Model simulation method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a model simulation method and device, electronic equipment and a storage medium. According to the scheme, the method comprises the following steps: constructing a semiconductor grid-controlled quantum dot model as a to-be-simulated model; according to the voltage on the first pumping electrode and the voltage on the second pumping electrode, lever arm coefficients corresponding to the first pumping electrode and the second pumping electrode, the target relation between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the coulomb interaction coefficient between the first quantum dot and the second quantum dot are obtained; determining Hamiltonian of the to-be-simulated model based on the lever arm coefficient, the target relationship and the coulomb interaction coefficient; and simulating the to-be-simulated model based on the Hamiltonian. Through the technical scheme provided by the embodiment of the invention, simulation of the semiconductor grid-controlled quantum dot model can be realized.

Description

Technical Field

[0001] This application relates to the field of quantum computing technology, and in particular to a model simulation method, apparatus, electronic device and storage medium. Background Technology

[0002] Semiconductor gated quantum dots are micro-nano devices with three-dimensional confined space. They have many excellent properties such as scalability, integrability, compatibility with modern semiconductor processes, ease of integration with classical measurement and control circuits, and the potential to overcome the limitations of extremely low temperature operating environments. They are considered one of the systems that are expected to realize universal quantum computing. Summary of the Invention

[0003] The purpose of this application is to provide a model simulation method, apparatus, electronic device, and storage medium to simulate semiconductor gate-controlled quantum dot models. The specific technical solution is as follows:

[0004] This application provides a model simulation method, the method comprising:

[0005] A semiconductor gated quantum dot model is constructed as a simulation model. The simulation model includes a first pump electrode, a second pump electrode, and a barrier electrode. The barrier electrode is located between the first pump electrode and the second pump electrode. A first quantum dot exists under the first pump electrode, and a second quantum dot exists under the second pump electrode.

[0006] Based on the voltages on the first pump electrode and the second pump electrode, the lever arm coefficients corresponding to the first pump electrode and the second pump electrode, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the Coulomb interaction coefficient between the first quantum dot and the second quantum dot are obtained respectively.

[0007] Based on the lever arm coefficient, the target relationship, and the Coulomb interaction coefficient, the Hamiltonian of the model to be simulated is determined;

[0008] The simulation of the model to be simulated is performed based on the Hamiltonian.

[0009] This application embodiment also provides a model simulation device, the device comprising:

[0010] A construction module is used to construct a semiconductor gated quantum dot model as a simulation model. The simulation model includes a first pump electrode, a second pump electrode, and a barrier electrode. The barrier electrode is located between the first pump electrode and the second pump electrode. A first quantum dot exists under the first pump electrode, and a second quantum dot exists under the second pump electrode.

[0011] The acquisition module is used to acquire, based on the voltages on the first pump electrode and the second pump electrode, the lever arm coefficients corresponding to the first pump electrode and the second pump electrode, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the Coulomb interaction coefficient between the first quantum dot and the second quantum dot, respectively.

[0012] The determination module is used to determine the Hamiltonian of the model to be simulated based on the lever arm coefficient, the target relationship, and the Coulomb interaction coefficient.

[0013] The simulation module is used to simulate the model to be simulated based on the Hamiltonian.

[0014] This application also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0015] Memory, used to store computer programs;

[0016] When the processor executes the program stored in the memory, it implements any of the steps of the model simulation method described above.

[0017] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the model simulation method steps described above.

[0018] This application also provides a computer program product containing instructions that, when run on a computer, cause the computer to execute any of the model simulation methods described above.

[0019] Beneficial effects of the embodiments in this application:

[0020] The technical solution provided in this application, after constructing the simulation model, can obtain relevant parameters of the simulation model based on the voltages of the two pump electrodes on the simulation model, namely, the lever arm coefficients corresponding to the first and second pump electrodes, the target relationship between the tunneling coefficient between the first and second quantum dots and the voltage of the barrier electrode, and the Coulomb correlation coefficient between the first and second quantum dots. Based on the lever arm coefficients, the target relationship and the Coulomb interaction coefficient, the Hamiltonian of the simulation model is determined, and the simulation of the simulation model is performed based on the Hamiltonian, thereby realizing the simulation of the semiconductor gate-controlled quantum dot model.

[0021] Of course, implementing any product or method of this application does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the first flowchart of the model simulation method provided in the embodiments of this application;

[0024] Figure 2 A schematic diagram of a semiconductor gate-controlled quantum dot model provided in an embodiment of this application;

[0025] Figure 3 This is a second flowchart illustrating the model simulation method provided in the embodiments of this application;

[0026] Figure 4 A schematic diagram of the first method for determining the lever arm coefficient provided in an embodiment of this application;

[0027] Figure 5 A schematic diagram of a fitting curve between voltage change and energy level provided in an embodiment of this application;

[0028] Figure 6 A schematic diagram of a second method for determining the lever arm coefficient provided in an embodiment of this application;

[0029] Figure 7 A schematic flowchart of a target relationship determination method provided in an embodiment of this application;

[0030] Figure 8-a A schematic diagram illustrating the symmetrical distribution of the overall ground state wave function provided in this application embodiment;

[0031] Figure 8-b A schematic diagram of the antisymmetric distribution of the global excited-state wave function provided in an embodiment of this application;

[0032] Figure 8-c A schematic diagram of a third fitting curve provided in an embodiment of this application;

[0033] Figure 9 A schematic diagram of a process for determining the Coulomb interaction coefficient provided in an embodiment of this application;

[0034] Figure 10-a This is a first schematic diagram of the locality of the wave function provided in an embodiment of this application;

[0035] Figure 10-bThis is a second schematic diagram of the locality of the wave function provided in an embodiment of this application;

[0036] Figure 11 A schematic diagram of the model simulation device provided in the embodiments of this application;

[0037] Figure 12 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0038] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0039] The relevant terms in this application's embodiments are explained as follows:

[0040] Leverage factor (also known as energy conversion factor): It usually reflects the influence of the gate voltage on the quantum dot energy level. Specifically, it can be expressed as the degree of response of the quantum dot energy level to the gate voltage change of the semiconductor gate-controlled quantum dot.

[0041] Tunneling coefficient: used to describe the tunneling coupling strength between two quantum dots.

[0042] Coulomb interaction: used to describe the interaction between electrons in a quantum dot through an electromagnetic field.

[0043] In related technologies, the simulation of semiconductor gated quantum dots is achieved by varying the gate voltage over a wide range and scanning the area. After each voltage change, a new finite element simulation needs to be performed to obtain the experimental signals corresponding to different voltages. This process of simulating semiconductor gated quantum dots based on the experimental signals corresponding to all voltages results in a lengthy simulation process.

[0044] To address the problems in related technologies, embodiments of this application provide a model simulation method. For example... Figure 1 As shown, Figure 1 This is a schematic diagram of a first embodiment of the model simulation method provided in this application. This method can be applied to any electronic device equipped with semiconductor simulation software. Figure 1 The method shown includes the following steps.

[0045] Step S101: Construct a semiconductor gated quantum dot model as the simulation model. The simulation model includes a first pump electrode, a second pump electrode, and a barrier electrode. The barrier electrode is located between the first pump electrode and the second pump electrode. A first quantum dot exists under the first pump electrode, and a second quantum dot exists under the second pump electrode.

[0046] Step S102: Based on the voltages on the first pump electrode and the second pump electrode, obtain the lever arm coefficients corresponding to the first pump electrode and the second pump electrode, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the Coulomb interaction coefficient between the first quantum dot and the second quantum dot, respectively.

[0047] Step S103: Determine the Hamiltonian of the model to be simulated based on the lever arm coefficient, target relationship and Coulomb interaction coefficient.

[0048] Step S104: Simulate the model to be simulated based on the Hamiltonian.

[0049] In this embodiment, the semiconductor simulation software described above can support software for finite element simulation of semiconductor devices, such as Quantum-Technology Computer-Aided-Design (QTCAD). No specific limitation is made to the aforementioned semiconductor simulation software.

[0050] Through the above Figure 1 The method shown allows for the acquisition of relevant parameters of the simulation model after the model is constructed, based on the voltages of the two pump electrodes on the model. These parameters include the lever arm coefficients corresponding to the first and second pump electrodes, the target relationship between the tunneling coefficient between the first and second quantum dots and the voltage of the barrier electrode, and the Coulomb correlation coefficient between the first and second quantum dots. Based on the lever arm coefficients, the target relationship, and the Coulomb interaction coefficient, the Hamiltonian of the model is determined. The simulation of the model is then performed based on this Hamiltonian, thus realizing the simulation of the semiconductor gated quantum dot model.

[0051] Furthermore, compared to related technologies, the simulation process of the semiconductor gated quantum dot model is divided into device-level simulation and parameter-level simulation. During device-level simulation, various parameters corresponding to the semiconductor gated quantum dot model are obtained based on the voltages on the barrier electrodes corresponding to the first and second quantum dots. Therefore, during parameter-level simulation, the Hamiltonian is directly calculated based on the various parameters of the semiconductor gated quantum dot model determined during device-level simulation. Simulation is then performed based on the Hamiltonian, avoiding the need for continuous finite element simulation operations during the semiconductor gated quantum dot model simulation process, effectively shortening the simulation time.

[0052] The embodiments of this application will be described below through specific examples.

[0053] Regarding step S101 above, namely constructing a semiconductor gated quantum dot model as the simulation model, the simulation model includes a first pump electrode, a second pump electrode, and a barrier electrode. The barrier electrode is located between the first pump electrode and the second pump electrode. A first quantum dot exists under the first pump electrode, and a second quantum dot exists under the second pump electrode.

[0054] The aforementioned semiconductor gated quantum dot model can be constructed by the user using electronic devices within the aforementioned semiconductor simulation software. For example... Figure 2 As shown, Figure 2 This is a schematic diagram of a semiconductor gate-controlled quantum dot model provided in an embodiment of this application. Figure 2 The semiconductor gated quantum dot model shown includes: two confinement electrodes (i.e., confinement electrode 1 and confinement electrode 2), two lead electrodes (i.e., lead electrode 1 and lead electrode 2), two pump electrodes (i.e., pump electrode 1 and pump electrode 2), and three barrier electrodes (i.e. barrier electrode 1 to barrier electrode 3).

[0055] When the above-mentioned simulation model is the above-mentioned Figure 2 When using the semiconductor gate-controlled quantum dot model shown, the first pump electrode can be... Figure 2 In the quantum dot model shown, for any pump electrode, such as pump electrode 1, the second pump electrode mentioned above can be... Figure 2 In the quantum dot model shown, another pump electrode besides the first pump electrode is represented, such as pump electrode 2. For ease of understanding, the following explanation uses pump electrode 1 as the first pump electrode and pump electrode 2 as the second pump electrode, and does not constitute any limitation. Furthermore, the aforementioned barrier electrode can be... Figure 2 The barrier electrode 2 is located between the two pump electrodes in the quantum dot model shown.

[0056] In an optional embodiment, when constructing the aforementioned simulation model, the user can design the quantum dot model using semiconductor simulation software provided by the electronic device. This includes designing each electrode and its corresponding parameters within the semiconductor gated quantum dot model to obtain model parameters. The electronic device can then utilize the semiconductor simulation software to generate, based on these model parameters, parameters such as... Figure 2 The semiconductor gated quantum dot model shown is used to obtain the simulation model. Here, the model parameters corresponding to the semiconductor gated quantum dot model are not specifically limited.

[0057] Regarding step S102 above, that is, based on the voltage on the first pump electrode and the second pump electrode, the lever arm coefficient corresponding to the first pump electrode and the second pump electrode, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the Coulomb interaction coefficient between the first quantum dot and the second quantum dot are obtained respectively.

[0058] In this step, the electronic device can provide a way to adjust the voltages on the first and second pump electrodes, thereby changing the voltages on the first and second pump electrodes. With the voltages on the first and second pump electrodes continuously changing, the electronic device can obtain the lever arm coefficients corresponding to the first and second pump electrodes, the target relationship between the tunneling coefficient between the first and second quantum dots and the voltage of the barrier electrode, and the Coulomb interaction coefficient between the first and second quantum dots.

[0059] In an optional embodiment, the leverage coefficients corresponding to the first pump electrode and the second pump electrode can be expressed as: the leverage coefficient corresponding to the first pump electrode (denoted as the first leverage coefficient), and the leverage coefficient corresponding to the second pump electrode (denoted as the second leverage coefficient). Alternatively, it can be expressed as: the leverage coefficient composed of the first leverage coefficient of the first pump electrode and the second leverage coefficient of the second pump electrode. Furthermore, the leverage coefficients can be represented in matrix form.

[0060] In an optional embodiment, the above-mentioned target relationship can be expressed as: a fitting curve of the tunneling coefficient between the first quantum dot and the second quantum dot as a function of the voltage change on the barrier electrode, or it can be expressed as: a functional relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage change on the barrier electrode.

[0061] In an optional embodiment, the Coulomb interaction coefficients described above can be represented as a fourth-order tensor.

[0062] In the embodiments of this application, the representation of the above-mentioned lever arm coefficient, target relationship, and Coulomb interaction coefficient is not specifically limited. The methods for obtaining the above-mentioned lever arm coefficient, target relationship, and Coulomb interaction coefficient are described below and will not be repeated here.

[0063] For step S103 above, that is, determining the Hamiltonian of the model to be simulated based on the lever arm coefficient, the target relationship and the Coulomb interaction coefficient.

[0064] In one alternative embodiment, the electronic device may use the following formula to determine the Hamiltonian of the model to be simulated;

[0065]

[0066] Among them, HDQD Let α, d, and σ be the Hamiltonians of the model to be simulated, d be the three quantum numbers, α = L and R represent the left and right quantum points, σ ​​represent the spin, and S represent the energy level. 'a' is the lever arm coefficient, V L V is the voltage of the left quantum dot. R Let ΔV be the voltage across the right quantum dot, and ΔV be the voltage change. The voltage V was obtained from the finite element simulation. L and V R The energy levels at time, c and σ is the annihilation operator, t is the tunneling coefficient, V is the Coulomb interaction coefficient, β, γ, and δ are quantum dots, and σ is the annihilation operator. ′ It is spin.

[0067] As mentioned above Figure 2 As shown, the Hamiltonian H mentioned above DQD The left quantum dot can be the first quantum dot mentioned above, and the right quantum dot can be the second quantum dot mentioned above. The values ​​of β, γ, and δ can be referenced to the values ​​of α mentioned above, i.e., β = L, R, γ = L, R, δ = L, R. Here, no specific limitations are made on the left and right quantum dots. Furthermore, the Hamiltonian H mentioned above... DQD The three quantum numbers α, d, and σ in the two quantum dots can represent a quantum state in the two quantum dots.

[0068] For step S104 above, that is, to simulate the model to be simulated based on the Hamiltonian.

[0069] In this step, the electronic device can perform various simulations on the model to be simulated based on the aforementioned Hamiltonian, such as transport simulation and quantum bit simulation. The simulation process can be found in related technologies on simulations based on Hamiltonians, and will not be described in detail here.

[0070] In one optional embodiment, for the aforementioned semiconductor simulation software, users can develop relevant simulation tools for semiconductor gated quantum dot models based on the Hamiltonian. Users can trigger the relevant simulation tools through clicks or other operations to simulate the aforementioned model.

[0071] In an optional embodiment, according to the above... Figure 1 The method shown in this application also provides a model simulation method. For example... Figure 3 As shown, Figure 3 This is a schematic diagram of a second flowchart of the model simulation method provided in an embodiment of this application. Figure 3 The method shown refines the above step S102 into the following steps, namely steps S1021-S1023.

[0072] Step S1021: Determine the lever arm coefficient corresponding to the first pump electrode based on the first correspondence between the voltage change on the first pump electrode and the energy levels of the two quantum dots, and determine the lever arm coefficient corresponding to the second pump electrode based on the second correspondence between the voltage change on the second pump electrode and the energy levels of the two quantum dots.

[0073] For the first quantum dot, the electronic device can adjust the voltage on the first pump electrode to obtain the correspondence between the voltage change on the first pump electrode and the energy levels of the two quantum dots (denoted as the first correspondence). The electronic device can determine the lever arm coefficient (i.e., the first lever arm coefficient) corresponding to the first pump electrode based on the first correspondence.

[0074] For the second quantum dot, the electronic device can adjust the voltage on the second pump electrode to obtain the correspondence between the voltage change on the second pump electrode and the energy levels of the two quantum dots (denoted as the second correspondence). The electronic device can then determine the lever arm coefficient (i.e., the second lever arm coefficient) corresponding to the second pump electrode based on this second correspondence.

[0075] The adjustment of the voltage on the first pump electrode and the second pump electrode can be expressed as the adjustment of the corresponding input voltage on the first pump electrode and the second pump electrode in the semiconductor simulation software.

[0076] Step S1022: Based on the energy difference between the first quantum dot and the second quantum dot under the first voltage condition, determine the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode. The first voltage condition is the voltage corresponding to the first pump electrode and the second pump electrode when the overall ground state wave function of the first quantum dot and the second quantum dot is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed under different preset voltages.

[0077] In the embodiments of this application, for two identical quantum dots in a quantum dot system, by adjusting the voltage on the corresponding electrodes, the overall wave function of the coupled quantum dots can be made to have a symmetrical or antisymmetric distribution. A symmetrical distribution indicates that the electron distributions of the quantum dots are identical, while an antisymmetric distribution indicates that the electron distributions of the quantum dots are complementary.

[0078] The electronic device can apply different voltages (denoted as preset voltages) to the aforementioned barrier electrodes. For each preset voltage, the electronic device can continuously adjust the voltages on the first pump electrode and / or the second pump electrode until the overall ground state wavefunctions corresponding to the first and second quantum dots are symmetrically distributed or the overall excited state wavefunctions are antisymmetrically distributed. At this point, the electronic device can determine the tunneling coefficient between the first and second quantum dots based on the energy difference between them at the current moment. This tunneling coefficient is the tunneling coefficient corresponding to the preset voltage.

[0079] The adjustment of the voltage on the pump electrode can be an adjustment of the voltage on the first pump electrode, an adjustment of the voltage on the second pump electrode, or an adjustment of the voltage on both the first and second pump electrodes. No specific limitation is made here regarding the adjustment of the voltage on the pump electrode.

[0080] After determining the tunneling coefficient corresponding to each preset voltage, the electronic device can determine the target relationship between the tunneling coefficient of the first quantum dot and the second quantum dot and the voltage of the barrier electrode.

[0081] In this embodiment of the application, for each preset voltage, if the first quantum dot and the second quantum dot correspond to a symmetrical distribution of the overall ground state wave function or an antisymmetric distribution of the overall excited state wave function, then the voltage on the first pump electrode and the second pump electrode at the current moment is a voltage condition corresponding to the preset voltage in the first voltage condition.

[0082] Step S1023: Calculate the Coulomb interaction coefficient between the first quantum dot and the second quantum dot based on the global wave function of the first quantum dot or the second quantum dot under the second voltage condition. The second voltage condition is the voltage at which the global wave function of the first quantum dot and the second quantum dot is localized at the first quantum dot or localized at the second quantum dot.

[0083] In this embodiment, the coupling of two quantum dots can lead to the localization or delocalization of electrons between the quantum dots. Localization means that electrons are primarily distributed at one quantum dot, while delocalization means that the electron distribution extends to both quantum dots. The electronic device can adjust the voltage on the first or second pump electrode until the overall wavefunction corresponding to the first and second quantum dots is localized at the first quantum dot or at the second quantum dot.

[0084] When the global wave function corresponding to the first quantum dot and the second quantum dot is localized at the first quantum dot, or when the global wave function corresponding to the first quantum dot and the second quantum dot is localized at the second quantum dot, the electronic device can determine the Coulomb interaction coefficient between the first quantum dot and the second quantum dot by means of finite element simulation based on the global wave function corresponding to the first quantum dot and the second quantum dot.

[0085] In this embodiment of the application, if the overall wave function corresponding to the first quantum dot and the second quantum dot is localized at the first quantum dot or at the second quantum dot, then the voltage on the first pump electrode and the second pump electrode at the current moment is one of the voltage conditions in the second voltage condition.

[0086] In the above Figure 3In the illustrated embodiment, only the sequential execution of steps S1021, S1022, and S1023 is used as an example for explanation. In addition, steps S1021, S1022, and S1023 can also be executed simultaneously or sequentially. Here, the specific execution order of S1021, S1022, and S1023 is not limited.

[0087] Through the above steps S1021-S1023, the electronic device can obtain the lever arm coefficient, objective function and Coulomb interaction coefficient by adjusting the voltage on the first pump electrode and the second pump electrode. This enables the simulation and extraction of relevant parameters in the device simulation layer of the semiconductor gated quantum dot, providing the parameters required for Hamiltonian calculation in the subsequent parameter layer simulation of the semiconductor gated quantum dot, and ensuring the normal progress of the semiconductor gated quantum dot model simulation process.

[0088] In an optional embodiment, according to the above... Figure 3 The method shown in this application embodiment also provides a method for determining the lever arm coefficient. For example... Figure 4 As shown, Figure 4 This is a schematic flowchart of a first method for determining the lever arm coefficient provided in an embodiment of this application. The method includes the following steps.

[0089] Step S401: During the process of adjusting the voltage on the first pump electrode, obtain the preset number of energy levels corresponding to the two quantum dots under different voltage changes.

[0090] In this step, the electronic device can adjust the voltage applied to the first pump electrode. During the voltage adjustment process, the voltage change is different for each adjustment. Upon completion of each voltage adjustment, the electronic device can acquire a preset number of energy levels corresponding to the first and second quantum dots, thus obtaining the preset number of energy levels corresponding to the current voltage change, and consequently, the preset number of energy levels corresponding to each voltage change.

[0091] The above preset quantity can be set according to user needs, etc. Here, no specific limit is made on the above preset quantity.

[0092] In the embodiments of this application, the preset number of energy levels corresponding to the first and second quantum dots under each voltage change can be obtained by solving the Poisson equation and the Schrödinger equation using the finite element method.

[0093] In an optional embodiment, the above Poisson equation can be expressed as:

[0094]

[0095] in, Here, φ is the Laplace operator, ρ is the electric potential, ρ is the electron charge density, and ε is the dielectric constant.

[0096] In an optional embodiment, the above Schrödinger equation can be expressed as:

[0097]

[0098] in, Here, m is the reduced Planck constant, and m is the mass of the electron. Let Ψ(r) be the Laplace operator, Ψ(r) be the wave function representing the quantum state of the electron at position r, V(r) be the potential energy function representing the influence of the external potential field on the electron, and E be the energy eigenvalue.

[0099] Given that the adjusted voltage is known, the potential distribution φ(r) corresponding to the quantum dot (i.e., the first and second quantum dots mentioned above) can be obtained by solving the Poisson equation. Based on this potential distribution φ(r), a series of wave functions corresponding to the quantum dot (such as {Ψ0(r), Ψ1(r), ..., Ψ...)} can be obtained by solving the Schrödinger equation. n (r)}) and a series of energy eigenvalues ​​(e.g., {E0, E1, ..., E...}) n The number of wave functions and energy eigenvalues ​​is n+1. The solution process for the Poisson and Schrödinger equations can be found in relevant technical documentation and will not be detailed here.

[0100] The aforementioned preset number of energy levels can be any preset number of energy eigenvalues ​​from a series of energy eigenvalues. For ease of understanding, taking a preset number of 3 as an example, the aforementioned preset number of energy eigenvalues ​​can be {E0, E1, ..., E...} n Any three energy levels in the set {E0, E1, E2}. Here, the selection of the aforementioned preset number of energy levels is not specifically limited.

[0101] For ease of understanding, combined with Figure 5 Let's take an example to illustrate. Figure 5 This is a schematic diagram of a fitting curve between voltage change and energy level provided in an embodiment of this application.

[0102] The electronic device can acquire the six energy levels corresponding to the first and second quantum dots by adjusting the voltage on the first pump electrode, with voltage changes of 0, 1, 2, 3, 4, and 5 respectively. For example, when the voltage change is 2, Figure 5 The energy levels corresponding to the voltage change of 2 on curves 501-506 are the six energy levels obtained by the electronic device when the voltage change is 2.

[0103] Through the above step S401, a predetermined number of energy levels will exist for each voltage change. Furthermore, the predetermined number of energy levels selected for each voltage change will occupy the same position within a series of energy eigenvalues. For example, for each voltage change, {E0, E1, E2, E3, E4, E5} from a series of energy eigenvalues ​​will be selected as the predetermined number of energy levels.

[0104] Step S402: Based on a preset number of energy levels corresponding to the two quantum dots under each voltage change, generate a preset number of first fitting curves. Each first fitting curve is used to indicate the first correspondence between the voltage change on the first pump electrode and the energy levels of the two quantum dots.

[0105] In this step, since the preset number of energy levels selected for each voltage change are all in the same position in a series of energy eigenvalues, the electronic device can plot the corresponding fitting curve (denoted as the first fitting curve) for each energy level located at the same position in a series of energy eigenvalues, based on the energy level corresponding to each voltage change.

[0106] For ease of understanding, in conjunction with the above Figure 5 Let's take an example. Through step S401 above, the electronic device can obtain {E0, E1, E2, E3, E4, E5} from a series of energy eigenvalues ​​under different voltage changes as a preset number of energy levels. The electronic device can draw the corresponding energy levels for each voltage change, specifically for E0, E1, E2, E3, E4, and E5. Figure 5 The curves shown are 501-506.

[0107] Step S403: Obtain the slope corresponding to each first fitted curve to obtain the lever arm coefficient corresponding to the first pump electrode.

[0108] For ease of understanding, the above will still be used. Figure 5 Let's take an example to illustrate. Electronic devices can obtain data from bottom to top. Figure 5 The slopes of curves 506, 505, 504, 503, 502, and 501 are used to obtain the lever arm coefficient a1 corresponding to the first pump electrode, as shown below. In the first lever coefficient a1, each row of matrix elements corresponds to an energy level, such as -0.23027222 corresponding to the energy level of curve 506, as shown in E0 above.

[0109] Steps S401-S403 above are a refinement of the process of obtaining the lever arm coefficient corresponding to the first pump electrode in step S1021 above.

[0110] Through the above steps S401 to this step S403, the electronic device can represent the first correspondence between the voltage change on the first pump electrode and the energy levels of the two quantum dots by curve fitting, thereby determining the slope of each first fitting curve and obtaining the lever arm coefficient corresponding to the first pump electrode, so that the determined first lever arm coefficient can accurately represent the response degree of the energy levels of the two quantum dots to the voltage change on the first pump electrode in the simulation model.

[0111] In an optional embodiment, according to the above... Figure 3 The method shown in this application embodiment also provides a method for determining the lever arm coefficient. For example... Figure 6 As shown, Figure 6 This is a second flowchart illustrating the method for determining the lever arm coefficient provided in an embodiment of this application. The method includes the following steps.

[0112] Step S601: During the process of adjusting the voltage on the second pump electrode, obtain the preset number of energy levels corresponding to the two quantum dots under different voltage changes.

[0113] Step S602: Based on a preset number of energy levels corresponding to the two quantum dots under each voltage change, generate a preset number of second fitting curves. Each second fitting curve is used to indicate the second correspondence between the voltage change on the second pump electrode and the energy levels of the two quantum dots.

[0114] Step S603: Obtain the slope of each second fitted curve to obtain the lever arm coefficient corresponding to the second pump electrode.

[0115] Steps S601-S603 above are a refinement of the process of obtaining the lever arm coefficient corresponding to the second pump electrode in step S1021 above. The execution method of steps S601-S603 above can be referred to the execution method of steps S401-S403 above, and will not be specifically described here.

[0116] Through the above steps S601-S603, the electronic device can represent the second correspondence between the voltage change on the second pump electrode and the energy levels of the two quantum dots by curve fitting, thereby determining the slope of each second fitting curve and obtaining the lever arm coefficient corresponding to the second pump electrode, so that the determined second lever arm coefficient can accurately represent the response degree of the energy levels of the two quantum dots to the voltage change on the second pump electrode in the simulation model.

[0117] In an optional embodiment, after obtaining the first lever arm coefficient and the second lever arm coefficient, the electronic device can combine the first lever arm coefficient and the second lever arm coefficient. For ease of understanding, the first lever arm coefficient is used... Second lever arm coefficient Taking this as an example, the combined lever arm coefficient In the lever coefficient a, each row corresponds to the same energy level, such as (-0.23027222 -0.03861415) corresponding to the above E0; each column corresponds to a different pump electrode, such as the left column corresponding to the first pump electrode and the right column corresponding to the second pump electrode.

[0118] In an optional embodiment, according to the above... Figure 3 The method shown in this application embodiment also provides a method for determining target relationships. For example... Figure 7 As shown, Figure 7 This is a flowchart illustrating a target relationship determination method provided in an embodiment of this application. The method includes the following steps.

[0119] Step S701: For each preset voltage, with the preset voltage applied to the barrier electrode, adjust the voltage of the first pump electrode and / or the second pump electrode.

[0120] The preset voltage can be set by the user based on experience, etc. Here, there is no specific limitation on the preset voltage or the number of preset voltages.

[0121] Step S702: Based on the voltages on the first pump electrode and the second pump electrode, obtain the first ground state wave function of the first quantum dot and the second ground state wave function of the second quantum dot, respectively.

[0122] In this embodiment, based on the voltage applied to the first pump electrode and the second pump electrode at the current moment, the electronic device can obtain a series of wave functions corresponding to the first quantum dot and a series of wave functions corresponding to the second quantum dot by solving the Poisson equation and the Schrödinger equation.

[0123] The series of wave functions corresponding to the first and second quantum dots mentioned above includes ground state wave functions and excited state wave functions. Electronic devices can obtain the ground state wave function from the series of wave functions corresponding to the first quantum dot to obtain the first ground state wave function, and obtain the ground state wave function from the series of wave functions corresponding to the second quantum dot to obtain the second ground state wave function.

[0124] The ground state wavefunction mentioned above is the wavefunction corresponding to the lowest energy eigenvalue, which is the wavefunction Ψ0(r) corresponding to the lowest energy eigenvalue E0 obtained by solving the Schrödinger equation.

[0125] Step S703: Based on the first ground state wave function or the second ground state wave function, determine whether the overall ground state wave functions corresponding to the first quantum dot and the second quantum dot are symmetrically distributed, or determine whether the overall excited state wave functions corresponding to the first quantum dot and the second quantum dot are antisymmetrically distributed.

[0126] In one optional embodiment, the electronic device can determine whether the overall ground state wave function after the coupling of the first quantum dot and the second quantum dot is symmetrically distributed based on the first ground state wave function or the second ground state wave function described above.

[0127] For ease of understanding, combined with Figure 8-a Let's take an example to illustrate. Figure 8-a This is a schematic diagram illustrating a symmetrical distribution of the overall ground state wavefunction provided in an embodiment of this application. Figure 8-a In the diagram, the overall ground state wavefunction consists of a left half 801 and a right half 802. The color corresponding to the left half 801 and the right half 802, i.e., blue, indicates that the ground state wavefunction is negative. Since the left half 801 and the right half 802 are symmetrical about the axis of symmetry 803, and since they share the same color, the electronic device can determine that the left half 801 and the right half 802 are symmetrically distributed, meaning the overall ground state wavefunction is symmetrically distributed.

[0128] For ease of understanding, only the first ground state wavefunction will be used as an example. Depending on the voltage applied to the first barrier electrode, the distance and symmetry between the first ground state wavefunctions corresponding to the first quantum dot are different. After obtaining the aforementioned first ground state wavefunction, the electronic device can map the first ground state wavefunction as follows: Figure 8-a The diagram shows the wave function distribution. When the generated wave function distribution diagram is consistent with... Figure 8-a When the distributions shown differ, the electronic device can determine that the overall ground state wavefunctions corresponding to the first and second quantum dots do not have a symmetrical distribution. When the generated wavefunction distribution diagram differs from... Figure 8-a When the distributions shown are the same, the electronic device can determine that the global ground state wave function of the first quantum dot and the second quantum dot are symmetrically distributed.

[0129] In another alternative embodiment, the electronic device can determine whether the overall excited state wave function after the coupling of the first quantum dot and the second quantum dot is antisymmetric based on the first ground state wave function or the second ground state wave function described above.

[0130] For ease of understanding, combined with Figure 8-b Let's take an example to illustrate. Figure 8-b This is a schematic diagram illustrating the antisymmetric distribution of the global excited-state wavefunction provided in an embodiment of this application. Figure 8-bIn the diagram, the overall excited-state wavefunction consists of a left half 804 and a right half 805. The colors corresponding to the left and right halves of the excited-state wavefunction represent the positive and negative values, respectively: blue for negative and red for positive. Since the left and right halves of the excited-state wavefunction are symmetrical about the axis of symmetry 806, and their colors are different, the electronic device can determine that the left and right halves of the excited-state wavefunction are antisymmetric, i.e., the overall excited-state wavefunction is antisymmetric.

[0131] For ease of understanding, we will continue to use the first ground state wavefunction as an example. Depending on the voltage applied to the first barrier electrode, the distance and antisymmetry between the first ground state wavefunctions corresponding to the first quantum dot are different. After obtaining the aforementioned first ground state wavefunction, the electronic device can map the first ground state wavefunction as follows: Figure 8-b The diagram shows the wave function distribution. When the generated wave function distribution diagram is consistent with... Figure 8-b When the distributions shown differ from those shown, the electronic device can determine that the overall excited-state wavefunctions corresponding to the first and second quantum dots do not have an antisymmetric distribution. When the generated wavefunction distribution diagram differs from... Figure 8-b When the distributions shown are the same, the electronic device can determine the antisymmetric distribution of the global excited state wave function corresponding to the first quantum dot and the second quantum dot.

[0132] Step S704: If the overall ground state wave function does not have a symmetrical distribution or the overall excited state wave function does not have an antisymmetric distribution, then return to the step of adjusting the voltage of the first pump electrode and / or the second pump electrode until the overall ground state wave function has a symmetrical distribution or the overall excited state wave function has an antisymmetric distribution.

[0133] In this step, if the global ground state wavefunctions corresponding to the first and second quantum dots at the current moment are not symmetrically distributed, or if the global excited state wavefunctions corresponding to the first and second quantum dots at the current moment are not antisymmetrically distributed, the electronic device can determine that the voltages on the first and second pump electrodes do not match the voltage condition corresponding to the currently preset voltage in the first voltage condition. At this time, the electronic device can readjust the voltage, that is, return to step S701 above to adjust the voltages of the first and / or second pump electrodes until the global ground state wavefunction at the current moment is symmetrically distributed or the global excited state wavefunction at the current moment is antisymmetrically distributed.

[0134] In the embodiments of this application, the adjustment process of the voltage on the first pump electrode and / or the second pump electrode may require one or more adjustments. When multiple adjustments are performed, the adjustment step size of each adjustment process can be determined based on the degree of deviation of the overall wave function corresponding to the first quantum dot and the second quantum dot about the axis of symmetry. Here, the adjustment process of the voltage on the first pump electrode and / or the second pump electrode is not specifically limited.

[0135] Step S705: If the overall ground state wave function is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed, then obtain the energy difference between the first quantum dot and the second quantum dot.

[0136] In this step, if the global ground state wavefunction is symmetrically distributed at the current moment, or if the global excited state wavefunction is antisymmetrically distributed at the current moment, the electronic device can determine that the first pump electrode and the second pump electrode match the voltage condition corresponding to the preset voltage at the current moment in the first voltage condition. At this time, the electronic device can obtain the energy eigenvalue corresponding to the first ground state wavefunction at the current moment (denoted as the first energy eigenvalue) and the energy eigenvalue corresponding to the second ground state wavefunction at the current moment (denoted as the second energy eigenvalue), thereby calculating the difference between the first energy eigenvalue and the second energy eigenvalue to obtain the energy difference between the first quantum dot and the second quantum dot. This energy difference is the energy difference of the aforementioned barrier electrode under the preset voltage at the current moment.

[0137] Step S705 can be performed after step S703 or after step S704.

[0138] Step S706: Half of the energy difference is determined as the tunneling coefficient of the first quantum dot and the second quantum dot at the preset voltage.

[0139] In this step, for each preset voltage on the barrier electrode, the electronic device can determine half of the energy difference at that preset voltage as the tunneling coefficient of the first quantum dot and the second quantum dot at that preset voltage.

[0140] Step S707: Determine the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode based on the tunneling coefficient at each preset voltage.

[0141] In an optional embodiment, based on the tunneling coefficient at each preset voltage, the electronic device can generate a fitting curve (denoted as the third fitting curve) indicating the relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the preset voltage on the barrier electrode. This third fitting curve is used to describe the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode.

[0142] For ease of understanding, combined with Figure 8-cLet's take an example to illustrate. Figure 8-c This is a schematic diagram of a third fitting curve provided in an embodiment of this application. Figure 8-c In the diagram, the five coordinate points, such as coordinate point 807, represent the mapping of the tunneling coefficients obtained under different preset voltages. The electronic device can fit each coordinate point to obtain curve 808, which is the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode.

[0143] In another optional embodiment, after obtaining the third fitting curve, the electronic device may also obtain the fitting function corresponding to the third fitting curve and determine the fitting function as the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode.

[0144] Steps S701-S707 above are a refinement of step S1022 above.

[0145] Through the above steps S701-S707, the electronic device can obtain half of the energy difference between the first quantum dot and the second quantum dot when the overall ground state wave function is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed, by adjusting the voltage of the first pump electrode and / or the second pump electrode under different preset voltages applied to the barrier electrode. This yields the tunneling coefficient between the first quantum dot and the second quantum dot. Based on the tunneling coefficient under each preset voltage, the target relationship between the tunneling coefficient and the barrier electrode voltage is determined, ensuring the accuracy of the determined target relationship.

[0146] In an optional embodiment, according to the above... Figure 3 The method shown in this application also provides a method for determining the Coulomb interaction coefficient. For example... Figure 9 As shown, Figure 9 This is a schematic flowchart illustrating the determination of the Coulomb interaction coefficient provided in an embodiment of this application. The method includes the following steps.

[0147] Step S901: Adjust the voltage of the first pump electrode and / or the second pump electrode.

[0148] Step S902: Based on the voltages on the first pump electrode and the second pump electrode, obtain the third ground state wave function of the first quantum dot and the fourth ground state wave function of the second quantum dot.

[0149] In this step, the electronic device can obtain the third ground state wave function of the first quantum dot based on the voltage on the first pump electrode at the current moment; and the electronic device can obtain the fourth ground state wave function of the second quantum dot based on the voltage on the second pump electrode at the current moment, i.e., the adjusted voltage.

[0150] The acquisition of the third and fourth ground state wave functions can be referred to the acquisition methods of the first and second ground state wave functions, respectively, and will not be specifically explained here.

[0151] Step S903: Based on the third ground state wave function or the fourth ground state wave function, determine whether the overall wave function corresponding to the first quantum dot and the second quantum dot is localized within a preset region at the location of the first quantum dot, or whether it is localized within a preset region at the location of the second quantum dot.

[0152] In this embodiment, by adjusting the voltage on the first pump electrode and the second pump electrode, the wave functions corresponding to the first quantum dot and the second quantum dot can be coupled.

[0153] In one optional embodiment, after obtaining the third ground state wavefunction, the electronic device can determine whether the third ground state wavefunction is localized within a preset region at the location of the first quantum dot. That is, it determines whether the overall wavefunction between the first and second quantum dots is localized within the preset region at the location of the first quantum dot.

[0154] For ease of understanding, combined with Figure 10-a Let's take an example to illustrate. Figure 10-a This is a first schematic diagram illustrating the locality of the wave function provided in an embodiment of this application. Figure 10-a In this context, the ground state wavefunction 1001 is localized within a predetermined region at the location of the first quantum dot. Point 1002 is the starting point of the symmetry axis, and point 1003 is the ending point of the symmetry axis. Electronic devices can map the third ground state wavefunction as follows: Figure 10-a The diagram shows the wave function distribution. If the generated wave function distribution diagram is consistent with... Figure 10-a When the distribution shown differs from the given pattern, the electronic device can determine that the overall wavefunction is not localized within the preset region where the first quantum dot is located. If the generated wavefunction distribution diagram differs from... Figure 10-a When the distribution shown is the same, the electronic device can determine that the overall wave function is localized within a preset region where the first quantum dot is located.

[0155] In another optional embodiment, after obtaining the aforementioned fourth ground state wavefunction, the electronic device can determine whether the fourth ground state wavefunction is localized within a preset region at the location of the second quantum dot. That is, it determines whether the overall wavefunction between the first and second quantum dots is localized within the preset region at the location of the second quantum dot.

[0156] For ease of understanding, combined with Figure 10-b Let's take an example to illustrate. Figure 10-b This is a second schematic diagram illustrating the locality of the wave function provided in an embodiment of this application. Figure 10-bIn the above, the ground state wavefunction 1004 is located within a predetermined region at the location of the second quantum dot. Point 1005 is the starting point of the symmetry axis, and point 1006 is the ending point of the symmetry axis. Electronic devices can map the above fourth ground state wavefunction as follows: Figure 10-b The diagram shows the wave function distribution. If the generated wave function distribution diagram is consistent with... Figure 10-b When the distribution shown differs from the schematic diagram, the electronic device can determine that the overall wavefunction is not localized within the preset region where the second quantum dot is located. If the generated wavefunction distribution diagram differs from the schematic diagram shown, the electronic device can determine that the overall wavefunction is not localized within the preset region where the second quantum dot is located. Figure 10-b When the distribution shown is the same, the electronic device can determine that the overall wave function is localized within a preset region where the second quantum dot is located.

[0157] The preset regions corresponding to the first and second quantum dots can be set based on user experience, etc. Here, no specific limitation is made on the preset regions.

[0158] Step S904: If the overall wave function is not localized within the preset region where the first quantum dot is located, or if the overall wave function is not localized within the preset region where the second quantum dot is located, then return to the step of adjusting the voltage of the first pump electrode and / or the second pump electrode until the overall wave function is localized within the preset region where the first quantum dot is located, or until the overall wave function is localized within the preset region where the second quantum dot is located.

[0159] In this step, when the electronic device determines that the overall wave function is not localized within the preset region where the first quantum dot is located, or when the overall wave function is not localized within the preset region where the second quantum dot is located, it can determine that the voltage on the first pump electrode and the second pump electrode at the current moment does not satisfy the second voltage condition. At this time, the electronic device can readjust the voltage, that is, return to step S901 until the overall wave function at the current moment is localized within the preset region where the first quantum dot is located, or until the overall wave function at the current moment is localized within the preset region where the second quantum dot is located.

[0160] Step S905: If the overall wave function is localized within a preset region where the first quantum dot is located, or if the overall wave function is localized within a preset region where the second quantum dot is located, then the Coulomb interaction coefficient between the first quantum dot and the second quantum dot is determined by finite element simulation based on the third ground state wave function or the fourth ground state wave function.

[0161] In this step, if the global wavefunction is localized within a preset region at the location of the first quantum dot, or if the global wavefunction is localized within a preset region at the location of the second quantum dot, the electronic device can determine that the voltages on the first and second pump electrodes at the current moment satisfy the aforementioned second voltage condition. At this time, the electronic device can obtain the Coulomb interaction coefficients corresponding to the first and second quantum dots through finite element simulation based on the aforementioned third or fourth ground state wavefunction.

[0162] In an alternative embodiment, the electronic device can determine the Coulomb interaction coefficient between the first quantum dot and the second quantum dot using the following formula.

[0163]

[0164] Where V is the Coulomb interaction coefficient, e is the elementary charge, ∫dr1 is the integral operation over r1, and r1 is the position of the first quantum dot. The charge concentration at point r1 Let ψ be the complex conjugate of the wavefunction corresponding to the electron at position r1 in the i-state. k (r1) is the wave function of the electron at position r1 in the k state. ∫dr2 represents the integration operation with respect to r2, where r2 is the location of the second quantum dot, and G(r1,r2) is the Green's function with respect to r1 and r2. The charge concentration at point r2, Let ψ be the complex conjugate of the wavefunction corresponding to the electron at position r2 in state j. l (r2) is the wave function of the second electron at r2 in the l state, i and j are the states after electron scattering, and k and l are the states before electron scattering.

[0165] Step S905 can be performed after step S903 or after step S904. The specific execution of step S905 is not limited here. Furthermore, steps S901-S905 are a refinement of step S1023.

[0166] Through steps S901-S905, during the voltage adjustment process on the first and second pump electrodes, the Coulomb interaction between the first and second quantum dots remains approximately unchanged. The electronic device can determine the Coulomb interaction coefficient between the first and second quantum dots through finite element simulation, which provides a guarantee for the calculation of Hamiltonian in the subsequent parameter layer simulation, thereby ensuring the normal progress of the semiconductor gate-controlled quantum dot model simulation process.

[0167] Based on the same inventive concept, and according to the model simulation method provided in the above embodiments of this application, this application also provides a model simulation device. For example... Figure 11 As shown, Figure 11 This is a schematic diagram of a model simulation device provided in an embodiment of this application. The device includes the following modules.

[0168] The construction module 1101 is used to construct a semiconductor gated quantum dot model as a simulation model. The simulation model includes a first pump electrode, a second pump electrode, and a barrier electrode. The barrier electrode is located between the first pump electrode and the second pump electrode. A first quantum dot exists under the first pump electrode, and a second quantum dot exists under the second pump electrode.

[0169] The acquisition module 1102 is used to acquire, based on the voltage on the first pump electrode and the second pump electrode, the lever arm coefficient corresponding to the first pump electrode and the second pump electrode, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the Coulomb interaction coefficient between the first quantum dot and the second quantum dot, respectively.

[0170] Module 1103 is used to determine the Hamiltonian of the model to be simulated based on the lever arm coefficient, target relationship and Coulomb interaction coefficient;

[0171] Simulation module 1104 is used to simulate the model to be simulated based on Hamiltonian.

[0172] Optionally, the above-mentioned acquisition module 1102 includes:

[0173] The first determining submodule is used to determine the lever arm coefficient corresponding to the first pump electrode based on the first correspondence between the voltage change on the first pump electrode and the energy levels of the two quantum dots, and to determine the lever arm coefficient corresponding to the second pump electrode based on the second correspondence between the voltage change on the second pump electrode and the energy levels of the two quantum dots.

[0174] The second determining submodule is used to determine the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode based on the energy difference between the first quantum dot and the second quantum dot under the first voltage condition. The first voltage condition is the voltage corresponding to the first pump electrode and the second pump electrode when the overall ground state wave function of the first quantum dot and the second quantum dot is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed under different preset voltages.

[0175] The calculation submodule is used to calculate the Coulomb interaction coefficient between the first quantum dot and the second quantum dot based on the global wave function of the first quantum dot or the second quantum dot under a second voltage condition. The second voltage condition is the voltage at which the global wave function of the first quantum dot and the second quantum dot is localized at the first quantum dot or localized at the second quantum dot.

[0176] Optionally, the first determining submodule can be used to obtain a preset number of energy levels corresponding to two quantum dots under different voltage changes during the process of adjusting the voltage on the first pump electrode.

[0177] Based on a preset number of energy levels corresponding to the two quantum dots under each voltage change, a preset number of first fitting curves are generated. Each first fitting curve is used to indicate the first correspondence between the voltage change on the first pump electrode and the energy levels of the two quantum dots.

[0178] Obtain the slope corresponding to each first fitted curve to get the lever arm coefficient corresponding to the first pump electrode.

[0179] Optionally, the first determining submodule can be used to obtain a preset number of energy levels corresponding to the two quantum dots under different voltage changes during the process of adjusting the voltage on the second pump electrode.

[0180] Based on a preset number of energy levels corresponding to the two quantum dots under each voltage change, a preset number of second fitting curves are generated. Each second fitting curve is used to indicate the second correspondence between the voltage change on the second pump electrode and the energy levels of the two quantum dots.

[0181] Obtain the slope of each second fitted curve to get the lever arm coefficient corresponding to the second pump electrode.

[0182] Optionally, the aforementioned second determining submodule can be specifically used to adjust the voltage of the first pump electrode and / or the second pump electrode when the preset voltage is applied to the barrier electrode for each preset voltage.

[0183] Based on the voltages on the first pump electrode and the second pump electrode, the first ground state wave function of the first quantum dot and the second ground state wave function of the second quantum dot are obtained respectively.

[0184] Based on the first ground state wave function or the second ground state wave function, determine whether the overall ground state wave functions corresponding to the first quantum dot and the second quantum dot are symmetrically distributed, or determine whether the overall excited state wave functions corresponding to the first quantum dot and the second quantum dot are antisymmetrically distributed;

[0185] If the overall ground state wave function is not symmetrically distributed or the overall excited state wave function is not antisymmetrically distributed, then return to the step of adjusting the voltage of the first pump electrode and / or the second pump electrode until the overall ground state wave function is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed.

[0186] If the global ground state wave function is symmetrically distributed or the global excited state wave function is antisymmetrically distributed, then the energy difference between the first quantum dot and the second quantum dot can be obtained.

[0187] Half of the energy difference is determined as the tunneling coefficient of the first quantum dot and the second quantum dot at the preset voltage;

[0188] Based on the tunneling coefficient at each preset voltage, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode is determined.

[0189] Optionally, the aforementioned calculation submodule can be used to adjust the voltage of the first pump electrode and / or the second pump electrode.

[0190] Based on the voltages on the first and second pump electrodes, the third ground state wave function of the first quantum dot and the fourth ground state wave function of the second quantum dot are obtained;

[0191] Based on the third or fourth ground state wave function, determine whether the overall wave function corresponding to the first quantum dot and the second quantum dot is localized in a preset region at the location of the first quantum dot, or whether it is localized in a preset region at the location of the second quantum dot.

[0192] If the overall wave function is not localized within the preset region where the first quantum dot is located, or if the overall wave function is not localized within the preset region where the second quantum dot is located, then return to the step of adjusting the voltage of the first pump electrode and / or the second pump electrode until the overall wave function is localized within the preset region where the first quantum dot is located, or until the overall wave function is localized within the preset region where the second quantum dot is located.

[0193] If the global wave function is localized within a predetermined region at the location of the first quantum dot, or if the global wave function is localized within a predetermined region at the location of the second quantum dot, then the Coulomb interaction coefficient between the first and second quantum dots can be determined by finite element simulation based on the third or fourth ground state wave function.

[0194] Optionally, the aforementioned determining module 1103 can be used to determine the Hamiltonian of the model to be simulated using the following formula;

[0195]

[0196] Among them, H DQDLet α, d, and σ be the Hamiltonians of the model to be simulated, α = L and R represent the left and right quantum points, σ ​​represent spin, and d represent the energy level. 'a' is the lever arm coefficient, V L V is the voltage of the left quantum dot. R Let ΔV be the voltage across the right quantum dot, and ΔV be the voltage change. The voltage V was obtained from the finite element simulation. L and V R The energy levels at time, c and σ is the annihilation operator, t is the tunneling coefficient, V is the Coulomb interaction coefficient, β, γ, and δ are quantum dots, and σ is the annihilation operator. ′ It is spin.

[0197] The apparatus provided in this application, after constructing the model to be simulated, can obtain relevant parameters of the simulation model based on the voltages of the two pump electrodes on the model to be simulated, namely, the lever arm coefficients corresponding to the first quantum dot and the second quantum dot, the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode, and the Coulomb correlation coefficient between the first quantum dot and the second quantum dot. Based on the lever arm coefficients, the target relationship and the Coulomb interaction coefficient, the Hamiltonian of the model to be simulated is determined, and the simulation of the model to be simulated is performed based on the Hamiltonian, thereby realizing the simulation of the semiconductor gate-controlled quantum dot model.

[0198] Based on the same inventive concept, and according to the model simulation method provided in the above embodiments of this application, this application also provides an electronic device, such as... Figure 12 As shown, it includes a processor 1201, a communication interface 1202, a memory 1203, and a communication bus 1204. The processor 1201, the communication interface 1202, and the memory 1203 communicate with each other through the communication bus 1204.

[0199] Memory 1203 is used to store computer programs;

[0200] The processor 1201 is used to execute the program stored in the memory 1203 to implement any of the above-described method steps for model simulation.

[0201] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0202] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0203] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0204] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0205] Based on the same inventive concept, and according to the model simulation method provided in the above embodiments of this application, this application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above model simulation methods.

[0206] Based on the same inventive concept, and according to the model simulation method provided in the above embodiments of this application, this application also provides a computer program product containing instructions, which, when run on a computer, causes the computer to execute any of the model simulation methods in the above embodiments.

[0207] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (SSD)).

[0208] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0209] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, embodiments such as apparatuses, electronic devices, computer-readable storage media, and computer program products are basically similar to the method embodiments, and therefore the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0210] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A model simulation method characterized by, The method comprises: constructing a semiconductor gate-controlled quantum dot model as a to-be-simulated model, the to-be-simulated model comprising a first pumping electrode, a second pumping electrode, and a barrier electrode between the first pumping electrode and the second pumping electrode, a first quantum dot existing below the first pumping electrode, and a second quantum dot existing below the second pumping electrode; according to voltages on the first pumping electrode and the second pumping electrode, obtaining an arm coefficient corresponding to the first pumping electrode and the second pumping electrode, a target relationship between a tunneling coefficient between the first quantum dot and the second quantum dot and a voltage of the barrier electrode, and a Coulomb interaction coefficient between the first quantum dot and the second quantum dot; based on the arm coefficient, the target relationship, and the Coulomb interaction coefficient, determining a Hamiltonian of the to-be-simulated model; based on the Hamiltonian, simulating the to-be-simulated model.

2. The method of claim 1, wherein, The step of obtaining, according to voltages on the first pumping electrode and the second pumping electrode, an arm coefficient corresponding to the first pumping electrode and the second pumping electrode, a target relationship between a tunneling coefficient between the first quantum dot and the second quantum dot and a voltage of the barrier electrode, and a Coulomb interaction coefficient between the first quantum dot and the second quantum dot comprises: determining, according to a first corresponding relationship between a voltage change amount on the first pumping electrode and energy levels of two quantum dots, an arm coefficient corresponding to the first pumping electrode, and determining, according to a second corresponding relationship between a voltage change amount on the second pumping electrode and energy levels of two quantum dots, an arm coefficient corresponding to the second pumping electrode; determining, according to an energy difference between the first quantum dot and the second quantum dot under a first voltage condition, a target relationship between a tunneling coefficient between the first quantum dot and the second quantum dot and a voltage of the barrier electrode, the first voltage condition being that, when the first quantum dot and the second quantum dot correspond to a symmetric distribution of an overall ground state wave function or an antisymmetric distribution of an overall excited state wave function of the barrier electrode under different preset voltages, voltages corresponding to the first pumping electrode and the second pumping electrode; calculating, according to an overall wave function of the first quantum dot or the second quantum dot under a second voltage condition, a Coulomb interaction coefficient between the first quantum dot and the second quantum dot, the second voltage condition being a voltage when the first quantum dot and the second quantum dot correspond to a local distribution of an overall wave function at the first quantum dot or at the second quantum dot.

3. The method of claim 2, wherein, The step of determining, according to a first corresponding relationship between a voltage change amount on the first pumping electrode and energy levels of two quantum dots, an arm coefficient corresponding to the first pumping electrode comprises: in the process of adjusting the voltage on the first pumping electrode, obtaining a preset number of energy levels corresponding to two quantum dots under different voltage changes; generate a preset number of first fitting curves corresponding to the two quantum dots under each voltage change amount, each first fitting curve being used to indicate a first corresponding relationship between the voltage change amount on the first pumping electrode and the energy levels of the two quantum dots; obtain the slope corresponding to each first fitting curve to obtain the arm coefficient corresponding to the first pumping electrode.

4. The method of claim 2, wherein, The step of determining the arm coefficient corresponding to the second pumping electrode according to the second corresponding relationship between the voltage change amount on the second pumping electrode and the energy levels of the two quantum dots comprises: obtaining a preset number of energy levels corresponding to the two quantum dots under different voltage change amounts during the adjustment of the voltage on the second pumping electrode; generate a preset number of second fitting curves corresponding to the two quantum dots under each voltage change amount, each second fitting curve being used to indicate a second corresponding relationship between the voltage change amount on the second pumping electrode and the energy levels of the two quantum dots; obtain the slope corresponding to each second fitting curve to obtain the arm coefficient corresponding to the second pumping electrode.

5. The method of claim 2, wherein, The step of determining the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode according to the energy difference between the first quantum dot and the second quantum dot under the first voltage condition comprises: for each preset voltage, adjusting the voltage of the first pumping electrode and / or the second pumping electrode under the condition that the preset voltage is applied to the barrier electrode; obtaining the first ground state wave function of the first quantum dot and the second ground state wave function of the second quantum dot according to the voltages on the first pumping electrode and the second pumping electrode, respectively; determining whether the overall ground state wave function corresponding to the first quantum dot and the second quantum dot is symmetrically distributed or whether the overall excited state wave function corresponding to the first quantum dot and the second quantum dot is antisymmetrically distributed based on the first ground state wave function or the second ground state wave function; if the overall ground state wave function is not symmetrically distributed or the overall excited state wave function is not antisymmetrically distributed, return to perform the step of adjusting the voltage of the first pumping electrode and / or the second pumping electrode until the overall ground state wave function is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed; if the overall ground state wave function is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed, obtain the energy difference between the first quantum dot and the second quantum dot; determining half of the energy difference as the tunneling coefficient of the first quantum dot and the second quantum dot under the preset voltage; determining the target relationship between the tunneling coefficient between the first quantum dot and the second quantum dot and the voltage of the barrier electrode according to the tunneling coefficient under each preset voltage.

6. The method of claim 2, wherein, The step of calculating the Coulomb interaction coefficient between the first quantum dot and the second quantum dot according to the overall wave function of the first quantum dot or the second quantum dot under the second voltage condition comprises: adjusting the voltage of the first pumping electrode and / or the second pumping electrode; According to voltages on the first pumping electrode and the second pumping electrode, a third ground state wave function of the first quantum dot and a fourth ground state wave function of the second quantum dot are obtained; Based on the third ground state wave function or the fourth ground state wave function, it is determined whether an overall wave function corresponding to the first quantum dot and the second quantum dot is localized in a preset region at the position of the first quantum dot or in a preset region at the position of the second quantum dot; If the overall wave function is not localized in the preset region at the position of the first quantum dot or the overall wave function is not localized in the preset region at the position of the second quantum dot, the step of adjusting the voltages of the first pumping electrode and / or the second pumping electrode is returned to be executed until the overall wave function is localized in the preset region at the position of the first quantum dot or until the overall wave function is localized in the preset region at the position of the second quantum dot; If the overall wave function is localized in the preset region at the position of the first quantum dot or the overall wave function is localized in the preset region at the position of the second quantum dot, a finite element simulation is performed to determine a Coulomb interaction coefficient between the first quantum dot and the second quantum dot according to the third ground state wave function or the fourth ground state wave function.

7. The method of claim 1, wherein, The step of determining the Hamiltonian of the to-be-simulated model based on the lever coefficient, the target relationship and the Coulomb interaction coefficient comprises: The Hamiltonian of the to-be-simulated model is determined by using the following formula: where H DQD is the Hamiltonian of the model to be simulated, α, d, σ are three quantum numbers, α = L, R represents left and right quantum dots, σ represents spin, d represents energy level, a is the arm coefficient, V L is the voltage of the left quantum dot, V R is the voltage of the right quantum dot, ΔV is the voltage change, is the energy level when the voltage obtained by finite element simulation is V L and V R , c and are annihilation operators, t is the tunneling coefficient, V is the Coulomb interaction coefficient, β, γ, δ are quantum dots, and σ' is spin.

8. A model simulation apparatus characterized by comprising: The device comprises: A construction module is configured to construct a semiconductor gate-controlled quantum dot model as a to-be-simulated model, wherein the to-be-simulated model comprises a first pumping electrode, a second pumping electrode and a barrier electrode, the barrier electrode is located between the first pumping electrode and the second pumping electrode, a first quantum dot exists below the first pumping electrode, and a second quantum dot exists below the second pumping electrode; An acquisition module is configured to acquire a lever coefficient corresponding to the first pumping electrode and the second pumping electrode, a target relationship between a tunneling coefficient between the first quantum dot and the second quantum dot and a voltage of the barrier electrode, and a Coulomb interaction coefficient between the first quantum dot and the second quantum dot according to voltages on the first pumping electrode and the second pumping electrode. A determination module is configured to determine a Hamiltonian of the to-be-simulated model based on the lever coefficient, the target relationship and the Coulomb interaction coefficient. A simulation module is configured to simulate the to-be-simulated model based on the Hamiltonian.

9. An electronic device, comprising: The device comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete communication with each other through the communication bus. The memory is configured to store a computer program. The processor is configured to execute the program stored on the memory to implement the method steps in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer program is stored in the computer readable storage medium, and the computer program is executed by the processor to implement the method steps in any one of claims 1-7.

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