Simulating Large PEPs Tensor Networks on Small Quantum Devices

Abstract

We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an N x M square-lattice PEPs network, for arbitrary M, of bond dimension 2 can be performed using N + 2 qubits. We employ this approach to calculate the values of a long-range loop observable in the topological Wen plaquette model by mapping a 3 x 3 PEPs tensor network to a 5-qubit quantum circuit and executing it on the Honeywell System Model H1-1 trapped-ion device. We find that, for this system size, the noisy observable values are sufficient for observing the phase transition from topological to trivial order, as the Wen model is perturbed by a magnetic field term in the Hamiltonian. Our results serve as a proof-of-concept of the utility of the measure-and-reuse approach for simulating large two-dimensional quantum systems on small quantum devices.