Spin-orbit qubit using quantum dots
Methods and apparatus of quantum information processing using quantum dots are provided. Electrons from a 2DEG are confined to the quantum dots and subjected to a magnetic field having a component directed parallel to the interface. Due to interfacial asymmetries, there is created an effective magnetic field that perturbs the energies of the spin states via an interfacial spin-orbit (SO) interaction. This SO interaction is utilized to controllably produce rotations of the electronic spin state, such as X-rotations of the electronic spin state in a double quantum dot (DQD) singlet-triplet (ST) qubit. The desired state rotations are controlled solely by the use of electrical pulses.
1. A method of quantum information processing using a lateral double quantum dot (DQD) disposed at a substrate surface and having a first quantum dot (QD 1 ) tunnel-coupled to a second quantum dot (QD 2 ), comprising:
populating QD 1 with two confined electrons;
transferring one confined electron to QD 2 to create a (1, 1) charge state;
performing at least two state rotations on the confined electrons while the DQD is in the (1, 1) charge state; and
reading out a final quantum state of the DQD,
wherein:
the at least two state rotations are performed while exposing the DQD to an externally sourced magnetic field having a component directed parallel to the substrate surface;
the performing of each of the at least two state rotations consists of applying a voltage pulse sequence to a planar gate electrode or combination of planar gate electrodes that is electrostatically coupled to the confined electrons so as to vary a relative tuning between QD 1 and QD 2 ;
at least a first one of the voltage pulse sequences comprises maintaining, for a first specified duration, a first relative tuning between QD 1 and QD 2 ; and
at least a second one of the voltage pulse sequences comprises maintaining, for a second specified duration, a second relative tuning between QD 1 and QD 2 that is different from the first relative tuning.
2. The method of claim 1 , wherein QD 1 and QD 2 are laterally disposed relative to each other.
3. The method of claim 1 , wherein the populating, transferring, state-rotation-performing, and readout steps are cyclically repeated multiple times.
4. The method of claim 1 , further comprising forming QD 1 and QD 2 by applying voltages to planar gate electrodes that overlie the substrate surface.
5. The method of claim 1 , wherein the substrate surface is a surface of a silicon body, and wherein the surface of the silicon body is directly overlain by a layer of silicon oxide.
6. The method of claim 1 , wherein the state-rotating voltage-pulse sequences are applied to a single layer of polysilicon planar gate electrodes that overlie the layer of silicon oxide.
7. The method of claim 1 , wherein the at least two state rotations comprise:
at least one state rotation that, at least in part, is a rotation between singlet and triplet states of the DQD; and
at least one state rotation that, at least in part, is a rotation between |↑↓ and |↓↑ states of the DQD.
8. A method of quantum information processing using a single-electron spin qubit embodied in a quantum dot (QD) disposed at a silicon substrate surface overlain by a layer of silicon oxide, comprising:
populating the QD with a confined electron having two spin states relative to a quantization axis;
performing at least one state rotation on the confined electron; and
reading out a final quantum state of the QD,
wherein:
the at least one state rotation is performed while exposing the QD to an externally sourced magnetic field having a component directed parallel to the substrate surface;
the QD has a tuning state that moves up and down in energy in response to a voltage applied to a controlling gate electrode arrangement;
the performing of the at least one state rotation consists of applying a voltage pulse sequence to the controlling gate electrode arrangement; and
the voltage pulse sequence is effective to invoke an effective magnetic field perpendicular to the quantization axis of the spin state of the QD electron and to induce spin state rotations.