Flopping-mode electric dipole spin resonance

1. A nanoscale semiconductor quantum device, comprising:

at least one magnetic field source configured to supply an inhomogeneous magnetic field;

at least one semiconducting layer; and

one or more conducting layers comprising a source and a drain and configured to:

define at least two quantum states in the at least one semiconducting layer; and

cause, based on an oscillating electrical signal supplied by the one or more conducting layers, an electron to move back and forth between the at least two quantum states in the presence of the inhomogeneous magnetic field, wherein the movement of the electron between the at least two quantum states generates an oscillating magnetic field to drive a quantum transition between a spin-up state and spin-down state of the electron thereby implementing a qubit gate on a spin state of the electron,

wherein the at least one magnetic field source is located in a first layer of a material stack of the device and the one or more conducting layers are located in a second layer, of the material stack, different from the first layer.

2. The device of claim 1 , wherein the at least two quantum states comprise a gate defined silicon double quantum dot, and wherein the oscillating electrical signal has one or more of a microwave frequency, a radio frequency, or a frequency in a range of about 3 kHz to about 300 GHz.

3. The device of claim 1 , wherein the at least one magnetic field source comprises at least one micro-magnet that is electrically isolated from the at least one semiconducting layer and the one or more conducting layers.

4. The device of claim 1 , wherein the one or more conducting layers comprise a first conducting layer comprising one or more barrier gates configured to define the at least two quantum states, and wherein the one or more conducting layers comprise a second conducting layer comprising one or more plunger gates configured to cause the electron to move between the at least two quantum states.

5. The device of claim 1 , wherein the one or more conducting layers comprise a first plunger gate configured to apply the oscillating electrical signal to move the electron between the at least two quantum states and a second plunger gate configured to electrically couple a charge of the electron to an electric field of a cavity for spin-state readout.

6. The device of claim 1 , wherein the one or more conducting layers are configured to cause the electron to move back and forth based on simultaneously applying a microwave frequency burst and a square voltage pulse to a plunger gate of the one or more conducting layers thereby driving a coherent spin rotation within a specific rotation angle defined by a value of detuning set by the square voltage pulse.

7. The device of claim 1 , wherein the at least two quantum states are biased to within a few micro-electron volts of zero detuning such that the at least two quantum states are on resonance.

8. The device of claim 1 , wherein the inhomogeneous magnetic field extends into a portion of the at least one semiconducting layer in which the electron moves back and forth between the at least two quantum states.

9. The device of claim 1 , wherein the at least one magnetic field source causes a magnetic field gradient sufficiently large to cause a change in the magnetic field, in a range of about 1 mT to about 1000 mT, as the electron moves between the at least two quantum states.

10. A system for operating a nanoscale semiconductor quantum device, the system comprising:

a signal generator configured to generate an oscillating electrical signal; and

a structure disposed in a cavity, the structure comprising:

at least one magnetic field source configured to supply an inhomogeneous magnetic field;

at least one semiconducting layer; and

one or more conducting layers comprising a source and a drain and configured to:

define at least two quantum states in the at least one semiconducting layer; and

cause, based on the oscillating electrical signal generated by the signal generator and supplied by the one or more conducting layers, an electron to move back and forth between the at least two quantum states in the presence of the inhomogeneous magnetic field, wherein the movement of the electron between the at least two quantum states generates an oscillating magnetic field to drive a quantum transition between a spin-up state and spin-down state of the electron thereby implementing a qubit gate on a spin state of the electron,

wherein the at least one magnetic field source is located in a first layer of a material stack of the structure and the one or more conducting layers are located in a second layer, of the material stack, different from the first layer.

11. The system of claim 10 , wherein the at least two quantum states comprise a gate defined silicon double quantum dot, and wherein the oscillating electrical signal has one or more of a microwave frequency, a radio frequency, or a frequency in a range of about 3 kHz to about 300 GHz.

12. The system of claim 10 , wherein the at least one magnetic field source comprises at least one micro-magnet that is electrically isolated from the at least one semiconducting layer and the one or more conducting layers.

13. The system of claim 10 , wherein the one or more conducting layers comprise a first conducting layer comprising one or more barrier gates configured to define the at least two quantum states, and wherein the one or more conducting layers comprise a second conducting layer comprising one or more plunger gates configured to cause the electron to move between the at least two quantum states.

14. The system of claim 10 , wherein the one or more conducting layers comprise a first plunger gate configured to apply the oscillating electrical signal and a second plunger gate configured to electrically couple a charge of the electron to an electric field of the cavity.

15. The system of claim 10 , wherein the one or more conducting layers are configured to cause the electron to move back and forth based on simultaneously applying a microwave frequency burst and a square voltage pulse, generated by the signal generator, to a plunger gate of the one or more conducting layers thereby driving a coherent spin rotation within a specific rotation angle defined by a value of detuning set by the square voltage pulse.