Quantum Monte Carlo and Stabilizer States

Abstract

The Quantum-Monte-Carlo technique known as the Stochastic Series Expansion (SSE) relies on a crucial no-branching condition: the SSE sampling is carried out in the computational basis, and the no-branching assumption ensures that superpositions of basis-states do not appear when operators are applied. Without this proviso, the number of complex amplitudes would grow exponentially with the number of qubits and would eventually overwhelm the memory and processing power of a classical computer. However, the action of Clifford group elements on stabilizer states can be very efficiently described without resorting to an amplitude description. We explore how stabilizer states allow an extension of the SSE technique, and we give an example of a toy model that can be studied in this way. The method is also illustrated using the Transverse-Field Ising model.