A Rubik's Cube inspired approach to Clifford synthesis

TL;DR

A machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity that 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.

Abstract

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.

Figures (4)

• Figure 1: The fraction of solved instances as a function of CNOT count for both the beam search algorithm with beam width $w=3$ (solid curve) and the built-in Qiskit method (dashed line).
• Figure 2: Fraction of problem instances solved. (Left): The cumulative fraction of problem instances solved by the greedy algorithm as a function of weighted distance, for a range of circuit widths. (Center): The analogous plot for the beam search algorithm with beam width $w=3$. (Right): The Qiskit method.
• Figure 3: The Pearson correlation loss evaluated at each step in the training process.
• Figure 4: The Pearson correlation loss attained at the end of the training process for the two different scalings of $L_{\text{max}}$.