Logical qubit encoding surface

1. A quantum computing device comprising:

a logical qubit encoding surface including a plurality of plaquettes, wherein:

each plaquette of the plurality of plaquettes includes a plurality of measurement-based qubits;

the plurality of measurement-based qubits includes four data qubits and a first ancilla qubit; and

the first ancilla qubit is electrically connected, via separate corresponding electrical connections, to the four data qubits and a second ancilla qubit included in the logical qubit encoding surface.

2. The quantum computing device of claim 1 , wherein the four data qubits of the plaquette are arranged in a square.

3. The quantum computing device of claim 2 , wherein the first ancilla qubit is located within the square.

4. The quantum computing device of claim 2 , wherein the respective data qubits included in the plurality of plaquettes are arranged in a rectangular grid.

5. The quantum computing device of claim 4 , wherein, for each plaquette of the plurality of plaquettes, the electrical connection between the first ancilla qubit and the second ancilla qubit extends in a direction perpendicular to an edge of the rectangular grid that is closest to a midpoint between the first ancilla qubit and the second ancilla qubit.

6. The quantum computing device of claim 1 , further comprising:

a measurement device configured to:

perform a measurement of a logical qubit encoded by the logical qubit encoding surface; and

measure a respective stabilizer operator of each plaquette included in the logical qubit encoding surface; and

a classical computing device configured to identify an error in the measurement of the logical qubit based on respective measurement results of the stabilizer operators.

7. The quantum computing device of claim 6 , wherein each stabilizer operator is a product of four Pauli X operators or four Pauli Z operators of the four respective data qubits included in the plaquette.

8. The quantum computing device of claim 7 , wherein:

the measurement device is configured to measure the product of the four Pauli X operators for each of a first set of plaquettes and the product of the four Pauli Z operators for each of a second set of plaquettes; and

the plurality of plaquettes are arranged in a rectangular grid including a first plurality of respective grid positions of the first set of plaquettes that alternate with a second plurality of respective grid positions of the second set of plaquettes.

9. The quantum computing device of claim 6 , wherein, for each plaquette, the measurement device is configured to measure the respective stabilizer operator of the plaquette at least in part by:

preparing the second ancilla qubit to have a |+ state;

applying one or more respective controlled not (CNOT) gates to the plaquette, wherein for each CNOT gate, a data qubit of the four data qubits is a target qubit; and

performing a second ancilla measurement at the second ancilla qubit subsequently to applying the one or more CNOT gates.

10. The quantum computing device of claim 9 , wherein the second ancilla measurement is a measurement of a Pauli X operator or a Pauli Z operator.

11. The quantum computing device of claim 9 , wherein applying each CNOT gate includes:

performing a plurality of first ancilla measurements of at least the first ancilla qubit, wherein each first ancilla measurement is a one-qubit measurement or a two-qubit measurement; and

for each first ancilla measurement, subsequently to that first ancilla measurement, performing a Pauli update on at least the first ancilla qubit.

12. A method for use with a quantum computing device, the method comprising:

at a measurement device:

performing a measurement of a logical qubit encoded by a logical qubit encoding surface including a plurality of plaquettes, wherein:

each plaquette of the plurality of plaquettes includes a plurality of measurement-based qubits;

the plurality of measurement-based qubits includes four data qubits and a first ancilla qubit; and

the first ancilla qubit is electrically connected, via separate corresponding electrical connections, to the four data qubits and a second ancilla qubit included in the logical qubit encoding surface; and

measuring a respective stabilizer operator of each plaquette included in the logical qubit encoding surface; and

at a classical computing device, identifying an error in the measurement of the logical qubit based on respective measurement results of the stabilizer operators.

13. The method of claim 12 , wherein measuring the stabilizer operator includes:

preparing the second ancilla qubit to have a |+ state;

applying one or more respective controlled not (CNOT) gates to the plaquette, wherein for each CNOT gate, a data qubit of the four data qubits is a target qubit; and

performing a second ancilla measurement at the second ancilla qubit subsequently to applying the one or more CNOT gates.

14. The method of claim 13 , wherein the second ancilla measurement is a measurement of a Pauli X operator or a Pauli Z operator.

15. The method of claim 13 , wherein applying each CNOT gate includes:

performing a plurality of first ancilla measurements of at least the first ancilla qubit, wherein each first ancilla measurement is a one-qubit measurement or a two-qubit measurement; and

for each first ancilla measurement, subsequently to that first ancilla measurement, performing a Pauli update on at least the first ancilla qubit.

16. The method of claim 12 , wherein the stabilizer operator includes a product of four Pauli X operators or four Pauli Z operators.

17. A method for use with a quantum computing device, the method comprising:

performing a surface code error correction at a logical qubit encoding surface including a plurality of measurement-based physical qubits, wherein:

the plurality of measurement-based physical qubits includes four data qubits, a first ancilla qubit, and a second ancilla qubit;

the first ancilla qubit is electrically connected, via separate corresponding electrical connections, to the four data qubits and the second ancilla qubit;

performing the surface code error correction includes implementing one or more two-qubit logic gates; and

implementing each two-qubit logic gate includes performing a plurality of measurements, wherein each measurement is a one-qubit measurement or a two-qubit measurement.

18. The method of claim 17 , wherein, for each measurement-based physical qubit included in the logical qubit encoding surface, performing the surface code error correction includes performing at most five two-qubit measurements at that physical qubit.

19. The method of claim 18 , wherein, for each measurement-based physical qubit included in the logical qubit encoding surface, performing the surface code error correction includes performing at most four two-qubit measurements at that physical qubit.