A preprint reports a quantum-circuit calculation that the authors say produced total-amplitude results comparable to MadGraph and interference output that outperformed it for a comparable number of tested phase-space points. But the circuit was simulated classically with Qiskit, and the comparison was limited to the tested points.
The underlying question was whether one quantum circuit could estimate two things at once: the full Drell-Yan cross section and the isolated interference between two Standard Model contributions, more efficiently or accurately than standard deterministic classical approaches. In plain terms, the cross section is the integrated output of the scattering calculation, while interference is the part of the result created by the photon and Z contributions being combined.
A circuit for two signals
Drell-Yan here refers to the tested partonic channel in which an up quark and an anti-up quark produce a photon or Z boson that leads to a pair of muons. The numerical test used one helicity configuration, or fixed spin arrangement, and Feynman gauge with its parameter set to 1.
The method translates the relevant scattering diagrams into simple gates based on Feynman rules, including gates for interaction vertices and particle propagators. It is designed to evaluate amplitudes across phase-space points while also producing the quantities needed for an integrated cross section.
To pull out the interference term, the circuit rotates the measurement into the X basis, using a Hadamard operation, a Z operation and a second Hadamard operation, then takes an expectation-value measurement, essentially an average over repeated outcomes. The target was the photon-Z interference term, specifically the contribution formed from the photon amplitude and the complex-conjugate Z amplitude, multiplied by two.
What the small test found
The final amplitude-level test used an energy-and-angle grid covering energy values from 80 to 100 and angles from 0 to pi. It was divided into eight points along each dimension, with three qubits assigned to each of the energy and angle registers; the reported run used 50 batches.
The two reported matrix-average errors were 31.117% and 55.305%. A separate quotient matrix had an average value of 3.826%. These figures are averages across the evaluation, not formal interval estimates, so they describe the reported grid-level behavior rather than a guarantee at every energy and angle.
To turn point-by-point outputs into cross sections, the researchers summed the discrete angular results at each energy point. They estimated the uncertainty from this phase-space discretization through standard error propagation.
The bottleneck is still sampling
The authors also examined whether the same calculation could keep both estimates reliable at once. They report that the circuit's uncertainty quotient stayed closer to the ideal line across the studied energy range, and that both the full and interference cross sections could be estimated simultaneously.
That result has a practical catch. The authors identify the low probability of measuring the vacuum state that encodes the physical amplitude as the main limitation. Because the relevant outcome can be rare, the method requires many circuit samples; the paper points to amplitude amplification and alternative readout strategies as possible ways to address the bottleneck.
In a separate angular test, four points were not found by the circuit. The paper attributes those missing results to probability amplitudes that rapidly became very small as the angle increased. That matters because the cross-section integration sums over angular results, linking the sampling problem directly to the final estimate.
A narrow test, for now
The paper also reports logarithmic qubit scaling with phase-space discretization resolution, meaning the qubit requirement follows a logarithmic pattern as the grid becomes finer.
The reported evidence remains confined to the tested channel, one helicity configuration and a classically simulated circuit. The comparison with MadGraph was made for the phase-space points studied, and the circuit was not tested on real quantum hardware. Its performance in broader scattering setups and on actual devices therefore remains untested.
The document is an arXiv version 1 preprint dated 28 August 2026.
Paper data and sources
Original title: Quantum computation of partonic Drell-Yan scattering cross sections and interference effects
Authors: Erik Bashore, Stefano Moretti, Timea Vitos
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text