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arXiv:2605.06907 · Physics Letters B

A collider as a quantum computer

Wei Xie, Ji-Chong Yang

hep-phquant-phSubmitted May 7, 2026• Announced May 11, 2026• 0 citations
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Abstract

Scattering processes in high-energy physics are inherently quantum mechanical, yet are typically analyzed at the level of final states, where entanglement appears as a property of the outcome rather than a consequence of the underlying dynamics. We reformulate scattering at the level of the process itself by representing helicity transition matrices as quantum circuits. Once the kinematic configuration and scattering channel are fixed, the problem reduces to a finite-dimensional quantum map, making a circuit description natural. Within this framework, an example of the process $e^+e^-\to μ^+μ^-$ is shown, which decomposes into unitary and non-unitary components, corresponding to coherent mixing and postselection effects. This representation reorganizes the amplitude into distinct operational elements, providing a perspective in which collider processes can be viewed as constrained quantum circuits and their entanglement structure can be understood in terms of the underlying circuit dynamics, opening the door to analyzing their properties using the language of quantum information.

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22 pages, 4 figures

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Scattering processes in high-energy physics are inherently quantum mechanical, yet are typically analyzed at the level of final states, where entanglement appears as a property of the outcome rather than a consequence of the underlying dynamics. We reformulate scattering at the level of the process itself by representing helicity transition matrices as quantum circuits. Once the kinematic configuration and scattering channel are fixed, the problem reduces to a finite-dimensional quantum map, making a circuit description natural. Within this framework, an example of the process e+e−→μ+μ−e^+e^-\to μ^+μ^-e+e−→μ+μ− is shown, which decomposes into unitary and non-unitary components, corresponding to coherent mixing and postselection effects. This representation reorganizes the amplitude into distinct operational elements, providing a perspective in which collider processes can be viewed as constrained quantum circuits and their entanglement structure can be understood in terms of the underlying circuit dynamics, opening the door to analyzing their properties using the language of quantum information.
Precision measurements at electron-positron colliders provide stringent tests of the Standard Model and powerful probes of possible higher-dimensional interactions. We present a hybrid quantum-classical framework for computing leading-order helicity amplitudes for e+e−→ℓ+ℓ−e^+e^-\to \ell^+\ell^-e+e−→ℓ+ℓ− scattering on gate-based quantum hardware and using the resulting cross sections to constrain both Standard Model couplings and effective field theory operators. In our approach, external kinematics are encoded into single-qubit Weyl spinors, and full helicity amplitudes are reconstructed by coherently combining diagrammatic contributions within a single quantum circuit. Classical post-processing yields physical amplitudes and differential cross sections that can be directly compared with collider data. As a proof of concept, we compute unpolarised angular distributions and perform binned likelihood fits to precision electron-positron measurements. The extracted bounds are statistically consistent with Standard Model expectations, demonstrating that quantum-assisted amplitude evaluation can interface directly with phenomenological analyses and experimental data. This work establishes a concrete pathway toward applying quantum computing to precision collider physics and effective field theory studies.
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The efficient simulation of accurate collider data at modern collider experiments will be crucial for the detection of Beyond the Standard Model signatures in the search for new physics. Simulation of collision processes at hadron colliders like the LHC are carried out by Monte Carlo event generators which simulate the evolution from an initial hard scattering event, downwards in energy scales, towards the formation of long lived particles. However, as we enter a new era of higher luminosity experiments, accurate simulations of these pseudo-event generated data will become further computationally intensive with the vast amounts of data to generate. With the rapid development of quantum computing hardware, quantum computation offers itself as an alternative computing paradigm that may be harnessed to provide a natural framework to model several physical processes in high-energy physics, where the inherent quantum features of the device may be exploited to provide speedups or enhance current simulations. In this thesis, we present general and extendable quantum algorithms for two crucial parts of event generation: the calculation of matrix elements for the hard interaction and the QCD parton shower stage. First, a novel algorithm is proposed for the calculation of helicity amplitudes by outlining a proposal of constructing helicity spinors directly on a quantum circuit and manipulating the spinors to compute helicity amplitudes. This was used to calculate multiple helicity amplitudes for simple tree level scattering processes simultaneously as a proof-of-principle demonstration. The second algorithm outlines a proposal for a Monte Carlo-inspired parton shower algorithm which was used to simulate two shower steps of a simplified QCD model. The final algorithm extends the quantum parton shower algorithm onto a quantum walk framework which demonstrates significant scaling improvements, simulating more realistic shower depths. These algorithms utilise the quantum computers’ ability to remain in a quantum state throughout the computation and represents a first step towards a quantum computing algorithm describing full collision events at the LHC.
Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic framework for analyzing quantum operators by mapping unitary matrices to directed graphs; we term these structures \emph{Imperfect Graphs} or more formally as \emph{Topological Structure of Superpositions}(TSS) as a tool to devise better Quantum Algorithms. In this framework, we represent computational basis states as vertices. A directed edge exists between two vertices if and only if there is a non-zero amplitude transition between them, effectively mapping the support of the unitary operator. In this paper we deliberately discard probability amplitudes and phase information to isolate the connectivity and reachability properties of the operator. We demonstrate how TSS intuitively helps describe gates such as the Hadamard, Pauli-(X,Y,Z) gates, etc \cite{nielsen2000}. This framework provides a novel perspective for viewing quantum circuits as discrete dynamical systems \cite{childs2009,aharonov2001} Keywords: Quantum Algorithms, Unitary Matrix Approach, Topological Structure of Superpositions (TSS), Graph Theory
Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.