Coherent Quantum Evaluation of Collider Amplitudes for Effective Field Theory Constraints

Abstract

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 $e^+e^-\to \ell^+\ell^-$ 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.

Figures (9)

• Figure 1: Algorithm overview: EFT parameters determine diagram coefficients $c_d$ and hence the LCU preparation weights. The quantum circuit evaluates the (helicity-resolved or helicity-averaged) amplitude via bracket-extraction blocks and a controlled accumulator rotation; classical post-processing converts the measured accumulator probability into $\mathrm{d}\sigma/\mathrm{d}\cos\theta$ and performs the binned likelihood fit to collider data.
• Figure 2: Compact quantum-circuit schematic for the $s$-channel block (full two-diagram layout shown above, with a zoom-in of the bracket-product subroutine at right). Each external leg $i$ is encoded as a two-wire Weyl bundle $(\lambda_i,\tilde{\lambda}_i)$, prepared by $W_i\equiv\chi(\theta_i,\phi_i)$ and unprepared by $W_i^\dagger=\chi^\dagger(\theta_i,\phi_i)$. The helicity logic block $\mathcal{F}_{\mathrm{hel}}$ coherently computes the flags $(v_1,v_2)$ and a selector bit $b$ that chooses the required spinor contraction. Bracket products are exposed with Bell-inverse gadgets $B^\dagger$: the Type A path implements $\langle23\rangle[14]$ (red region, $b=1$), while the Type B path implements $\langle24\rangle[13]$ (blue region, $b=0$). The resulting scalar is copied to the accumulator register $A$ via controlled $R_y$ rotations (with the appropriate coefficient, e.g. $c_{\mathrm{same}}$ or $c_{\mathrm{opps}}$), and then all work registers are uncomputed with $B$. For multi-diagram runs, the LCU index register is prepared with $P(C_s,C_t)$ and unprepared with $P^\dagger(C_s,C_t)$.
• Figure 3: Closure test comparing $|\mathcal{M}_{\rm QC}|^2$ to an independent classical spinor-helicity evaluation as a function of $\cos\theta$. Examples include the dimuon $s$-channel and Bhabha $s/t$ contributions, the interference term, and their LCU combination.
• Figure 4: Differential cross-section overlays with data. Data points with error bars are compared to the SM prediction and representative EFT benchmark curves derived from the quantum-computed amplitudes.
• Figure 5: Likelihood contours in the $(c_{RR/LL},c_{RL/LR})$ plane extracted from the quantum-evaluated likelihood, shown at $68\%$ and $95\%$ confidence level (solid and dashed, respectively). The best-fit point from the fit is indicated along with the SM reference point. This figure illustrates the correlation structure induced by interference terms and provides a direct test that the circuit-encoded amplitude reproduces the analytic likelihood geometry.