Compilation technique for surface code architecture

A method for implementing a quantum circuit in order to maximize a number of tasks to be performed in parallel on a calculation cluster with a fixed connectivity, the quantum circuit comprising a plurality of qubits as well as operators executed on said qubits, said operators comprising a sequence of

• π
• 4
• Pauli rotation gates, a surface code layout comprising an arrangement of said quantum circuit on a quantum chip, the arrangement comprising at least a tree comprising a plurality of vertices and links between the vertices, each
• π
• 4
• Pauli rotation gate corresponding to a subtree of the tree, the method comprising:
• generating iteratively a directed acyclic graph (DAG) of said quantum circuit, a front layer of the DAG being a set of the
• π
• 4
• Pauli rotation gates that can be effectively implemented at each iteration;
• and
• selecting in said front layer of the DAG a subset of the
• π
• 4
• Pauli rotation gates, called a selected subset, among subsets, called non intersecting subsets, in which the subtrees do not to intersect, by applying the following method for implementing the tree:
• in said set, selecting subsets, called pre-selected subsets, such that the subtrees associated respectively to said subsets are pairwise disjoint;
• comparing the number of vertices associated to each of the pre-selected subsets;
• and
• among the pre-selected subsets, choosing the subset for which the number of vertices is highest.