Methods for qubit readout

1. A method for readout of a singlet-triplet qubit in a donor based quantum processing element, the method comprising the steps of:

initialising the singlet-triplet qubit in a ground state |G ;

performing a shelving readout;

using a final measured charge configuration of the singlet-triplet qubit to determine information about a current Zeeman energy difference, wherein the determined information about the current Zeeman energy difference is the sign of the Zeeman energy difference; and

using the information about the current Zeeman energy difference to adjust mapping of the shelving readout.

2. The method of claim 1 , wherein the donor based quantum processing element comprises:

a semiconductor substrate,

a dielectric material forming an interface with the semiconductor substrate,

one or more gate electrodes, and

a double quantum dot system comprising two dopant dots embedded in the semiconductor substrate, each dopant dot comprising one or more dopant atoms and two or more electrons or holes confined in the double dot system.

3. The method of claim 2 , wherein the spin of the two or more electrons or holes are entangled to form a singlet state and three triplet states.

4. The method of claim 3 , wherein a singlet-triplet qubit is encoded in the |S singlet state and a |T 0 triplet state.

5. The method of claim 2 , wherein performing the shelving readout comprises: mapping the spin state |↑↓ and |↑↓ of two or the two or more electrons or holes to charge configurations (0,2) and (1,1), respectively.

6. The method of claim 2 , wherein performing the shelving readout comprises:

starting the singlet-triplet qubit in a (1,1) charge configuration;

moving the singlet-triplet qubit from the (1, 1) configuration to a (1,2) charge configuration by applying potentials to the one or more gate electrodes;

moving the singlet-triplet qubit back to the (1,1) charge configuration by applying potentials to the one or more gate electrodes; and

adiabatically changing a detuning to move the singlet-triplet qubit to a (0,2) charge configuration.

7. The method of claim 2 , wherein the two or more electrons or holes are loaded on to the dopant dots via at least one gate electrode of the one or more gate electrodes.

8. The method of claim 2 , wherein the dopant atoms are phosphorus atoms.

9. The method of claim 2 , wherein the semiconductor substrate is silicon and the dielectric is silicon dioxide.

10. The method of claim 2 , wherein the semiconductor substrate is isotopically purified silicon-28 and the dielectric is silicon dioxide.

11. The method of claim 2 , wherein the gate of the one or more gate electrodes are manufactured within the semiconductor substrate to control the donor dots.

12. The method of claim 1 , further comprising performing a qubit operation.

13. The method of claim 12 , further comprising:

performing a second shelving readout; and

applying the information about the current Zeeman energy difference to adjust mapping of the second shelving readout.