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arXiv · 2211.02684

Digital Quantum Simulation of Scalar Yukawa Coupling

Thierry N. Kaldenbach·Matthias Heller·Gernot Alber·Vladimir M. Stojanovic
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Abstract

Motivated by the revitalized interest in the digital simulation of medium- and high-energy physics phenomena, we investigate the dynamics following a Yukawa-interaction quench on IBM Q. Adopting the zero-dimensional version of the scalar Yukawa-coupling model as our point of departure, we design low-depth quantum circuits emulating its dynamics with up to three bosons. In the one-boson case we demonstrate circuit compression, i.e., a constant-depth circuit containing only two controlled-NOT (CNOT) gates. In the more complex three-boson case, we design a circuit in which one Trotter step entails $8$ CNOTs. Using an analogy with the traveling-salesman problem, we also provide a CNOT-cost estimate for higher boson-number truncations. Based on these circuits, we quantify the system dynamics by evaluating the expected boson number at an arbitrary time after the quench and the survival probability of the initial vacuum state (the Loschmidt echo). We also utilize these circuits to drive adiabatic transitions and compute the energies of the ground- and first-excited states of the considered model. Finally, through error mitigation -- i.e, zero-noise extrapolation -- we demonstrate a good agreement of our results with a numerically-exact classical benchmark.

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Thierry N. Kaldenbach, Matthias Heller, Gernot Alber, Vladimir M. Stojanovic. 2022-11-04. Digital Quantum Simulation of Scalar Yukawa Coupling. https://doi.org/10.3390/quantum6030024

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