⚛️ phenomenology

Quantum computation of partonic Drell-Yan scattering cross sections and interference effects

This paper presents a general quantum circuit framework that utilizes specialized vertex and propagator gates to efficiently compute partonic Drell-Yan scattering cross sections and isolate interference effects through basis rotation, marking a significant step toward simulating arbitrary scattering processes on quantum devices.

Original authors: Erik Bashore, Stefano Moretti, Timea Vitos

Published 2026-08-31

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Erik Bashore, Stefano Moretti, Timea Vitos

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

In the high-energy world of particle physics, scientists study the fundamental building blocks of the universe by smashing particles together at incredible speeds. When these particles collide, they do not simply bounce off one another; they transform, creating new particles in a process governed by the laws of quantum mechanics. To predict what happens in these collisions, physicists use a set of rules that allow them to calculate the probability of specific outcomes. These calculations often involve adding up different possible scenarios, or "paths," that a collision could take. Sometimes, these paths reinforce each other, making an outcome more likely, while at other times they cancel each other out, making it less likely. This delicate balancing act, known as interference, is crucial for understanding the universe, but calculating it for complex collisions is a massive computational challenge that pushes the limits of even the most powerful supercomputers.

Recently, researchers have begun exploring whether quantum computers, which operate on the strange principles of quantum mechanics themselves, might offer a better way to handle these calculations. Instead of trying to force a classical computer to simulate quantum behavior step-by-step, a quantum computer can naturally represent these multiple possibilities at once. A team of physicists from Sweden, Norway, Hungary, and the United Kingdom has taken a significant step in this direction. They have designed a specific quantum circuit—a blueprint for a quantum calculation—to model a fundamental particle interaction known as the Drell-Yan process. In this scenario, a quark and an antiquark collide to produce a pair of leptons, such as electrons or muons, often passing through an intermediate stage involving a photon or a Z boson. While this process is relatively simple compared to the chaotic collisions seen in modern particle accelerators, it contains the essential features of interference that make real-world calculations difficult.

The researchers' goal was to build a quantum "machine" that could not only calculate the total probability of this collision happening but also isolate the specific contribution of the interference between the different paths. In their design, they translated the standard rules of particle physics into a series of quantum operations, or gates. They created specific tools to represent the incoming and outgoing particles, the interaction points where particles meet, and the invisible carriers of force that travel between them. By arranging these tools into a single circuit, they created a system where the quantum computer could hold the information for multiple collision scenarios simultaneously. The brilliance of their approach lies in how they extract the answer. Instead of running the calculation once for one scenario and then again for another, their circuit runs all scenarios at once. By simply changing the way they measure the final result, they can pull out the total probability or, with a slight adjustment, separate out the interference effect that occurs when the different paths overlap.

To test their idea, the team did not use a physical quantum computer, as current devices are too noisy and unreliable for such precise work. Instead, they simulated the entire process on a classical computer using software designed to mimic how a quantum machine would behave. They set up a simulation where the quantum circuit evaluated the collision across a range of energies and angles, effectively scanning a grid of possibilities. The results were promising. The simulation showed that the quantum circuit could accurately reproduce the expected outcomes for the total collision probability, matching the results of established classical methods. More importantly, it successfully isolated the interference pattern, a task that is notoriously difficult to separate from the total signal in complex calculations. The team found that while the total probability remained stable, the interference signal became harder to detect near a specific energy level where the Z boson is most active, a known physical phenomenon where the interference naturally fades.

The study also demonstrated that the quantum approach could handle the integration of these results over a wide range of conditions to calculate a final, overall rate for the event. When the researchers compared their quantum simulation's ability to estimate both the total rate and the interference rate at the same time, they found a distinct advantage. While classical methods were slightly more precise at predicting the total rate at any single point, the quantum method was remarkably consistent at estimating both quantities simultaneously from the same set of data. This suggests that as quantum hardware improves, this type of circuit could become a powerful tool for physicists who need to understand not just the main outcome of a collision, but also the subtle, interfering effects that often hide new physics. The researchers acknowledge that their current design requires a large number of samples to get a clear answer, a limitation that future work will need to address. However, by proving that a quantum circuit can be built to handle these specific particle interactions and separate their complex components, they have laid a foundation for tackling even more complicated scattering processes in the future.

Technical Summary: Quantum Computation of Partonic Drell-Yan Scattering Cross Sections and Interference Effects

Problem Statement
The evaluation of scattering amplitudes in High Energy Physics (HEP), particularly within Quantum Chromodynamics (QCD), faces significant computational challenges due to the factorial growth of graph permutations, color structures, and helicity configurations as the number of external particles increases. While classical algorithms struggle with these complexities, Quantum Computing (QC) offers a potential avenue for efficiency. The Drell-Yan (DY) process ( $q\bar{q} \to \gamma/Z \to \ell^-\ell^+$ ) serves as an ideal, structurally simple testing ground. Although it involves only two Feynman diagrams with trivial color structure, it contains essential features for realistic phenomenology, specifically the interference between photon ( $\gamma$ ) and $Z$ boson exchanges. The challenge lies in constructing a quantum circuit that can not only compute the total cross-section but also efficiently isolate and measure the interference terms ( $2\text{Re}[M_\gamma M_Z^*]$ ) simultaneously, a task that is computationally demanding in classical deterministic approaches when analyzing sub-leading terms.

Methodology
The authors propose a gate-based quantum circuit designed to simulate the partonic DY process without Parton Distribution Functions (PDFs). The methodology involves translating standard Feynman rules into specific quantum gates acting on a set of qubit registers ( $R = \{v, i, U, a, p\}$ ), representing vertices, indices, unitarity, ancillas, and particles.

Gate Construction:
- Spinor Gates ( $U_p, \bar{U}_p$ ): Encode normalized spinor components into probability amplitudes on vertex registers.
- Vertex Gates ( $V$ ): Implement the vector and axial-vector couplings of the $V f \bar{f}$ interaction, placing Dirac bilinears ( $\gamma_\mu, \gamma_\mu\gamma_5$ ) onto the vertex register controlled by index and particle registers.
- Propagator Gates ( $P$ ): Encode the internal bosonic propagator, splitting terms into scalar and tensorial parts to handle pole factors ( $m_0, m_1$ ) dependent on the boson mass and gauge parameter.
Circuit Architecture:
- The circuit utilizes a particle register ( $p$ ) to encode internal bosons ( $\gamma$ and $Z$ ) via basis states. A Hadamard transform on this register creates a superposition, allowing the simultaneous computation of amplitudes $M_\gamma$ and $M_Z$ .
- Interference Isolation: To isolate the interference term without disturbing the full amplitude calculation, the authors employ a basis rotation. By projecting the "work" registers (excluding the particle register) onto the vacuum state, the resulting density matrix of the particle register contains off-diagonal terms representing the interference. Measuring the expectation value $\langle X \rangle$ (via a Hadamard rotation followed by computational basis measurement) directly yields the interference contribution $2\text{Re}[M_\gamma M_Z^*]$ , while the standard measurement yields $|M_\gamma + M_Z|^2$ .
Phase Space Integration:
- To approximate the integrated cross-section, the authors discretize the phase space (PS) using quantum registers for energy ( $E$ ) and scattering angle ( $\Theta$ ).
- Superposition is used to evaluate multiple PS points simultaneously. The energy register controls the propagator gate (pole terms), while the angle register controls the outgoing spinor gates.
- A compensation factor $C(s_k)$ is applied to the output to correct for normalization effects arising from Hadamard transforms, ancilla additions, and spinor rescaling.

Key Contributions

General Circuit Design: The paper presents a modular quantum circuit where building blocks (vertex, propagator, spinor gates) are reusable for more complex scattering processes.
Simultaneous Interference Extraction: A novel method is demonstrated to extract isolated interference effects via a simple basis rotation in the particle register, allowing the simultaneous estimation of the full squared amplitude and the interference term from the same circuit execution.
Phase Space Superposition: The integration of energy and angle registers enables the evaluation of a discretized phase space grid in a single circuit run, leveraging quantum superposition to avoid iterative classical sampling.
Proof-of-Concept Simulation: The circuit was simulated using Qiskit (classical simulation) for the process $u\bar{u} \to \gamma/Z \to \mu^-\mu^+$ , covering energy ranges $[80, 100]$ GeV and angular distributions, as testing on current Noisy Intermediate-Scale Quantum (NISQ) devices was deemed infeasible due to the circuit's complexity and noise sensitivity.

Results

Amplitude Level: The circuit successfully reproduced analytical expectations for the full amplitude squared ( $|M|^2$ ) and the interference pattern across the tested phase space.
Accuracy: While the full amplitude remained stable, the isolated interference term showed increased difficulty in resolution near the $Z$ resonance, where the interference naturally approaches zero and amplitudes become small.
Cross-Section Integration: The discretized integration of the amplitude outputs yielded cross-sections ( $\sigma$ ) and interference cross-sections ( $\sigma_{int}$ ) comparable to numerical integration of analytical expressions and MadGraph simulations.
Uncertainty Analysis: A key finding is that while MadGraph (using the same Monte Carlo samples) provided lower individual uncertainties for specific points, the quantum circuit demonstrated a more balanced uncertainty quotient ( $\delta\sigma / \delta\sigma_{int}$ ) across the energy range. This suggests the quantum method is capable of reliably estimating both the total and interference cross-sections simultaneously with comparable precision.

Significance and Claims
The authors claim this work constitutes a step toward the implementation of arbitrary scattering process computations and efficient interference analyses on quantum devices. The significance lies in demonstrating that quantum circuits can:

Map field-theoretic ingredients (spinors, vertices, propagators) directly to unitary operations.
Simultaneously estimate full cross-sections and sub-leading interference terms, which are crucial for precision studies and Beyond the Standard Model (BSM) searches.
Offer a potential efficiency advantage in estimating multiple correlated quantities simultaneously compared to standard deterministic approaches.

The paper remains modest regarding immediate practical application, acknowledging that the low probability of measuring the vacuum state (encoding the physical amplitude) necessitates a large number of samples, a bottleneck that may require amplitude amplification or alternative readout strategies. Future extensions proposed include the inclusion of importance sampling, helicity sums, PDFs, and extensions to BSM analyses (e.g., $Z'$ bosons).

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