Hybrid Analog-Digital Simulation of the Abelian Higgs model

TL;DR

This paper demonstrates hybrid analog-digital and gate-based quantum simulation protocols of the (1+1)D Abelian Higgs model using superconducting transmon qutrits, showcasing real-time dynamics and scalability prospects for gauge theories.

Contribution

It introduces and experimentally implements a novel hybrid analog-digital simulation protocol for the Abelian Higgs model on transmon qutrits, advancing resource-efficient quantum simulations of gauge theories.

Findings

Successful real-time simulation of AHM observables

Implementation of Floquet and Trotterized protocols

Discussion on scalability to other gauge models

Abstract

To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories, including unexplored regimes of the QCD phase diagram. In this work, using superconducting transmon qutrit processors, we formulate and implement a pulse-based, three-level, hybrid analog-digital simulation protocol of the (1+1) dimensional Abelian Higgs model (AHM) on two sites. Alongside this approach, we experimentally realize a gate-based implementation of the same model. Using the natural mapping of the three-level truncation of the transmon Hilbert space to the spin-1 truncated AHM, we observe real time dynamics of AHM field observables, which are analogous to electric field operators, with both protocols. For the analog-digital protocol, we engineer a Floquet simulation with a combination of local analog drives, driven modification of the natural interaction Hamiltonian of the two transmons, and dynamical decoupling pulses. For the digital protocol, we use a state-of-the-art qutrit processor to implement a Trotterized simulation of the model incorporating advanced error mitigation techniques. We further discuss the scalability of the two approaches, and their potential to be extended to the simulation of other model Hamiltonians. Our experiments demonstrate a viable platform for future studies of spin-1 and SU(3) based gauge theory models on current and near-term transmon qutrit processors.