Quantum Monte Carlo and Stabilizer States

Understand

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.