Superconducting pairing correlations on a trapped-ion quantum computer

Abstract

The Fermi-Hubbard model is the starting point for the simulation of many strongly correlated materials, including high-temperature superconductors, whose modelling is a key motivation for the construction of quantum simulation and computing devices. However, the detection of superconducting pairing correlations has so far remained out of reach, both because of their off-diagonal character - which makes them inaccessible to local density measurements - and because of the difficulty of preparing superconducting states. Here, we report measurement of significant pairing correlations in three different regimes of Fermi-Hubbard models simulated on Quantinuum's Helios trapped-ion quantum computer. Specifically, we measure non-equilibrium pairing induced by an electromagnetic field in the half-filled square lattice model, d-wave pairing in an approximate ground state of the checkerboard Hubbard model at $1/6$-doping, and s-wave pairing in a bilayer model relevant to nickelate superconductors. These results show that a quantum computer can reliably create and probe physically relevant states with superconducting pairing correlations, opening a path to the exploration of superconductivity with quantum computers.

7+63 pages, 3+29 figures. v2: added an author, updated author contributions, competing interest, acknowledgement, updated references, fixed typos and added some diagrams to Supplementary Section S4, updated Supplementary Figure S27b, v3: corrected typo in author name