Simulating Large PEPs Tensor Networks on Small Quantum Devices

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×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 3×3 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 diagnosing topological vs. 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.