Method for executing a quantum error correction cycle in a quantum computer

A method for executing a quantum error correction cycle in a quantum computer provided with a substrate of qubits arranged in repeated unit cells, wherein a data qubits are coupled to respective X-ancillary qubits and Z-ancillary qubits, wherein the X-ancillary qubits are capable of measuring a first quantum variable and the Z-ancillary qubits are capable of measuring a second quantum variable of said data qubits by a nearest neighbor interaction provided only between said data qubits and said ancillary qubits, wherein said nearest neighbor interaction is provided by detuning a transition frequency of any of the data qubits and ancillary qubits into a coupling frequency for providing a coherent 2-qubit gate, and wherein said method comprises:

• providing a plurality of the data qubits on a first grid, wherein a unit cell comprises four data qubits;
• and
• providing a plurality of X-ancillary qubits and Z-ancillary qubits on a second grid, said second grid shifted relative to the first grid, so that one of the ancillary qubits is central to the four data qubits of the unit cell, and the X-ancillary qubits and Z-ancillary qubits are each further arranged in respective diametral positions relative to one of the data qubits of the unit cell, said unit cell thereby further comprising two X-ancillary qubits and two Z-ancillary qubits;
• wherein each one of the data qubits each unit cell is subsequently brought in a coupling resonance with any of the X-ancillary qubits and Z-ancillary qubits by;
• simultaneous coupling of first ones of the ancillary qubits with a respective neighboring data qubit;
• and subsequent couplings of said first ones with the other neighboring data qubits;
• followed by
• simultaneous coupling of second ones of the ancillary qubits with a neighboring data qubit;
• and subsequent couplings of said second ancillary qubit with the other neighboring data qubits,
• wherein a first data qubits are kept operating at a first frequency, a second data qubits are kept operating at a third frequency on said grid, and said ancillary qubits are kept operating at a second frequency between said first and third frequencies;
• wherein a coupling frequency is provided by detuning any of the first data qubits in an intermediate frequency between the first and second frequency;
• wherein a coupling frequency is provided by detuning any of the ancillary qubits in an intermediate frequency between the second and third frequency, and wherein said first frequency, said second frequency and said third frequency are sufficiently different to avoid coupling of the data qubits and the ancillary qubits outside the coupling frequency, or
• wherein a first pair of the ancillary qubits are kept operating at a first frequency, a second pair of the ancillary qubits are kept operating at a third frequency, and said data qubits are kept operating at a second frequency between said first frequency and said third frequency;
• wherein a coupling frequency is provided by detuning any of the first pair of the ancillary qubits in an intermediate frequency between the first frequency and the second frequency;
• wherein a coupling frequency is provided by detuning any of the data qubits in an intermediate frequency between the second frequency and the third frequency, and wherein said first frequency, said second frequency and said third frequency are sufficiently different to avoid coupling of the data qubits and the ancillary qubits outside the coupling frequency.