Quantum computing for energy correlators

In recent years, energy correlators have emerged as powerful observables for probing the fragmentation dynamics of high-energy collisions. We introduce the first numerical strategy for calculating energy correlators using the Hamiltonian lattice approach, providing access to the intriguing nonperturbative dynamics of these observables. Furthermore, motivated by rapid advances in quantum computing hardware and algorithms, we propose a quantum algorithm for calculating energy correlators in quantum field theories. This algorithm includes ground state preparation, the application of source, sink, energy flux and real-time evolution operators, and the Hadamard test. We validate our approach by applying it to the SU(2) pure gauge theory in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:math> dimensions on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>3</c:mn><c:mo>×</c:mo><c:mn>3</c:mn></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>5</e:mn><e:mo>×</e:mo><e:mn>5</e:mn></e:math> honeycomb lattices with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>j</g:mi><g:mi>max</g:mi></g:msub><g:mo>=</g:mo><g:mfrac><g:mn>1</g:mn><g:mn>2</g:mn></g:mfrac></g:math> at various couplings, utilizing both classical methods and the quantum algorithm, the latter tested using the IBM emulator for specific configurations. The results are consistent with the expected behavior of the strong coupling regime and motivate a more comprehensive study to probe the confinement dynamics across the weak and strong coupling regimes.