Quantum Resource Comparison for Two Leading Surface Code Lattice Surgery Approaches

Understand

Hamiltonian simulation is one of the most promising candidates for the demonstration of quantum advantage within the next ten years, and several studies have proposed end-to-end resource estimates for executing such algorithms on fault-tolerant quantum processors.

• Usually, these resource estimates are based upon the assumption that quantum error correction is implemented using the surface code, and that the best surface code compilation scheme involves serializing input circuits by eliminating all Clifford gates.
• This transformation is thought to make best use of the native multi-body measurement (lattice surgery) instruction set available to surface codes.
• Some work, however, has suggested that direct compilation from Clifford+T to lattice surgery operations may be beneficial for circuits that have high degrees of logical parallelism.