A Rubik's Cube inspired approach to Clifford synthesis
This addresses the problem of optimizing quantum circuit compilation for specific quantum devices, though it is incremental as it builds on existing Clifford synthesis methods.
The authors tackled the problem of Clifford synthesis (decomposing Clifford elements into gate sequences) by developing a machine learning approach inspired by Rubik's Cube similarities, which when successful often yields fewer gates than existing algorithms and allows flexible incorporation of gate sets, device topologies, and gate fidelities.
The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than existing synthesis algorithms. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may incorporated, thus allowing for the approach to be tailored to a specific device.