Probing Phases of Quantum Matter with an Ion-Trap Tensor-Network Quantum Eigensolver
M. Meth, Viacheslav Kuzmin, Rick van Bijnen, Lukas Postler, Roman Stricker, R. Blatt, Martin Ringbauer, Thomas Monz, Pietro Silvi, Philipp Claudius Schindler · Physical Review X · 2022
Tensor-network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations.Employing TN Ansatz states directly on a quantum simulator can potentially offer an exponential computational advantage over purely numerical simulation.We implement a quantum-encoded TN Ansatz state using a variational quantum eigensolver on an ion-trap quantum computer that approximates 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 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 the qubits in neighboring ions.