Vertex Lattice Models Simulated with Quantum Circuits

Classical planar vertex models afford transfer matrices with real and positive entries, which makes this class of models suitable for quantum simulations. In this work, we support this statement by building explicit quantum circuits that implement the actions of the transfer matrices on arbitrary many-qubit states. The number of qubits and the depth of the circuits grow linearly with the size of the system. Furthermore, we present tests using quantum simulators and demonstrate that important physical quantities can be extracted, such as the eigen-vector corresponding to the largest eigenvalue of the transfer matrix and the ratio of the second to first largest eigenvalue. Challenges steaming from the non-unitarity of the transfer matrix are discussed.