CN117474114A - Quantum bit based on topological insulator, quantum computing device and single-double-electron quantum gate operation method - Google Patents
Quantum bit based on topological insulator, quantum computing device and single-double-electron quantum gate operation method Download PDFInfo
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Abstract
The invention discloses a quantum bit based on a topological insulator, a quantum computing device and a single-double electron quantum gate operation method, wherein the quantum bit is manufactured by adopting the topological insulator, and the quantum bit of the topological insulator is bound in a quantum dot by a periodically oscillating or high-strength electric field aiming at a quantum dot sequence manufactured by the topological insulator; controlling the movement of the quantum bit in the quantum dot by an electric field pulse signal to realize the regulation and control of the single quantum bit; the double-quantum bit logic gate and quantum entanglement are realized by coulomb force and applying a proper electric field to two adjacent quantum bits; reading of the qubit position information is achieved by deriving electrons from the quantum dots. The quantum bit based on the topological insulator material provided by the invention utilizes the unique anti-noise property of the topological insulator material, and can effectively reduce the interference of impurities and noise on the quantum bit, thereby increasing the decoherence time of the quantum bit and improving the quantum computing performance.
Description
Technical Field
The invention relates to the field of quantum computing, in particular to a quantum bit based on a topological insulator, a quantum computing device and a single-double-electron quantum gate operation method.
Background
Quantum computing technology is being developed as a kindThe new computing technology has been paid more and more attention in recent years, and by utilizing the superposition and entanglement of quantum mechanics to perform computer operation, the quantum computer will greatly accelerate the operation efficiency of the computer, and solve some computing problems which cannot be solved by the current classical computer. As an information carrier, a classical bit has two states, 0 and 1, N bits can form a series of length N; however, one qubit can realize the superposition state of 0 and 1 through superposition, and when N is more than or equal to 2, the qubit can form 2 through quantum entanglement N The superposition state formed by the entanglement states brings huge operation space for the quantum computing process, and by using a proper quantum algorithm, the quantum computer solves the problem that all computing time of a classical computer cannot be solved. Quantum computers are now in a stage of improving hardware performance and exploring optimal platforms, and small-scale prototypes have emerged and can solve some specific computational problems. For existing quantum computer platforms, the short decoherence time is almost a problem that all platforms face in common. Due to the quantum characteristics of a quantum bit, the existence time can be different from a few nanoseconds to a few minutes, and a formed quantum computer needs to realize tens of thousands of operations within decoherence time to ensure the accuracy of a result. In recent years, with the continuous progress of micro-nano processing technology, the hardware quality of quantum computers is greatly improved and promoted. However, the implementation of quantum computers also faces many challenges, and it is still difficult to achieve the manufacturing requirements at the existing hardware condition level.
Compared with the traditional computer, the quantum computing device is a device for realizing quantum computing by operating the quantum bit, and the quantum computing device in the current research mainly comprises a semiconductor quantum computing device, a superconductor quantum computing device, a neutral atom quantum computing device, an ion trap quantum computing device and a photon quantum computing device. Among other things, semiconductor quantum computing devices have the potential for scaling due to their advantage of being able to be integrated onto small chips to form multi-bit arrays.
The traditional semiconductor qubit has two types of charge qubit and spin qubit, wherein the charge qubit has wide application in the field of quantum technology due to the characteristics of sensitivity to electric field perception and readability. The conventional charge quantum computing device uses an aluminum gallium arsenic semiconductor material, and common structures are a coulomb island, a source electrode, a drain electrode, a conductive channel connected with the source electrode and the drain electrode, and a gate electrode for controlling a certain carrier type in the channel. By adjusting the gate voltage, channel closure and communication can be achieved.
In charge quantum computing, the quantum state being manipulated is usually a single electron state, and due to charge noise in a background environment, electrons are very easy to lose their own quantum state, decoherence occurs, and quantum computing operability is lost. The electronic device made of AlGaAs material has certain noise, so that the decoherence time of the traditional charge quantum computing device is extremely short.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a quantum bit, a quantum computing device and a single-double-electron quantum gate operation method for a topological insulator, which concretely comprises the following technical scheme:
a qubit based on a topological insulator, the qubit comprising a single-electron transistor with a coulomb island, a source electrode, a drain electrode and two grid electrodes, wherein the coulomb island, the source electrode, the drain electrode and the grid electrodes of the single-electron transistor are integrally arranged on a silicon dioxide substrate formed on the surface of a silicon substrate, the quantum dot is used as the coulomb island of the single-electron transistor, the coulomb island is connected with the source electrode and the drain electrode through tunneling barriers, and the coulomb island is coupled with the two grid electrodes in a capacitive form; depositing an alumina protective layer on the coulomb island, the tunneling barrier, the source electrode, the drain electrode and the grid electrode;
the quantum dots are topological insulator quantum dots, and the thickness of the quantum dots is less than or equal to seven nanometers; the areas between the coulomb island and the source, drain and gate are thinned so that electrons are confined in the quantum dots and cannot escape;
the single-electron transistor is placed in an electric field along the thickness direction of the quantum dot, and the drain electrode output end of the single-electron transistor is connected with the electronic reading circuit.
Further, the regions between the coulomb island and the source, drain and gate are thinned by N2 plasma etching by three to five nanometers.
A quantum computing device of quantum bit based on topological insulator, comprising a quantum dot array formed by at least two quantum dots, wherein the distance between any two quantum dots is not less than twenty nanometers along the thickness direction of the quantum dots; the distance between any two quantum dots is not more than twenty nanometers along the direction perpendicular to the thickness of the quantum dots, and at least one conducting grid for coupling the two quantum dots is arranged between two adjacent quantum dots in the quantum dot array along the direction.
A method of operating a topology insulator based single electron quantum gate, the method being implemented based on the above-described topology insulator based quantum bit quantum computing device, the method comprising:
step one: applying a periodically oscillating electric field along the thickness direction of the quantum dot on the constructed topological insulator quantum dot, wherein the quantum dot is used as a coulomb island of a single-electron transistor, and discrete energy levels of the coulomb island are coupled in the periodically oscillating electric field to generate a Laratio oscillation, so that electrons are calibrated to a standard initial quantum state;
step two: applying an electric field with constant intensity along the thickness direction of the quantum dots to enable the quantum bits to move on the Bulobz sphere; generating a square wave sequence by changing the direction of an electric field, wherein the electric field strength determines the axial direction of the movement of the quantum bit on the Bulobz sphere; the electric fields in opposite directions will generate a pair of mutually perpendicular motion axes X 'and Z' which are obtained by rotating the coordinate axes X, Z of the Buluoch sphere by an angle A DEG together; under the action of the electric field square wave sequence, the quantum bit rotates around the motion axes X 'and Z' to generate angular displacement; the action duration of the square wave sequence determines the rotating angle of the quantum bit on the Buloch sphere;
the action duration of the electric field square wave sequence is controlled through the relation between the rotation angle of the quantum bit on the Buroche sphere around a certain coordinate axis and the rotation angles around X 'and Z' coordinate axes and the angular velocity of the quantum bit motion, so that the quantum bit reaches any preset position of the Buroche sphere.
Further, the quantum bit is moved for a complete period through an applied electric field square wave sequence with constant intensity and direction, so that the axial angle of the quantum bit on a certain coordinate axis and the angular speed of movement are obtained; wherein the angular velocities along the X 'and Z' axes of motion are the same.
Further, the relationship between the rotation angle of the qubit on the bloch sphere around a certain coordinate axis and the rotation angles around the X 'and Z' coordinate axes is:
when the quantum bit is to be controlled, the motion angle alpha of the quantum bit along a certain coordinate axis of the Buluoch sphere is equivalent to the rotation angle beta of the quantum bit around the motion axis Z' firstly 1 And then rotate around the motion axis X' by an angle beta 2 And then rotate around the motion axis Z' by an angle beta 3 。
Further, when the quantum bit is to be controlled to move along the X-axis of the Bulhz sphere by an angle alpha, beta is required 1 、β 2 、β 3 The method comprises the following steps:
β 1 ＝β 3
sinβ 2 ＝(sinβ 1 )(1+cosβ 2 )；
beta required when manipulating the angle alpha of movement of the qubit along the Y-axis of the Bulobz sphere 1 、β 2 、β 3 The method comprises the following steps:
cosβ 2 ＝cosα
sinβ 2 ＝sinα；
beta required for manipulating the angle alpha of movement of a qubit along the Z axis of a bloch sphere 1 、β 2 、β 3 The method comprises the following steps:
β 1 ＝β 3
further, in the third step, the rotation angle a ° of the coordinate axis X to X' is positively correlated with the applied electric field intensity.
Further, the duration of action of the electric field square wave sequence is proportional to the magnitude of the angle by which the qubit rotates on the bloch sphere.
A method of operating a topology insulator based two-electron quantum gate, the method comprising:
step one: respectively applying periodic oscillating electric fields along the thickness direction of each quantum dot on the constructed adjacent topological insulator quantum dots, wherein the quantum dots are used as coulomb islands of single-electron transistors, and discrete energy levels of the coulomb islands are coupled in the periodic oscillating electric fields to generate ratio oscillation, so that electrons are calibrated to a standard initial quantum state;
step two: and respectively applying constant electric fields with the same strength and direction along the thickness direction of the quantum dots to the selected two adjacent quantum dots, so that adjacent quantum bits are coupled to generate quantum entanglement.
The beneficial effects of the invention are as follows:
1. the topological insulator quantum bit provided by the invention has the characteristics of resisting charge noise and impurity interference, and can improve the coherence time of the quantum bit, so that the quantum bit can be subjected to effective quantum computation with low error rate.
2. The topological insulator quantum computing device provided by the invention has the characteristic of high operation speed, and can be used for high-efficiency quantum computing.
3. The topological insulator quantum computing method provided by the invention has the characteristic of easy operation, and the global quantum computation can be performed by applying a simple square wave sequence electric field and a constant electric field.
Drawings
FIG. 1 is a schematic diagram of a topology insulator based qubit shown according to an exemplary embodiment; in the figure, 1 is a gate electrode, 2 is a quantum dot, 3 is a source electrode, 4 is a drain electrode, and 5 is a qubit.
FIG. 2 is a schematic diagram of a quantum computing device of topological insulator based qubits, as shown, according to an example embodiment; in the figure, 6 is a pass gate.
Fig. 3 is a schematic diagram illustrating a topology insulator-based single electron quantum gate operation method, according to an exemplary embodiment.
Fig. 4 is a schematic diagram illustrating a topology insulator-based two-electron quantum gate operation method according to an exemplary embodiment.
Fig. 5 is a flow chart illustrating a topology insulator based single electron quantum gate operation method according to an exemplary embodiment.
Fig. 6 is a flow chart illustrating a topology insulator based two electron quantum gate operation method according to an exemplary embodiment.
FIG. 7 is an example of motion along the Z axis on a single-qubit Bloch sphere and the corresponding square wave electric field sequence; the upper graph shows an example of movement of a single quantum bit on a bloch ball along a Z axis, and the lower graph shows corresponding square wave electric field sequence intensity and application time.
Detailed Description
The objects and effects of the present invention will become more apparent from the following detailed description of the preferred embodiments and the accompanying drawings, it being understood that the specific embodiments described herein are merely illustrative of the invention and not limiting thereof.
Referring to fig. 1, a quantum bit 5 based on a topological insulator of the present embodiment includes a single-electron transistor having two gates 1, quantum dots 2, a source 3, and a drain 4, wherein the two gates 1 are integrated on a silicon dioxide substrate formed on a silicon substrate surface, the quantum dots 2 are used as coulomb islands of the single-electron transistor, the coulomb islands are connected with the source 3 and the drain 4 by tunneling barriers, and the coulomb islands are capacitively coupled with the two gates 1; coulomb island, tunnel barrier, source 3, drain 4, and a protective layer of alumina is deposited on the gate 1.
The quantum dots 2 are topological insulator quantum dots, and the thickness is less than or equal to seven nanometers; the regions between the coulomb island and the source, drain and gate are thinned so that electrons are confined in the quantum dots and do not escape 2 Plasma etching thins three to five nanometers so that electrons are localized in the quantum dot region. The single-electron transistor is placed in an electric field along the thickness direction of the quantum dot, and the drain electrode output end of the single-electron transistor is connected with the electronic reading circuit.
As shown in fig. 2, the quantum bit-based quantum computing device of the present embodiment includes a quantum dot array formed of at least two quantum dots, and a distance between any two quantum dots is not less than twenty nanometers in a thickness direction of the quantum dots; along the direction perpendicular to the thickness of the quantum dots, the distance between any two quantum dots is not more than twenty nanometers, and in the quantum dot array in the direction, at least one conducting grid 6 for coupling the two quantum dots is arranged between two adjacent quantum dots, so that quantum entanglement can be generated between any two adjacent quantum dots in fig. 2.
The principle of the invention for improving quantum computing performance can be briefly summarized as follows: the surface electronic state of the topological insulator with the anti-noise and anti-impurity characteristics is utilized for quantum computation, so that the decoherence time of the quantum bit is prolonged equivalently, and the quantum computation performance can be improved.
The following theoretical detailed analysis illustrates the computational principle of a quantum computation method based on topological insulator qubits.
1. Quantum computation principle based on topological insulator qubits
Without loss of generality, consider N quantum dots built on a topological insulator film, forming a topological insulator qubit array system. For each row or column of the topological insulator qubit array system, 2 gates applying a square wave sequence and 2 pass gates coupling adjacent quantum dots, 1 source and 1 drain are connected around each quantum dot for controlling the behavior of the qubit in the quantum dot.
First, the quantum computing principle of single quantum bit is explained:
the hamiltonian H of a single electron system can be expressed as:
k || ＝k x -ik y .
wherein C is 0 、C 1 、C 2 、M 0 、M 1 、M2、B 0 、A 0 To experimentally obtain the system constant, k x ,k y ,k z Is the crystal momentum (crystal momentum)um) in x, y and z directions, E is an externally applied electric field, and can be divided into a periodic oscillating electric field, a stable static electric field and a square wave electric field sequence according to practical conditions.
For a single quantum dot, the free electrons of the coulomb island can be exhausted by adjusting the voltages of the source electrode, the drain electrode and the grid electrode, then single electrons are injected, an electric field which periodically oscillates and has the frequency equal to the ratio frequency is firstly used for initializing one electron to the 0 state of the quantum bit on the grid electrode, then a square wave sequence is generated through the grid electrode to change the position of the electron on the Buloch sphere, and quantum calculation of the single quantum bit is carried out.
Specifically, as shown in fig. 3 and 5, the single-electron quantum gate operation method based on the topological insulator of the present embodiment is implemented by a quantum computing device based on quantum bits of the topological insulator, and the method includes:
step one: and applying a periodically oscillating electric field along the thickness direction of the quantum dot on the constructed topological insulator quantum dot, wherein the frequency of the oscillating electric field is the ratio oscillating frequency, the amplitude of the oscillating electric field is the difference value of two discrete energy levels, and the intensity of the oscillating electric field is one half of the difference value of the discrete energy levels. The quantum dots are used as coulomb islands of single-electron transistors, and discrete energy levels of the coulomb islands are coupled in a periodic oscillating electric field to generate a Laratio oscillation, so that electrons are calibrated to a standard initial quantum state;
step two: applying an electric field with constant intensity along the thickness direction of the quantum dots to enable the quantum bits to move on the Bulobz sphere; generating a square wave sequence by changing the direction of an electric field, wherein the electric field strength determines the axial direction of the movement of the quantum bit on the Bulobz sphere; the opposite electric fields will produce a pair of mutually perpendicular axes of motion X 'and Z' corresponding to the axis X, Z of the bloch sphere rotated together by an angle a. The rotation angle a ° is positively correlated with the applied electric field strength. A=135° in this example; under the action of the electric field square wave sequence, the quantum bit rotates around the motion axes X 'and Z' to generate angular displacement; the rotation angular velocity of the quantum bit is constant, and the action duration of the square wave sequence determines the rotation angle of the quantum bit on the Buroche sphere.
The action duration t of the square wave sequence of the control electric field is obtained through the relation between the angle alpha of the quantum bit rotating on the Bulobz sphere around a certain coordinate axis n and the rotation angles around X 'and Z' coordinate axes and the angular velocity w of the quantum bit motion 1 ＝β 1 /w,t 2 ＝β 2 /w,t 3 ＝β 3 W, i.e. the duration of action of the electric field square wave sequence (t 1 ,t 2 ,t 3 ) Angle of rotation (beta) with respect to the qubit on the bloch sphere 1 ,β 2 ,β 3 ) The size is proportional. Thereby the quantum bit reaches any preset position of the Buloch sphere, which can be expressed as follows:
R n (α)＝Z′(β 1 )X′(β 2 )Z′(β 3 )
wherein R is n (α) is the operation of a qubit moving along the n-axis by an angle α, Z' (β) 1 ) Representing the angle beta of rotation of the qubit about the axis of motion Z 1 Is operated by X' (beta) 2 ) Representing the angle of rotation beta of the qubit about the axis of motion X 2 Is operated by Z' (beta) 3 ) Representing the angle of rotation beta of the qubit along the motion axis Z 3 Is performed according to the operation of (a).
Therefore, in order to obtain the duration of action of the square wave sequence of the control electric field, the angular velocity w of the qubit motion must be obtained first. The quantum bit is enabled to move for a complete period from an initial state through an applied electric field square wave sequence with constant intensity and direction, so that the axial angle of the quantum bit in a certain coordinate axis and the angular speed of movement are obtained; wherein the angular velocities along the X 'and Z' axes of motion are the same, wherein the axial angle of the motion axis is determined by the vertical line of the initial state and the Z axis pinch angle of the position of the qubit on the bloch sphere during half period. In this example, the X 'axis is rotated 135 counterclockwise about the X axis and the Z' axis is rotated 135 counterclockwise about the Z axis.
The relationship between the angle of rotation of the qubit on the bloch sphere about a certain coordinate axis and the rotation angles about the X 'and Z' coordinate axes is:
when the quantum bit is to be controlled, the motion angle alpha of the quantum bit along a certain coordinate axis of the Bulobz sphere is equivalent to the control of the quantum bitMotion axis Z' rotation angle beta 1 And then rotate around the motion axis X' by an angle beta 2 And then rotate around the motion axis Z' by an angle beta 3 。
To manipulate the angle alpha of movement of the qubit along the X-axis of the Bulobz sphere, the required beta 1 、β 2 、β 3 The method comprises the following steps:
β 1 ＝β 3
sinβ 2 ＝(sinβ 1 )(1+cosβ 2 )；
beta required when manipulating the angle alpha of movement of the qubit along the Y-axis of the Bulobz sphere 1 、β 2 、β 3 The method comprises the following steps:
cosβ 2 ＝cosα
sinβ 2 ＝sinα；
beta required for manipulating the angle alpha of movement of a qubit along the Z axis of a bloch sphere 1 、β 2 、β 3 For example, fig. 5 is an example:
β 1 ＝β 3
the quantum computing principle of two qubit entangled states is set forth below.
The distance between two adjacent qubits 1,2 in the topological insulator qubit array is l x Coulomb forces of two adjacent electrons:wherein e 1 ，e 2 Is the electron charge of electrons. The separation thereof needs to be sufficiently recent to generate a sufficiently large coulomb force to couple the qubits in the two quantum dots.
The systematic hamiltonian of two qubits is:
wherein, E is 0 Is the kinetic energy of electrons, E i (i=1, 2) is the difference between the intrinsic energy levels of qubits 1 and 2 under static electric field, which is a parameter that can be adjusted in experiments, positively correlated with the electric field strength acting on the qubit. Delta i Is the difference between the intrinsic energy levels of qubits 1 and 2 in the absence of static electric fields. J (J) i (i=1, 2) is the interaction force between two qubits.
By applying a static electric field of the same strength to the pass gates on the individual quantum dots 1 and 2, two qubits can be entangled or disentangled over a sufficiently long period of time. By adjusting the intensity of the electric field acting on the quantum dots 1 and 2, the energy level distribution of the Hamiltonian amount of the whole system can be adjusted, and when the energy levels of the two quantum dots are coupled, the two quantum bits are entangled.
Specifically, as shown in fig. 4 and 6, the method for operating a dual electron quantum gate based on a topological insulator according to the present embodiment includes:
step one: respectively applying periodic oscillating electric fields along the thickness direction of each quantum dot on the constructed adjacent topological insulator quantum dots, wherein the quantum dots are used as coulomb islands of single-electron transistors, and discrete energy levels of the coulomb islands are coupled in the periodic oscillating electric fields to generate ratio oscillation, so that electrons are calibrated to a standard initial quantum state;
step two: referring to fig. 7, a constant electric field in the thickness direction of the quantum dots of the same intensity and direction is applied to selected adjacent two quantum dots, respectively, so that adjacent quantum bits are coupled to generate quantum entanglement.
In a two electron quantum gate operation, the potential energy generated by the gate should be greater than the difference between the two discrete energy levels.
Finally, the electronic quantum gate operation method of the present embodiment is verified through numerical simulation. In this example, numerical simulations of quantum computing operations were performed using a 6 nm topological insulator film, assuming that two qubits have the same ratio oscillation frequency. In the simulation, a voltage with the intensity of +/-8.75 mV is used on the grid electrode, so that the quantum bits can respectively move around an X 'axis and a Z' axis, wherein the X 'axis is (1, 45 degrees, 180 degrees), the Z' axis is (1, 135 degrees, 180 degrees), and the coordinate axes are standard spherical coordinates. The relationship between the movement and the electric field application time is shown in fig. 7. The staggered leapfrog method is used to make the temporal evolution of the single qubit motion state. The electric field square wave sequence is calculated in the mode, and finally the quantum bit can reach any position of the Bulobz sphere.
For entanglement of two quantum bits, two quantum dots with the thickness of 6 nanometers and the transverse distance of 2 nanometers are selected, the energy level distribution in the quantum dots is changed by using a static electric field to couple target quantum states, and the quantum states of the two quantum bits are subjected to time evolution by a staggered leapfrog method. Under the above parameter conditions, when the conducting gate applies an electric field with the same magnitude and direction to the two quantum dots, the two quantum bits can form a periodical exchange (SWAP) gate, quantum entanglement can occur to the two quantum bits during one half period, and disentanglement can be performed to the two quantum bits during one complete period.
It will be appreciated by persons skilled in the art that the foregoing description is a preferred embodiment of the invention, and is not intended to limit the invention, but rather to limit the invention to the specific embodiments described, and that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for elements thereof, for the purposes of those skilled in the art. Modifications, equivalents, and alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. A qubit based on a topological insulator, which is characterized in that the qubit comprises a single-electron transistor with a coulomb island, a source electrode, a drain electrode and two grid electrodes, wherein the coulomb island, the source electrode, the drain electrode and the grid electrodes of the single-electron transistor are integrally arranged on a silicon dioxide substrate formed on the surface of a silicon substrate, the quantum dot is used as the coulomb island of the single-electron transistor, the coulomb island is connected with the source electrode and the drain electrode through tunneling barriers, and the coulomb island is coupled with the two grid electrodes in a capacitive mode; depositing an alumina protective layer on the coulomb island, the tunneling barrier, the source electrode, the drain electrode and the grid electrode;
the quantum dots are topological insulator quantum dots, and the thickness of the quantum dots is less than or equal to seven nanometers; the areas between the coulomb island and the source, drain and gate are thinned so that electrons are confined in the quantum dots and cannot escape;
the single-electron transistor is placed in an electric field along the thickness direction of the quantum dot, and the drain electrode output end of the single-electron transistor is connected with the electronic reading circuit.
2. The topological insulator based qubit according to claim 1, wherein the region between the coulomb island and the source, drain and gate is thinned by N2 plasma etching by three to five nanometers.
3. The quantum computing device of the quantum bit based on the topological insulator is characterized by comprising a quantum dot array formed by at least two quantum dots, wherein the distance between any two quantum dots is not less than twenty nanometers along the thickness direction of the quantum dots; the distance between any two quantum dots is not more than twenty nanometers along the direction perpendicular to the thickness of the quantum dots, and at least one conducting grid for coupling the two quantum dots is arranged between two adjacent quantum dots in the quantum dot array along the direction.
4. A method of topology insulator based single electron quantum gate operation, the method being implemented based on the quantum computing device of claim 3 based on quantum bits of topology insulators, the method comprising:
step one: applying a periodically oscillating electric field along the thickness direction of the quantum dot on the constructed topological insulator quantum dot, wherein the quantum dot is used as a coulomb island of a single-electron transistor, and discrete energy levels of the coulomb island are coupled in the periodically oscillating electric field to generate a Laratio oscillation, so that electrons are calibrated to a standard initial quantum state;
step two: applying an electric field with constant intensity along the thickness direction of the quantum dots to enable the quantum bits to move on the Bulobz sphere; generating a square wave sequence by changing the direction of an electric field, wherein the electric field strength determines the axial direction of the movement of the quantum bit on the Bulobz sphere; the electric fields in opposite directions will generate a pair of mutually perpendicular motion axes X 'and Z' which are obtained by rotating the coordinate axes X, Z of the Buluoch sphere by an angle A DEG together; under the action of the electric field square wave sequence, the quantum bit rotates around the motion axes X 'and Z' to generate angular displacement; the action duration of the square wave sequence determines the rotating angle of the quantum bit on the Buloch sphere;
the action duration of the electric field square wave sequence is controlled through the relation between the rotation angle of the quantum bit on the Buroche sphere around a certain coordinate axis and the rotation angles around X 'and Z' coordinate axes and the angular velocity of the quantum bit motion, so that the quantum bit reaches any preset position of the Buroche sphere.
5. The method for operating a topological insulator-based single-electron quantum gate according to claim 4, wherein the axial angle of the quantum bit in a certain coordinate axis and the angular velocity of the movement are obtained by moving the quantum bit for a complete period through an applied electric field square wave sequence with constant intensity and direction; wherein the angular velocities along the X 'and Z' axes of motion are the same.
6. The topology insulator-based single electron quantum gate operation method of claim 4, wherein the angle of rotation of the qubit on the bloch sphere about a certain coordinate axis is related to the rotation angle about the X 'and Z' coordinate axes by:
when the quantum bit is to be controlled, the motion angle alpha of the quantum bit along a certain coordinate axis of the Buluoch sphere is equivalent to the rotation angle beta of the quantum bit around the motion axis Z' firstly 1 And then rotate around the motion axis X' by an angle beta 2 And then rotate around the motion axis Z' by an angle beta 3 。
7. The method of topology insulator based single electron quantum gate operation of claim 6, wherein,
to manipulate the angle alpha of movement of the qubit along the X-axis of the Bulobz sphere, the required beta 1 、β 2 、β 3 The method comprises the following steps:
β 1 ＝β 3
sinβ 2 ＝(sinβ 1 )(1+cosβ 2 )；
beta required when manipulating the angle alpha of movement of the qubit along the Y-axis of the Bulobz sphere 1 、β 2 、β 3 The method comprises the following steps:
cosβ 2 ＝cosα
sinβ 2 ＝sinα；
beta required for manipulating the angle alpha of movement of a qubit along the Z axis of a bloch sphere 1 、β 2 、β 3 The method comprises the following steps:
β 1 ＝β 3
8. the method of claim 4, wherein in the third step, the rotation angle a ° of the coordinate axis X to X' is positively correlated with the applied electric field intensity.
9. The method of topological insulator based single electron quantum gate operation of claim 4, wherein the duration of the action of the electric field square wave sequence is proportional to the angular magnitude of the rotation of the qubit on the bloch sphere.
10. A method of operating a topology insulator-based two-electron quantum gate, the method comprising:
step one: respectively applying periodic oscillating electric fields along the thickness direction of each quantum dot on the constructed adjacent topological insulator quantum dots, wherein the quantum dots are used as coulomb islands of single-electron transistors, and discrete energy levels of the coulomb islands are coupled in the periodic oscillating electric fields to generate ratio oscillation, so that electrons are calibrated to a standard initial quantum state;
step two: and respectively applying constant electric fields with the same strength and direction along the thickness direction of the quantum dots to the selected two adjacent quantum dots, so that adjacent quantum bits are coupled to generate quantum entanglement.
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