The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on quantum computing introducing an algorithmic description of the method.The corner stone of the Shor...The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on quantum computing introducing an algorithmic description of the method.The corner stone of the Shor’s algorithm is the modular exponentiation that is themost computational component(in time and space).A linear depth unit based on phase estimation is introduced and a description of a generic version of a modular multiplier based on phases is introduced to build block of a gates to efficient modular exponentiation circuit.Our proposal includes numerical experiments achieved on both the IBM simulator using the Qiskit library and on quantum physical optimizers provided by IBM.The shor’s algorithm based on phase estimation succeeds in factoring integer numbers with more than 35 digits using circuits with about 100 qubits.展开更多
文摘The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on quantum computing introducing an algorithmic description of the method.The corner stone of the Shor’s algorithm is the modular exponentiation that is themost computational component(in time and space).A linear depth unit based on phase estimation is introduced and a description of a generic version of a modular multiplier based on phases is introduced to build block of a gates to efficient modular exponentiation circuit.Our proposal includes numerical experiments achieved on both the IBM simulator using the Qiskit library and on quantum physical optimizers provided by IBM.The shor’s algorithm based on phase estimation succeeds in factoring integer numbers with more than 35 digits using circuits with about 100 qubits.
