Quantum Field Theories (QFTs) play a central role in our understanding of nature. Despite significant progress in applying classical computational techniques to study few hadrons Lattice Quantum Chromodynamics [1] and dilute matter at finite temperatures [2], there are a number of roadblocks that prevent classical numerical approaches from tackling these theories at large scale and in their real-time dynamics. A fundamental challenge is related to the size of the Hilbert space of the quantum many-body system growing exponentially with the number of particles, making large-scale simulations classically intractable. Another challenge is related to the statistical nature of common computational methods, like Quantum Monte Carlo, used to study strongly interacting systems.

The aim of Pagano Lab is to carefully engineered trapped-ion quantum simulator that can directly realize Hamiltonians of quantum field theories, thereby providing a significant advantage with respect to the digital approach in scaling to systems up to sizes that can not be accessed with conventional computing techniques. To do so, we plan to use multiple degrees of freedom already present in the trapped-ion system, using for example multiple modes of motion to increase the flexibility in the Hamiltonian that can be directly implemented on the simulator [3]. Another important ingredient to directly map QFT onto a spin Hamiltonian is higher order interactions, which we plan to pursue with a generalized Molmer-Sorensen scheme [4]. Finally we plan to directly map the bosonic degrees of freedom present in multiple QFTs and nuclear physics models using both local and collective modes of motion present in trapped-ion systems [5].

References:
[1] Z. Davoudi, et al., “Nuclear matrix elements from lattice qcd for electroweak and beyond-standard- model processes,” (2020), arXiv:2008.11160 [hep-lat]
[2] A. Bazavov, et al., “USQCD white paper”, (2019), arXiv:1904.09951 [hep-lat]
[3] Z. Davoudi, M. Hafezi, C. Monroe, G. Pagano, A. Seif, A. Shaw,”Towards analog quantum simulations of lattice gauge theories with trapped ions“,
Physical Review Research, 2, 023015 (2020)
[4] B. Andrade, Z. Davoudi, T. Graß, M. Hafezi, G. Pagano, A. Seif
“Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation”
Quantum Sci. Technol. 7, 034001 (2022)
[5] Z. Davoudi, N. M. Linke and G. Pagano, “Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach“,
Physical Review Research 3, 043072 (2021).