A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spectral functions on a trapped-ion quantum computer for a one-dimensional Heisenberg model with disorder. Further, we design an error-mitigation technique which is effective at removing the noise from the measurement allowing clear signatures of localization to emerge as the disorder increases. Thus, we show that spectral functions can serve as a robust and scalable diagnostic of many-body localization on the current generation of quantum computers.

1 aZhu, D.1 aJohri, S.1 aNguyen, N., H.1 aAlderete, Huerta1 aLandsman, K., A.1 aLinke, N., M.1 aMonroe, C.1 aMatsuura, A., Y. uhttps://arxiv.org/abs/2006.1235501551nas a2200193 4500008004100000245009300041210006900134260001300203520092900216100002101145700001901166700002201185700001601207700002401223700002401247700002601271700002301297856003701320 2020 eng d00aQuantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer0 aQuantum walks and Dirac cellular automata on a programmable trap c2/6/20203 aThe quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

1 aAlderete, Huerta1 aSingh, Shivani1 aNguyen, Nhung, H.1 aZhu, Daiwei1 aBalu, Radhakrishnan1 aMonroe, Christopher1 aChandrashekar, C., M.1 aLinke, Norbert, M. uhttps://arxiv.org/abs/2002.02537