Microwave readout for flux-biased qubits

1. A method for determining if a quantum system including a superconducting qubit occupies a first state |0 or a second state |1 , the method comprising:

applying an input pulse to the superconducting qubit;

applying a signal having a frequency through a transmission line having an output and coupled to the superconducting qubit; and

measuring a resonance frequency from the superconducting qubit at the output port,

wherein the resonance frequency can be one of two distinct values, a distinct first value corresponding to a first quantum well, and a second distinct value corresponding to a second quantum well,

wherein if the resonant frequency is equal to the first value, then the qubit occupies the state |0 prior to applying the input pulse and the state |0 remained in the first quantum well after applying the input pulse, and if the resonant frequency is equal to the second value, then the qubit occupies the state |1 prior to applying the input pulse and the state |1 tunneled to the second quantum well subsequent to applying the input pulse.

2. The method as in claim 1 , wherein applying an input pulse to the superconducting qubit is performed by applying a first flux-biasing pulse to the superconducting qubit through an external circuit.

3. The method as in claim 1 , wherein the superconducting qubit comprises a Josephson junction coupled in parallel with a capacitor and a superconducting loop.

4. The method as in claim 3 , wherein the Josephson junction has an effective critical current ranging from about 0.5 to about 3 microamperes.

5. The method as in claim 4 , wherein the capacitor is in the range of about 0.2 to about 4 picofarads.

6. The method as in claim 4 , wherein the superconducting loop comprises a loop inductance being in the range of about 100 picohenrys to about 2 nanohenrys.

7. The method as in claim 4 , wherein the superconducting qubit has differing resonant frequencies ranging from about 1 to about 50 giga-hertz.

8. The method as in claim 1 , wherein the superconducting qubit is capacitively or inductively coupled to the transmission line.

9. The method as in claim 1 , wherein the superconducting qubit is capacitively coupled to the transmission line with a coupling capacitance ranging from about 0.1 to about 10 femtofarads.

10. The method as in claim 1 , wherein the superconducting qubit is inductively coupled to the transmission line with a mutual inductance ranging from about 0.1 to about 10 picohenrys.

11. The method as in claim 1 , wherein the superconducting qubit is a charge qubit, a hybrid qubit, a phase qubit, or a flux qubit having characteristics of two distinct, separate, and stable states of difference resonance frequencies each corresponding to the occupation of the first state or the second state prior to measurement.

12. The method as in claim 1 , wherein the superconducting qubit is directly coupled to the transmission line.

13. The method as claimed in claim 1 wherein the resonance frequency of the quantum system is measured via at least one of an output power or phase at an output port of the transmission line, wherein the measured output power or phase is indicative of whether the superconducting qubit is occupying the first state |0 or the second state |1 .

14. A method for determining if a quantum system including a superconducting qubit occupies a first state |0 or a second state |1 , the method comprising:

applying a flux biasing pulse to the superconducting qubit; and

measuring a resonance frequency from the superconducting qubit;

wherein the resonance frequency can be one of two distinct values, a first value corresponding to a first quantum well, a second value corresponding to a second quantum well,

wherein if the resonant frequency is equal to the first value, then the qubit occupies the state |0 prior to applying the flux biasing pulse and the state |0 remained in the first quantum well after applying the flux biasing, and if the resonant frequency is equal to the second value, then the qubit occupies the state |1 prior to applying the flux biasing pulse and the state |1 tunneled to the second quantum well subsequent to applying the flux biasing pulse.

15. A method for determining if a quantum system including a superconducting qubit occupies a first state |0 or a second state |1 , the method comprising:

applying a flux biasing pulse to the superconducting qubit;

applying a signal having a frequency through a transmission line having an output port and coupled to the superconducting qubit; and

measuring at least one of an output power or phase at the output port of the transmission line, wherein the measured output power or phase is indicative of whether the superconducting qubit is occupying the first state |0 or the second state |1 , the measured output power or phase corresponding to a resonance frequency from the superconducting qubit;

wherein the resonance frequency can be one of two distinct values, a first value corresponding to a first quantum well, a second value corresponding to a second quantum well,

wherein if the resonant frequency is equal to the first value, then the qubit occupies the state |0 prior to applying the flux biasing pulse and the state |0 remained in the first quantum well after applying the flux biasing, and if the resonant frequency is equal to the second value, then the qubit occupies the state |1 prior to applying the flux biasing pulse and the state |1 tunneled to the second quantum well subsequent to applying the flux biasing pulse.

16. The method as in claim 1 , wherein applying an input pulse to the superconducting qubit is performed by applying a first current-biasing pulse to the superconducting qubit through an external circuit.