According to one embodiment, an encoder includes a first element part and a controller. The first element part includes a first qubit, a second qubit couplable with the first qubit, a third qubit couplable with the second qubit, a fourth qubit couplable with the third qubit, a fifth qubit couplable with the fourth qubit, a sixth qubit couplable with the fifth qubit, a seventh qubit couplable with the sixth qubit, an eighth qubit couplable with the seventh qubit, and a ninth qubit couplable with the eighth qubit. The controller is configured to perform a first control. The first control includes encoding a surface code having a code distance of 3.