Quantum integration of elementary particle processes

We apply quantum integration to elementary particle-physics processes. In particular, we look at scattering processes such as <math altimg="si1.svg"><msup><mrow><mtext>e</mtext></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mtext>e</mtext></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mo stretchy="false">→</mo><mi>q</mi><mover accent="true"><mrow><mi>q</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></math> and <math altimg="si2.svg"><msup><mrow><mtext>e</mtext></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">+</mo></mrow></msup><msup><mrow><mtext>e</mtext></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mo stretchy="false">→</mo><mi>q</mi><msup><mrow><mover accent="true"><mrow><mi>q</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>′</mo></mrow></msup><mtext>W</mtext></math>. The corresponding probability distributions can be first appropriately loaded on a quantum computer using either quantum Generative Adversarial Networks or an exact method. The distributions are then integrated using the method of Quantum Amplitude Estimation which shows a quadratic speed-up with respect to classical techniques. In simulations of noiseless quantum computers, we obtain per-cent accurate results for one- and two-dimensional integration with up to six qubits. This work paves the way towards taking advantage of quantum algorithms for the integration of high-energy processes.