Quantum system for performing a cnot gate and quantum system for performing a repetition code using the same

A quantum system for performing a CNOT gate, the quantum system comprising:

• a command circuit for providing microwave radiation;
• a target cat qubit device comprising an asymmetrically threaded superconducting quantum interference device having flux lines through which radiation can be sent to modulate a common flux and optionally a differential flux, and connected to at least one resonant portion, wherein:
• the target cat qubit device has a first mode (a) with a first resonant frequency and a second mode (b) with a second resonant frequency;
• and
• the asymmetrically threaded superconducting quantum interference device is arranged such that when the command circuit delivers a radiation having the second resonant frequency to the at least one resonant portion to drive the second mode (b) and delivers radiation in the flux lines to modulate the common flux at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency, the target cat qubit device stabilizes a target cat qubit having the first resonant frequency, and
• a control superconducting qubit device having a third mode (q) with a third resonant frequency for hosting a control qubit having a confinement rate, the control superconducting qubit device being arranged such that a Rabi oscillation of the third mode (q) is induced when it is subject to a radiation having the third resonant frequency with a strength which is less than the control qubit confinement rate, the control superconducting qubit device being linearly coupled to the target cat qubit device such that the third mode (q) is linearly coupled with the asymmetrically threaded superconducting quantum interference device, wherein:
• the command circuit is arranged during a CNOT gate time window to deliver in the flux lines only a radiation at a frequency equal to the third resonant frequency to operate a CNOT gate between the target cat qubit and the control qubit, and arranged outside of the CNOT gate time window to deliver a radiation having the second resonant frequency to the at least one resonant portion to drive the second mode (b) and to deliver radiation in the flux lines to modulate the common flux at a frequency equal to the absolute value of the difference between twice the first resonant frequency and the second resonant frequency.