Studying many-body localization on a universal quantum computer

An interacting disordered system may exhibit localized or thermal behavior depending on the ratio of the disorder to interaction strength. The study of this phenomena has been proposed as an application of near-term quantum computers. However, it is known that most diagnostics of localization such as many-body level statistics and the failure of the eigenstate thermalization hypothesis do not survive coupling to a bath. One robust diagnostic theoretically known to survive introduction of noise are the spectral functions of local operators [1]. Signatures of localization in this diagnostic include a discrete spectrum and a gap at low frequencies. Here, we design an algorithm to compute the spectrum on a universal quantum computer using Trotterized time-evolution. Further, we implement the technique on a three-qubit trapped ion system and find that we can clearly discern the vanishing of the low-frequency response as the disorder increases. Thus, we show that for near-term quantum computers, spectral functions of local operators provide a robust and scalable diagnostic for distinguishing between localized and thermal phases.

[1] Sonika Johri, Rahul Nandkishore and R. N. Bhatt, Phys. Rev. Lett. 114 (11), 117401