Vertex Lattice Models Simulated with Quantum Circuits

Abstract

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.

References in corpus (7)

• Efficient classical simulation of slightly entangled quantum computations
• The theory of variational hybrid quantum-classical algorithms
• Nearly optimal lattice simulation by product formulas
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer
• Roadmap for quantum simulation of the fractional quantum Hall effect
• A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces