Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver

Abstract

Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can potentially offer an exponential advantage over purely numerical simulation. In particular, we demonstrate the optimization of a quantum-encoded TN ansatz state using a variational quantum eigensolver on an ion-trap quantum computer by preparing the ground states of the extended Su-Schrieffer-Heeger model. The generated states are characterized by estimating the topological invariants, verifying their topological order. Our TN encoding as a trapped ion circuit employs only single-site addressing optical pulses - the native operations naturally available on the platform. We reduce nearest-neighbor crosstalk by selecting different magnetic sublevels with well-separated transition frequencies to encode even and odd qubits.

17 pages, 14 figures

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• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• Constructing the spin-1 Haldane phase on a qudit quantum processor
• Quantum simulation of extended electron-phonon coupling models in a hybrid Rydberg atom setup
• Photonic variational quantum eigensolver for NISQ-compatible quantum technology