Abstract: Method for implementing a graph (G) comprising a plurality of vertices (V) and links (E) between the vertices, a set (R) being a collection of subsets (Ri) of said a given number of vertices (Rik) comprising: in said set (R), selecting subsets (Ri, Rj), called pre-selected subsets, such that a tree (Ti, Tj) is associated respectively to said subset (Ri, Rj), said associated trees (Ti, Tj) being pairwise disjoint and constructing (301) each tree (Ti); associating a weight to each said tree (Ti); choosing the subset for which the tree (Ti) has the highest weight.

Abstract: Method for implementing a graph (G) comprising a plurality of vertices (V) and links (E) between the vertices, a set (R) being a collection of subsets (Ri) of said a given number of vertices (Rik) comprising: in said set (R), selecting subsets (Ri, Rj), called pre-selected subsets, such that a tree (Ti, Tj) is associated respectively to said tree (Ti, Tj), said associated trees (Ti, Tj) being pairwise disjoint; comparing the number of vertices (Rik) associated to each of the pre-selected subset, among the pre-selected subsets, choosing the subset for which the number of vertices is the highest

Abstract: Method for implementing a quantum circuit comprising a plurality of qubits as well as operators executed on said qubits, said operators comprising a sequence of ? 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 with a plurality of subtrees, at each rotation gate corresponding a subtree of the tree, the method comprising: generating iteratively a directed acyclic graph of said quantum circuit, a front layer of the DAG being a set of rotations that can be effectively implemented at each iteration, and selecting in said front layer of the DAG a subset, called selected subset, of said set of rotations among subsets, called non intersecting subsets, in which the subtrees are arranged not to intersect.