Method for compiling a quantum circuit for a trapped-ion quantum processor, comprising: - an optional prior step of transforming the quantum circuit so that it contains only: * a predetermined first category of two-qubit quantum gates, * and/or one-qubit quantum gates, - a step of separating said quantum circuit into: * local layers comprising solely one-qubit quantum gates, * entangling layers comprising solely: ∘ two-qubit quantum gates of the first category, ∘ and/or one-qubit quantum gates of a predetermined second category, - a step of compiling local layers, comprising a calculation of local matrices of local layers to be applied to each qubit, - a step of compiling entangling layers, separate from the step of compiling the local layers, - the step of compiling the entangling layers transforming the quantum gates of these entangling layers so that they contain only: * N-qubit collective or entangling quantum gates of a predetermined third category, * one-qubit quantum gates of a predetermined fourth category, - a step of grouping together the compiled local layers and the compiled entangling layers in a compiled quantum circuit, and characterised in that: - the quantum circuit comprises a number of qubits greater than 10 qubits, preferably greater than 20 qubits and preferably greater than 30 qubits, and - the step of compiling the local layers also comprises: - a decomposition of each local matrix of a local layer into a sequence of quantum gates with a rotation on the Z axis, a rotation on the X axis and a rotation on the Z axis, - a sub-decomposition of the rotation on the X axis into a sequence of Hadamard quantum gates, with a Hadamard rotation on the Z axis, - a sub-sub-decomposition of the Hadamard gate into a sequence of quantum gates with a rotation on the Z axis, a rotation on the X axis and a rotation on the Z axis, all three rotations by an angle of π or π/2, - a mutualisation between qubits of the gates with rotation on the X axis by an angle of π/2. - an optional prior step of transforming the quantum circuit so that it contains only: * a predetermined first category of two-qubit quantum gates, * and/or one-qubit quantum gates, * a predetermined first category of two-qubit quantum gates, * and/or one-qubit quantum gates, - a step of separating said quantum circuit into: * local layers comprising solely one-qubit quantum gates, * entangling layers comprising solely: ∘ two-qubit quantum gates of the first category, ∘ and/or one-qubit quantum gates of a predetermined second category, * local layers comprising solely one-qubit quantum gates, * entangling layers comprising solely: ∘ two-qubit quantum gates of the first category, ∘ and/or one-qubit quantum gates of a predetermined second category, ∘ two-qubit quantum gates of the first category, ∘ and/or one-qubit quantum gates of a predetermined second category, - a step of compiling local layers, comprising a calculation of local matrices of local layers to be applied to each qubit, - a step of compiling entangling layers, separate from the step of compiling the local layers, - the step of compiling the entangling layers transforming the quantum gates of these entangling layers so that they contain only: * N-qubit collective or entangling quantum gates of a predetermined third category, * one-qubit quantum gates of a predetermined fourth category, * N-qubit collective or entangling quantum gates of a predetermined third category, * one-qubit quantum gates of a predetermined fourth category, - a step of grouping together the compiled local layers and the compiled entangling layers in a compiled quantum circuit, - the quantum circuit comprises a number of qubits greater than 10 qubits, preferably greater than 20 qubits and preferably greater than 30 qubits, and - the step of compiling the local layers also comprises: - a decomposition of each local matrix of a local layer into a sequence of quantum gates with a rotation on the Z axis, a rotation on the X axis and a rotation on the Z axis, - a sub-decomposition of the rotation on the X axis into a sequence of Hadamard quantum gates, with a Hadamard rotation on the Z axis, - a sub-sub-decomposition of the Hadamard gate into a sequence of quantum gates with a rotation on the Z axis, a rotation on the X axis and a rotation on the Z axis, all three rotations by an angle of π or π/2, - a mutualisation between qubits of the gates with rotation on the X axis by an angle of π/2. - a decomposition of each local matrix of a local layer into a sequence of quantum gates with a rotation on the Z axis, a rotation on the X axis and a rotation on the Z axis, - a sub-decomposition of the rotation on the X axis into a sequence of Hadamard quantum gates, with a Hadamard rotation on the Z axis, - a sub-sub-decomposition of the Hadamard gate into a sequence of quantum gates with a rotation on the Z axis, a rotation on the X axis and a rotation on the Z axis, all three rotations by an angle of π or π/2, - a mutualisation between qubits of the gates with rotation on the X axis by an angle of π/2.