Digital Quantum Simulation of the Kitaev Quantum Spin Liquid

Abstract: The ground state of the Kitaev quantum spin liquid on a honeycomb lattice is an intriguing many-body state characterized by its topological order and massive entanglement. One of the significant issues is to prepare and manipulate the ground state as well as excited states in a quantum simulator. Here, we provide a protocol to manipulate the Kitaev quantum spin liquid via digital quantum simulation. A series of unitary gates for the protocol is explicitly constructed, showing its circuit depth is an order of $\mathcal{O}(N)$ with the number of qubits, N. We demonstrate the efficiency of our protocol on the IBM Heron r2 processor for N = 8 and 12. We further validate our theoretical framework through numerical simulations, confirming high-fidelity quantum state control for system sizes up to N = 450, and discuss the possible implications of these results.