Universal Euler-Cartan Circuits for Quantum Field Theories

TL;DR

This paper introduces a hybrid quantum-classical algorithm using universal Euler-Cartan circuits to compute non-perturbative features of quantum field theories, enabling new insights into complex quantum phenomena.

Contribution

It presents a novel parametrized quantum circuit ansatz based on Euler and Cartan decompositions for quantum field theory simulations.

Findings

Successfully benchmarks energy spectra of lattice quantum field theories.

Provides low depth circuits for false vacua and excited states.

Enables exploration of mass ratios, scattering amplitudes, and false-vacuum decays.

Abstract

Quantum computers can efficiently solve problems which are widely believed to lie beyond the reach of classical computers. In the near-term, hybrid quantum-classical algorithms, which efficiently embed quantum hardware in classical frameworks, are crucial in bridging the vast divide in the performance of the purely-quantum algorithms and their classical counterparts. Here, a hybrid quantum-classical algorithm is presented for the computation of non-perturbative characteristics of quantum field theories. The presented algorithm relies on a universal parametrized quantum circuit ansatz based on Euler and Cartan's decompositions of single and two-qubit operators. It is benchmarked by computing the energy spectra of lattice realizations of quantum field theories with both short and long range interactions. Low depth circuits are provided for false vacua as well as highly excited states corresponding to mesonic and baryonic excitations occurring in the analyzed models. The described algorithm opens a hitherto-unexplored avenue for the investigation of mass-ratios, scattering amplitudes and false-vacuum decays in quantum field theories.