A computer-implemented method for quantum compiling for measurement-based unidirectional quantum computation, and related systems

A computer-implemented method for quantum compiling for measurement-based unidirectional quantum computation is described. In the method, electronic processing means 2 are provided with digital information corresponding to a 10 unitary operator or matrix U, representing a singlequbit or multi-qubit quantum operation to be carried out, through a measurement-based unidirectional quantum computation, by a quantum computer 1. The unitary operator or matrix are then decomposed 15 in terms of Pauli operators, by the aforesaid electronic processing means 2. The method, then, comprises directly converting, by the electronic processing means 2, the unitary operator or matrix U, decomposed in terms of Pauli 20 operators, into a graph G implementable on the quantum computer 1. The graph G represents a state of a cluster of qubits to be processed by the quantum computer 1 to carry out the desired said quantum operation. In the graph G, each graph vertex represents a respective qubit 25 of the cluster and each edge of the graph corresponds to 46 an entanglement to be imposed between the two qubits corresponding to the two vertices connected by the edge. The aforesaid step of directly converting comprises identifying the sub-set of entanglements to be 5 implemented between qubits of the cluster and identifying the sub-set of qubits of the cluster to be measured, to obtain the graph G representing the state of said cluster, based on the criterion that the measurement of the aforesaid identified sub-set of 10 qubits to be measured affects the output state of the other unmeasured qubits, through the aforesaid identified entanglements, in a manner corresponding to the quantum operation to be carried out. The method finally comprises the step of providing 15 to the quantum computer 1, by the electronic processing means 2, as the result of the quantum compiling, a graph description information Q(G) describing the aforesaid obtained graph (G). A computer implemented method for performing 20 measurement-based unidirectional quantum computation, based on the aforesaid computer-implemented method for quantum compiling, is also described. A quantum computing system, exploiting said computer-implemented methods, is also described.