Transmon qutrit-based simulation of spin-1 AKLT systems

TL;DR

This paper demonstrates the use of transmon qutrits to efficiently simulate spin-1 AKLT states, revealing topological properties and showcasing advantages over qubits in noisy quantum environments.

Contribution

It introduces calibrated microwave gates for transmon qutrits and applies them to simulate and analyze topologically non-trivial spin-1 systems, advancing quantum simulation capabilities.

Findings

High-fidelity ground state preparation of AKLT states

Measurement of non-trivial Berry phases in simulated systems

Qutrits outperform qubits under noise conditions

Abstract

Qutrit-based quantum circuits could help reduce the overall circuit depths, and hence the effect of noise, when the system of interest has a local dimension of three. Accessing second excited states in superconducting transmons provides a straightforward hardware realization of qutrits useful for such ternary encoding. In this work, we successfully calibrate microwave pulse gates to a low error rate to operate transmon qutrits. We use these qutrits to simulate one-dimensional spin-1 AKLT states (Affleck, Kennedy, Lieb, and Tasaki), which exhibit a multitude of interesting phenomena, such as topologically protected ground states, string order, and the existence of a robust Berry phase. We demonstrate the efficacy of qutrit-based simulation by preparing high-fidelity ground states of the AKLT Hamiltonian with open boundaries for various chain lengths. We then use ground state preparations of the perturbed AKLT Hamiltonian with periodic boundaries to calculate the Berry phase and illustrate non-trivial ground state topology. To establish the advantage of qutrits over qubits in the presence of noise, we present scalable methods for preparing the AKLT state and computing its Berry phase using tensor network simulations. Our work provides a pathway toward more general spin-1 physics simulations using transmon qutrits, with applications in chemistry, magnetism, and topological phases of matter.