a quantum computer a real advantage over a normal one.
- Analogy: Think of a Stabilizer state like a perfectly organized bookshelf. You can describe exactly where every book is with a simple list. A normal computer can handle this list easily.

The Missing Ingredient: Magic

If Stabilizer states are the "organized bookshelf," then Magic is the chaotic, impossible-to-predict mess that makes a quantum computer truly powerful.

The Problem: Scientists realized that just having entanglement (the connection) isn't enough to beat classical computers. You need something extra.
The Solution: That "something extra" is called Magic. It measures how much a quantum state deviates from being a simple, predictable Stabilizer state.
- Analogy: If a Stabilizer state is a simple recipe you can follow step-by-step, Magic is the secret, chaotic spice that makes the dish impossible to recreate without the original chef. Without Magic, a quantum computer is just a fancy calculator; with Magic, it becomes a super-computer.

The Experiment: Top Quarks as Magic Generators

The authors asked a simple question: Does the LHC naturally create these "Magic" states?

They looked at top quark pairs. When the LHC smashes protons together, it sometimes creates a top quark and an anti-top quark. These two particles are born with a complex relationship involving their "spin" (a type of quantum rotation).

The Discovery: The authors calculated the "Magic" of these top quark pairs. They found that, yes, the LHC naturally produces them.
Where is the Magic? It's not found at the very edges of the energy spectrum (like when the particles are barely moving or moving at maximum speed). In those extreme cases, the particles become either too simple (separable) or too perfectly connected (maximally entangled), which turns them back into "boring" Stabilizer states where Magic vanishes.
The Sweet Spot: The Magic is concentrated in the middle ranges of energy. This is where the top quarks are in a "mixed state"—a complex superposition that is neither too simple nor too perfectly ordered.

Why This Matters (According to the Paper)

The paper makes a few key points without promising future miracles:

A New Playground: The LHC is a natural factory for creating "Magic." This gives physicists a new way to study this elusive property using real-world data.
Magic vs. Entanglement: You can have entanglement without Magic, and you can have Magic without entanglement. They are different ingredients. The paper notes that while you need both to build a useful quantum algorithm, a single snapshot of a particle (like a top quark pair) doesn't need to have both at the exact same moment to be interesting.
Open Questions: The paper concludes that figuring out how to make and enhance Magic in any system is still a big open question. By studying top quarks, we might learn how to create Magic in other systems, which could eventually help us build better quantum computers.

In short: The paper claims that the LHC is already doing what quantum computer scientists are trying to do: it is naturally creating the "Magic" ingredient needed for quantum supremacy, hidden inside the collisions of top quarks.

Technical Summary: The Magic of Top Quarks

Problem Statement
While the application of high-energy colliders to test fundamental quantum properties, particularly entanglement via Bell inequalities, is well-established, other quantum information theoretic concepts remain underexplored in this domain. Specifically, the paper addresses the concept of "magic" (or non-stabiliserness), a property essential for achieving genuine computational advantage in quantum computing that cannot be explained by superposition or entanglement alone. The central problem is identifying whether high-energy physics processes, specifically top quark pair production at the Large Hadron Collider (LHC), naturally generate quantum states possessing this "magic" property, thereby offering a novel experimental playground for its study.

Methodology
The authors employ a framework bridging quantum information theory and particle physics phenomenology:

Theoretical Framework: The paper utilizes the concept of stabiliser states and the Gottesman-Knill theorem, which posits that quantum circuits composed solely of stabiliser states can be efficiently simulated classically. To achieve quantum advantage, a system requires "magic." The authors quantify this using Stabiliser Rényi Entropies ( $M_q$ ), specifically focusing on the Second Stabiliser Rényi Entropy ( $q=2$ ).
Formalism: Top-antitop ( $t\bar{t}$ ) pair production is modeled as a mixed quantum state described by a spin density matrix ( $\rho_I$ ). The general form of this matrix is expanded using Fano coefficients, which relate to the total cross-section, polarization, and spin correlations.
Calculation: The authors derive an explicit formula for the magic ( $\tilde{M}_2$ ) of a top quark pair based on the normalized Fano coefficients ( $B_i^{\pm}$ and $C_{ij}$ ). These coefficients are calculated within the Standard Model (SM) for different partonic initial states ( $q\bar{q}$ and $gg$) and kinematic configurations (invariant mass and scattering angle).

Key Contributions

Introduction of "Magic" to High Energy Physics: The paper introduces the concept of quantum magic as a measurable property in LHC processes, distinct from the more commonly studied entanglement.
Analytical Derivation: It provides a specific mathematical formulation (Eq. 6) to calculate the magic of top quark pairs directly from the spin density matrix parameters.
Phenomenological Analysis: The authors present the first calculations of magic for top quark production in the Standard Model, analyzing its behavior across different kinematic regimes and initial partonic channels.

Results

Kinematic Distribution: The calculated magic is non-zero and concentrated away from extreme kinematic limits, such as the production threshold and high-energy limits.
Vanishing at Extremes: In regions where the top quark final state becomes separable or maximally entangled, the magic vanishes. This is consistent with the theoretical expectation that these regions correspond to stabiliser states, which possess zero magic.
Independence from Entanglement: The results demonstrate that magic can be non-zero in regions where entanglement vanishes. The authors clarify that while both entanglement and magic are required for quantum computational advantage in algorithms, a specific intermediate state does not need to possess both properties simultaneously.
Channel Dependence: Combining partonic channels or averaging over angles tends to increase the measured magic, as this results in a more mixed state with a more complex Pauli spectrum.

Significance
The paper claims that the LHC naturally produces "magic" top quarks, providing a unique and accessible system for studying the generation and enhancement of magic in arbitrary quantum systems. This work suggests that top quark physics can serve as a testbed for understanding how to create non-stabiliser states, a critical open question in quantum computing. Furthermore, the authors posit that this intersection may offer insights into probing new physics and strengthening the dialogue between quantum computing and collider physics, though they note that further work is required to investigate these potential applications.

The Big Idea: Finding "Magic" in Particle Collisions

The Ingredients: Bits, Qubits, and Stabilizers

The Missing Ingredient: Magic

The Experiment: Top Quarks as Magic Generators

Why This Matters (According to the Paper)

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