Majorana zero mode parity interference reading method based on spin-orbital coupling field-free electric control modulation

Abstract

The application provides a Majorana zero mode parity interference reading method based on spin-orbital coupling field-free electric control modulation, relates to the technical field of topological quantum computation and condensed matter physics, and comprises the following steps: constructing a topological quantum bit reading structure, wherein the reading structure at least comprises a topological superconducting carrier for carrying at least two spatially separated Majorana zero modes, and a group of quantum dot structures coupled with the two spatially separated Majorana zero modes respectively to form at least two tunneling paths capable of constituting a closed virtual transition loop, so that a reading structure with adjustable tunneling paths is obtained; and based on the reading structure with adjustable tunneling paths, the spin-orbital coupling strength in the tunneling paths is adjusted through an electrical method. The application realizes interference reading of Majorana zero mode (MZM) parity information without additional magnetic flux modulation, and constructs a topological quantum bit reading architecture which can be controlled through an electrical method.

Description

Technical Field

[0001] This invention relates to the fields of topological quantum computing and condensed matter physics, and in particular to a Majorana zero-mode parity interferometry readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation. Background Technology

[0002] In condensed matter physics, Majorana zero modes are the core carriers of topological quantum computing units. Quantum information is encoded in their fermion parity states, and the controllable and precise reading of these parities is the key to the practical application of topological quantum computing.

[0003] The current mainstream Majorana zero-mode parity readout scheme is the interference modulation quantum capacitance readout scheme. This scheme constructs a one-dimensional topological superconductor using semiconductor-superconductor hybrid nanowires, couples the Majorana zero-mode at the nanowire end to a quantum dot to form an interference tunneling path, introduces magnetic flux through an external magnetic field, and uses the Akaronov-Bohm effect to accumulate electron interference phase, thereby modulating the effective tunneling amplitude between the quantum dot and the topological superconductor. This results in differences in the quantum capacitance of the quantum dot under different parity states, which are then detected using a radio frequency resonant cavity combined with radio frequency reflection measurement technology, enabling single-shot parity measurement. Preliminary physical verification of this scheme has been completed. The drawback of this scheme is that the interference phase modulation of parity readout depends entirely on the magnetic flux of the external magnetic field, and cannot achieve purely electrical control. This makes the magnetic field prone to crosstalk to neighboring quantum devices, which greatly increases the difficulty of isolation design for multi-qubit systems and hinders the large-scale integration of topological quantum computing chips. Moreover, the stable and precise control of magnetic flux requires a dedicated control unit, which increases the complexity of the device. It also has stringent requirements for power consumption and thermal load control in low-temperature environments, which contradicts the trend of chip miniaturization and high-density integration. Furthermore, improving the precision of magnetic field control will further increase the complexity of system design and debugging. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a Majorana zero-mode parity interferometric readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation, which realizes the interferometric readout of Majorana zero-mode (MZM) parity information without the need for external magnetic flux modulation, and constructs a topological qubit readout architecture that can be controlled electrically.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: A Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling magnetic field-free electrically controlled modulation, the method comprising: A topological qubit readout structure is constructed, the readout structure including at least a topological superconducting carrier for carrying at least two spatially separated Majorana zero modes; and a set of quantum dot structures, each coupled to two spatially separated Majorana zero modes, forming at least two tunneling paths that can constitute closed virtual transition loops, thus obtaining a readout structure with tunable tunneling paths. Based on the readout structure with adjustable tunneling path, the spin-orbit coupling strength in the tunneling path is electrically controlled so that when electrons propagate in different paths, their spin degrees of freedom precess under the action of spin-orbit coupling, thereby introducing a controllable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, and obtaining an electrical phase parameter for modulating the interference condition. According to the electrical phase parameters, the effective tunneling amplitude of the closed virtual transition circuit is made to exhibit a dependence on the parity state of the Majorana zero mode, thereby causing the ground state energy of the quantum dot and its quantum capacitance to undergo a distinguishable shift with the parity state, resulting in a quantum capacitance signal carrying parity information. By using a radio frequency readout circuit coupled to the quantum dot, the change in the quantum capacitance signal carrying parity information is measured, and this change is mapped to the parity information of the Majorana zero mode, thereby obtaining a parity state readout result based on pure electrical control without applying an external magnetic field.

[0006] Furthermore, a topological qubit readout structure is constructed, comprising at least a topological superconducting carrier for carrying at least two spatially separated Majorana zero modes; and a set of quantum dot structures coupled to the two spatially separated Majorana zero modes respectively, forming at least two tunneling paths that can constitute closed virtual transition loops, thus obtaining a readout structure with tunable tunneling paths, including: A topological superconducting support is prepared, wherein the topological superconducting support is selected from an iron-based superconducting material with intrinsic topological superconducting properties, thereby obtaining a support structure that can be used to support Majorana zero energy modes; Based on the carrier structure, at least two spatially separated Majorana zero modes are induced in the topological superconducting carrier through initialization operations, resulting in a topological superconducting unit containing parity information carrier. On one side of the topological superconducting unit, a set of quantum dot structures is prepared at a distance that forms tunnel coupling with two spatially separated Majorana zero modes. The quantum dots are then tunnel coupled with the two Majorana zero modes to form at least two tunneling paths that can constitute closed virtual transition loops, resulting in a coupled structure containing quantum dots and tunneling paths. Based on the coupling structure, by adjusting the gate voltage applied to the quantum dot, the quantum dot is made to enter a charge degeneracy state, and the tunneling coupling strength of the two tunneling paths tends to be balanced, thus obtaining a readout structure with an adjustable tunneling path in a test state.

[0007] Furthermore, by electrically controlling the spin-orbit coupling strength in the tunneling path, the electrons precess due to the spin degree of freedom under the spin-orbit coupling as they propagate in different paths. This introduces a controllable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, resulting in an electrical phase parameter for modulating the interference conditions, including: Based on the readout structure with an adjustable tunneling path in the test state, a spin-orbit coupling modulation gate is set on at least one of the two tunneling paths to obtain a phase modulation structure with an electrical control terminal. Based on a phase modulation structure with electrical control terminals, a scanning voltage is applied to the spin-orbit coupling modulation gate. By changing the amplitude of the scanning voltage, the spin-orbit coupling strength in the tunneling path is continuously controlled. When electrons propagate in different tunneling paths, their spin degrees of freedom precess at different angles under the action of spin-orbit coupling. This introduces a continuously variable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, resulting in an interference parameter scanning result containing different phase conditions. Based on the scanning results of the interference parameters, by simultaneously monitoring the output signal of the radio frequency readout circuit coupled to the quantum dot, the scanning voltage amplitude corresponding to the point where the output signal has the greatest difference due to different parity states is identified, and this is determined as the phase operating point, thus obtaining an electrical phase parameter for modulating the interference conditions.

[0008] Furthermore, based on the interference parameter scanning results, by simultaneously monitoring the output signal of the RF readout circuit coupled to the quantum dot, the scanning voltage amplitude corresponding to the point where the output signal exhibits the greatest difference due to parity state is identified, and this is determined as the phase operating point. This yields an electrical phase parameter for modulating the interference conditions, including: Based on the scanning results of interference parameters with different phase conditions, the correspondence between the output signal and the scanning voltage amplitude is extracted from the monitoring data recorded by the radio frequency readout circuit coupled to the quantum dot during the scanning process, and a set of output signal and voltage data pairs is obtained. By analyzing the output signal and voltage data pairs, the fluctuation amplitude of the output signal caused by different parity states under each scanning voltage amplitude is determined, and the distribution curve of the signal fluctuation amplitude as a function of scanning voltage is obtained. Based on the distribution curve of signal fluctuation amplitude as a function of scanning voltage, the scanning voltage amplitude corresponding to the maximum value of fluctuation amplitude is identified as a candidate phase operating point. The scanning voltage amplitude corresponding to the candidate phase operating point is fixed to obtain the electrical phase parameters used for modulation interference conditions.

[0009] Furthermore, based on the electrical phase parameters, the effective tunneling amplitude of the closed virtual transition loop exhibits a dependence on the Majorana zero-mode parity state, thereby causing a distinguishable shift in the ground state energy and quantum capacitance of the quantum dot with respect to the parity state, resulting in a quantum capacitance signal carrying parity information, including: Based on the electrical phase parameters used for modulation interference conditions, the voltage of the spin-orbit coupling modulation gate is fixed at the candidate phase operating point so that a certain relative complex phase difference is maintained between the tunneling amplitudes of the two tunneling paths, resulting in a readout structure in a parity-sensitive interference state. Based on the readout structure in a parity-sensitive interference state, by utilizing the relative complex phase difference between the two tunneling paths, the effective tunneling amplitude of the closed virtual transition loop is made to exhibit a dependence on the parity state of the fermions composed of the two Majorana zero modes, thus obtaining a parity-dependent tunneling coupling condition. Based on the parity-dependent tunneling coupling condition, the ground state energy of the quantum dot shifts accordingly with the current parity state, thereby making the quantum capacitance of the quantum dot exhibit distinguishable numerical differences under different parity states, thus obtaining a quantum capacitance signal carrying parity information.

[0010] Furthermore, based on the readout structure in a parity-sensitive interferometric state, and utilizing the relative complex phase difference between the two tunneling paths, the effective tunneling amplitude of the closed virtual transition loop exhibits a dependence on the parity state of the fermions formed by the two Majorana zero-energy modes, thus obtaining a parity-dependent tunneling coupling condition, including: Based on the readout structure in a parity-sensitive interferometric state, the tunneling amplitude expressions corresponding to the two tunneling paths are obtained, including the complex phase factor introduced by spin-orbit coupling, to obtain the tunneling amplitudes of the two paths carrying phase information. Based on the tunneling amplitudes of the two paths carrying phase information, and combined with the relative complex phase difference between the two tunneling paths, an expression for the total effective tunneling amplitude of the closed virtual transition loop with the relative complex phase difference as a variable parameter is constructed, resulting in a total effective tunneling amplitude function containing the relative complex phase difference parameter. Based on the total effective tunneling amplitude function, the fermion parity state composed of two Majorana zero modes is used as a variable to calculate the amplitude of the total effective tunneling amplitude under parity even state and parity odd state, respectively, and obtain the quantitative correspondence between the parity state and the effective tunneling amplitude. Based on the quantitative correspondence between parity state and effective tunneling amplitude, the law of change of effective tunneling amplitude with parity state under the current relative complex phase difference condition is determined, and the parity-dependent tunneling coupling condition is obtained.

[0011] Furthermore, through a radio frequency readout circuit coupled to the quantum dot, the change in the quantum capacitance signal carrying parity information is measured, and this change is mapped to the parity information of the Majorana zero mode. Thus, without applying an external magnetic field, a parity state readout result based on purely electrical control is obtained, including: Based on the parity-dependent tunneling coupling condition, the quantum dot is connected to a radio frequency resonant cavity via capacitive coupling, and the radio frequency resonant cavity is connected to a radio frequency readout circuit to obtain a quantum capacitance measurement link in a state to be measured. Based on the quantum capacitance measurement link in the test state, a probe microwave signal is applied to the radio frequency resonant cavity, and the reflection coefficient or transmission coefficient of the radio frequency resonant cavity is monitored at the same time to obtain a radio frequency response signal carrying quantum dot state information. Based on the radio frequency response signal carrying quantum dot state information, the quantum capacitance value of the quantum dot is extracted from the change in the reflection coefficient or transmission coefficient, and the measured value of the quantum capacitance corresponding to the current parity state is obtained. The measured value of the quantum capacitance corresponding to the current parity state is compared with the pre-calibrated parity-capacitance correspondence to obtain the comparison result. At the same time, the current parity state is determined to be either parity even or parity odd based on the comparison result, thus obtaining a parity state reading result based on pure electrical control.

[0012] The above-described solution of the present invention has at least the following beneficial effects: By employing an electrical method to control the spin-orbit coupling strength in the tunneling path, this approach overcomes the core technical problem of traditional methods where interference phase control relies entirely on external magnetic field flux and cannot be purely electrically controlled. This allows for the introduction of a controllable relative complex phase difference between tunneling paths without an external magnetic field. Furthermore, by using iron-based superconducting materials to construct the topological superconducting carrier and optimizing the tunneling path coupling, this approach overcomes the technical challenge of magnetic field crosstalk increasing the isolation design difficulty of multi-qubit systems. This reduces coupling interference between quantum devices and improves the feasibility of large-scale integration of topological quantum computing chips. Finally, by using an RF readout circuit to detect changes in quantum capacitance signals and map parity information... This technological approach overcomes the technical challenges of traditional methods that require dedicated control units for magnetic flux control, increasing device complexity and imposing stringent requirements on low-temperature environments. It simplifies the overall device structure, reduces power consumption and thermal load control requirements in low-temperature environments, and achieves purely electrical precision readout of Majorana zero-mode parity states. By employing a technique of calibrating the phase operating point and maintaining a defined relative complex phase difference, it overcomes the problem of traditional methods where improving magnetic field control precision increases system design and debugging complexity. This allows for precise control of interference conditions, improves the stability and distinguishability of the parity readout signal, and establishes a fully electrically controlled topological qubit readout architecture. Particularly when the topological superconducting carrier is an iron-based superconductor, a topological qubit realization and readout architecture completely free of external magnetic fields can be achieved. Attached Figure Description

[0013] Figure 1 This is a schematic flowchart of a Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation, provided by an embodiment of the present invention. Detailed Implementation

[0014] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0015] like Figure 1 As shown, embodiments of the present invention propose a Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation. The method includes the following steps: Step 1: Construct a topological qubit readout structure, which includes at least a topological superconducting carrier for carrying at least two spatially separated Majorana zero modes; and a set of quantum dot structures, which are coupled to the two spatially separated Majorana zero modes respectively to form at least two tunneling paths that can constitute closed virtual transition loops, thereby obtaining a readout structure with tunable tunneling paths. Step 2: Based on the readout structure with adjustable tunneling path, the spin-orbit coupling strength in the tunneling path is electrically controlled so that when electrons propagate in different paths, their spin degrees of freedom precess under the action of spin-orbit coupling, thereby introducing a controllable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, and obtaining an electrical phase parameter for modulating the interference condition. Step 3: According to the electrical phase parameters, the effective tunneling amplitude of the closed virtual transition circuit is made to exhibit a dependence on the parity state of the Majorana zero mode, thereby causing the ground state energy of the quantum dot and its quantum capacitance to undergo a distinguishable shift with the parity state, resulting in a quantum capacitance signal carrying parity information. Step 4: The change in the quantum capacitance signal carrying parity information is measured through a radio frequency readout circuit coupled to the quantum dot, and this change is mapped to the parity information of the Majorana zero mode, thereby obtaining a parity state readout result based on pure electrical control without applying an external magnetic field.

[0016] In this embodiment of the invention, magnetic field-free, purely electrically controlled readout of Majorana zero-mode parity is achieved, eliminating the reliance on traditional external magnetic field flux modulation. This method, through electrical means, controls the spin-orbit coupling strength, precisely introducing the relative complex phase difference between tunneling paths and achieving flexible modulation of interference conditions. The method allows for a precise correlation between the effective tunneling amplitude of the closed virtual transition loop and the parity state, resulting in a clearly distinguishable shift in the quantum capacitance with the parity state, ensuring the effective transmission of parity information. The radio frequency readout circuit accurately detects changes in the quantum capacitance signal and maps them to parity information, ensuring a stable and accurate readout process. This method effectively reduces the impact of magnetic field crosstalk on topological quantum computing architectures, improves the feasibility of large-scale integration of topological quantum computing chips, simplifies the overall device structure, reduces the configuration of additional control units, lowers design and debugging complexity, and improves the response speed and control accuracy of parity readout, providing a superior technical path for the engineering implementation of topological quantum computing.

[0017] In a preferred embodiment of the present invention, step 1 above may include: Step 1.1: Prepare a topological superconducting support. The topological superconducting support is selected from iron-based superconducting materials with intrinsic topological superconducting properties, resulting in a support structure that can be used to support Majorana zero modes. Specifically, this includes: preferentially selecting Fe(Te,Se) materials with intrinsic topological superconducting properties in the iron-based superconducting system as the core material for preparing the topological superconducting support; determining that a high-resistivity silicon wafer or sapphire is used as the insulating substrate to support the iron-based superconducting material; firstly, performing surface pretreatment on the insulating substrate, sequentially completing precision polishing, impurity-free cleaning, and complete removal of the oxide layer from the substrate, ensuring... The substrate surface is flat, clean, and free of any impurities, making it perfectly suited for the subsequent attachment and directional growth of superconducting materials. Based on the pretreated insulating substrate, a one-dimensional Fe(Te,Se) nanowire structure is prepared as a topological superconducting carrier. This nanowire is a continuous, unbroken one-dimensional linear structure with overall dimensions that strictly meet the integration requirements of micro- and nano-quantum devices. The width is controlled at the hundred-nanometer level, the thickness at the tens of nanometer level, and the length at the micrometer level. Furthermore, the structure has vertical sidewalls, regular edges, and few internal grain boundary defects, which can fully preserve the intrinsic topological superconducting properties of the Fe(Te,Se) material itself.

[0018] The resulting Fe(Te,Se) nanowire carrier structure is a one-dimensional topological superconducting substrate that combines a stable superconducting bandgap, intrinsically strong spin-orbit coupling, and a topologically nontrivial band structure. It can stably maintain its topological phase without a continuously applied external magnetic field, making it a suitable carrier for Majorana zero modes. Majorana zero modes are special fermionic quasiparticles whose antiparticles are themselves, and they can be stably bound at specific sites in topological superconductors. They are the core carriers for encoding quantum information in topological quantum computing, where quantum information can be nonlocally encoded in spatially separated Majorana zero modes. In the parity state of fermions formed by the Majorana zero mode, the Fe(Te,Se) nanowire carrier structure can achieve stable confinement and reliable support of the Majorana zero mode at its preset specific sites. At the same time, the physical size and electrical performance parameters of the carrier structure are highly matched with the actual implementation requirements of subsequent quantum dot coupling and tunneling path construction. It can be directly used as the carrier substrate for the Majorana zero mode in the subsequent preparation process, and finally, a Fe(Te,Se) nanowire carrier structure with regular structure, stable performance and can be directly used to support the Majorana zero mode is obtained.

[0019] Step 1.2: Based on the aforementioned carrier structure, at least two spatially separated Majorana zero modes are induced in the topological superconducting carrier through initialization operations to obtain a topological superconducting unit containing parity information carriers. Specifically, this includes: after the prepared Fe(Te,Se) nanowire carrier structure is stably fixed, it is placed in a low-temperature vacuum environment for gradient cooling. The cooling process is steadily controlled throughout to avoid structural or property damage to the material due to thermal stress. Finally, the ambient temperature is stabilized to a level far below the Fe(Te,Se) superconducting transition temperature to ensure that the nanowire material fully enters a stable superconducting state and that the intrinsic topological superconducting properties and spin-orbit coupling properties remain intact. Subsequently, a brief weak external magnetic field is applied to complete the initialization operation. The relevant parameters of the magnetic field are precisely controlled to precisely induce multiple mutually independent zero modes at multiple preset specific sites on the iron-based superconducting nanowire. The nanowires are constructed with vortex-state structures, each of which can stably confine a Majorana zero mode in its core region. This results in at least two spatially separated Majorana zero modes that are not directly coupled to each other. These spatially separated Majorana zero modes collectively constitute a fermion parity state, a quantum state determined by the occupancy number of the Majorana zero modes. This state is divided into even parity and odd parity. The core quantum information in topological quantum computing is encoded nonlocally in this fermion parity state, which thus becomes the core physical carrier of parity information. After the initialization operation is completed, the external magnetic field is immediately removed. The subsequent Majorana zero mode parity interferometry readout process does not require any magnetic field participation or control, ultimately resulting in a topological superconducting unit with a stable structure, intact properties, and containing the physical carrier of parity information.

[0020] Step 1.3: On one side of the topological superconducting unit, a set of quantum dot structures is prepared at a distance sufficient for tunneling coupling with two spatially separated Majorana zero modes. The quantum dots are then tunneled with the two Majorana zero modes to form at least two tunneling paths that can constitute closed virtual transition loops, resulting in a coupled structure containing quantum dots and tunneling paths. Specifically, this includes: preparing and coupling quantum dot structures in a pre-defined functional region on one side of the topological superconducting unit containing parity information carriers; performing a second precision cleaning of this pre-defined region to thoroughly remove residual impurities, oxide layers, and process contaminants from the surface, ensuring a clean and flat substrate environment for quantum dot preparation, providing a good foundation for structure preparation and coupling; and preparing a quantum dot core structure in the cleaned pre-defined region, ensuring the quantum dots are precisely positioned within the common coupling range of the two spatially separated Majorana zero modes, while precisely controlling the physical distance between the quantum dots and the two Majorana zero modes, keeping this distance precisely within the nanometer-scale tunneling coupling range. Within the critical range, it is ensured that the quantum dot can establish a reliable, stable, and electrically controllable tunneling coupling relationship with each of the two Majorana zero modes. Based on this stable tunneling coupling relationship, electrons can achieve bidirectional and controllable tunneling transport between the quantum dot and the two Majorana zero modes, thereby forming two tunneling paths that can constitute closed virtual transition loops. The first path is the tunneling channel from the quantum dot to the first Majorana zero mode, and the second path is the tunneling channel from the quantum dot to the second Majorana zero mode. The two tunneling paths are interconnected with the quantum dot as the core coupling node. They are not physical closed loops, but equivalent closed transport paths achieved by electrons through virtual transitions. Electrons can complete the virtual transition transport from one Majorana zero mode to another Majorana zero mode via the quantum dot along the two paths, together forming a complete closed virtual transition loop. This can effectively meet the core structural requirements of Majorana zero mode parity interferometry readout, and finally obtain a coupled structure that is structurally matched, stably coupled, and includes the quantum dot and the matching tunneling paths.

[0021] Step 1.4: Based on the coupling structure, by adjusting the gate voltage applied to the quantum dot, the quantum dot is brought into a charge degenerate state, and the tunneling coupling strength of the two tunneling paths tends to be balanced, resulting in a readout structure with an adjustable tunneling path in a test-ready state. Specifically, this includes: precisely fabricating a metal gate electrode in a predetermined gate region around the prepared quantum dot structure, ensuring no direct electrical contact between the gate electrode and the quantum dot, and that their capacitive coupling is within a controllable range; and constructing a gate voltage control loop based on this metal gate electrode. This loop is an independent electrical control loop specifically designed for quantum dot potential control. The system comprises a precision voltage output module, transmission line, filter module, and electrode connection terminal, enabling continuous gate voltage output, micro-step adjustment, and noiseless transmission. It can also be independently controlled without interference from other circuits. This gate voltage control loop applies a continuously adjustable gate voltage to the quantum dot, gradually fine-tuning the amplitude of the gate voltage in micro-steps. This slowly and smoothly changes the local potential distribution in the quantum dot region, allowing the quantum dot's electronic state to smoothly transition and stably enter a charge-degenerate state. In this state, the charge number of the quantum dot can continuously change with minute changes in the external potential, providing a stable physical basis for subsequent interference phase modulation and precise parity signal reading.

[0022] Simultaneously, the gate voltage is further finely gradient-controlled through the gate voltage regulation loop. The height and width of the tunneling barrier between the quantum dot and the two Majorana zero modes are synchronously adjusted by the change of local potential. The electron transport characteristics of the two tunneling paths are calibrated in real time, and the tunneling coupling strength of the two tunneling paths is gradually brought to a completely balanced equilibrium state. This allows the closed virtual transition loop to have a stable, symmetrical, and controllable interference tunneling physical basis, effectively eliminating signal offset, noise interference, and readout errors caused by the difference in coupling strength between the two paths. This ensures the stability, distinguishability, and accuracy of the subsequent interference signal, and finally yields a readout structure with adjustable tunneling paths that has been calibrated, has stable performance, and is in a test-ready state.

[0023] In a preferred embodiment of the present invention, step 2 above may include: Step 2.1: Based on the readout structure with adjustable tunneling paths in the test-state, a spin-orbit coupling modulation gate is set on at least one of the two tunneling paths to obtain a phase modulation structure with electrical control terminals. Specifically, this includes: based on the readout structure with adjustable tunneling paths that has been adjusted and is in the test-state, selecting the core region most sensitive to phase changes during electron tunneling transmission on at least one of the two tunneling paths, and deploying a dedicated electrode structure for controlling the spin-orbit coupling effect. This electrode structure is the spin-orbit coupling modulation gate. It is a functional electrode that achieves phase modulation through a local electric field. It consists of a conductive electrode, an insulating layer, and electrical lead-out terminals. It forms a non-contact capacitive coupling structure with the tunneling path below through the insulating layer. Without damaging the original structure of the tunneling path or affecting the normal tunneling transmission of electrons, it can change the local electric field distribution in the region where the tunneling path is located by external electrical signals. This changes the spin-orbit coupling strength of the charge carriers in the path, so that the phase characteristics of the tunneling path can be precisely controlled by electrical means. Finally, a phase modulation structure with independent electrical control terminals is obtained, which can achieve continuous and precise phase adjustment.

[0024] Step 2.2: Based on the phase modulation structure with electrically adjustable terminals, a scanning voltage is applied to the spin-orbit coupling modulation gate. By changing the amplitude of the scanning voltage, the spin-orbit coupling strength in the tunneling path is continuously adjusted. This causes the spin degree of freedom of electrons to precess at different angles under the spin-orbit coupling effect when they propagate in different tunneling paths. This introduces a continuously variable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, resulting in an interference parameter scanning result containing different phase conditions. Specifically, based on the already constructed phase modulation structure with electrically adjustable terminals, a set of continuously varying, small-step, and uniform scanning voltages is applied to the spin-orbit coupling modulation gate through the electrical adjustable terminals. As the amplitude of the scanning voltage gradually and smoothly changes, the spin degree of freedom of electrons in the tunneling path precesses at different angles under the spin-orbit coupling effect. The local electric field strength and distribution in the region are continuously and finely adjusted, thereby enabling continuous, linear, and stable control of the spin-orbit coupling strength of the charge carriers in the corresponding tunneling path. When electrons propagate in two different tunneling paths, their spin degrees of freedom will undergo spin precession at different angles under different spin-orbit coupling intensities. This difference in spin precession directly changes the phase evolution behavior of electrons during tunneling, thus introducing a continuously adjustable and controllable relative complex phase difference between the tunneling amplitudes of the two tunneling paths. During the entire process of the scanning voltage changing from the initial value to the final value, the phase conditions and interference state information corresponding to each set of scanning voltage amplitudes are synchronously collected and recorded, ultimately obtaining a set of interference parameter scanning results that cover multiple different phase conditions, are complete, and continuous.

[0025] Step 2.3: Based on the interference parameter scanning results, by simultaneously monitoring the output signal of the RF readout circuit coupled to the quantum dot, the scanning voltage amplitude corresponding to the maximum difference in the output signal due to different parity states is identified and determined as the phase operating point. This yields an electrical phase parameter for modulating interference conditions. Specifically, based on the obtained interference parameter scanning results containing different phase conditions, during the entire process of applying the scanning voltage to the spin-orbit coupled modulation gate, the response signal output by the RF readout circuit stably coupled to the quantum dot is simultaneously acquired and monitored in real time. The amplitude and trend of the output signal corresponding to the Majorana zero mode being in different fermion parity states under different scanning voltage amplitudes are fully recorded. By comparing and analyzing the distinguishability and difference amplitude of the output signal with parity state changes under different scanning voltages, the scanning voltage amplitude corresponding to the maximum difference and highest distinguishability of the output signal due to different parity states is accurately identified and determined. This amplitude is determined as the optimal phase operating point, and the fixed scanning voltage corresponding to this phase operating point is used as the control parameter for subsequent interference modulation. Finally, an electrical phase parameter that can be used for stable and precise modulation of interference conditions is obtained.

[0026] In a preferred embodiment of the present invention, step 2.3 above may include: Step 2.31: Based on the scanning results of interferometric parameters including different phase conditions, extract the correspondence between the output signal and the scanning voltage amplitude from the monitoring data recorded by the radio frequency readout circuit coupled to the quantum dot during the scanning process to obtain a set of output signal and voltage data pairs. Specifically, based on the obtained complete interferometric parameter scanning results including multiple different phase conditions, systematically organize the continuous monitoring data collected and stored in real time by the radio frequency readout circuit stably coupled to the quantum dot throughout the entire scanning voltage application process. From these complete and continuous monitoring data, extract the radio frequency output signal value corresponding to each acquisition moment and the scanning voltage amplitude applied to the spin-orbit coupling modulation gate at the same time in chronological order. Accurately match and correlate the radio frequency output signal value and the scanning voltage amplitude at the same moment to form multiple sets of one-to-one corresponding output signal and voltage data pairs to ensure that each set of data truly reflects the interferometric response state under the corresponding voltage, providing complete, accurate and orderly data support for subsequent signal fluctuation analysis.

[0027] Step 2.32 involves analyzing the output signal and voltage data pairs to determine the fluctuation amplitude of the output signal due to different parity states at each scanning voltage amplitude. This yields a distribution curve of the signal fluctuation amplitude as a function of the scanning voltage. Specifically, this includes: performing a point-by-point, voltage-value-by-voltage amplitude-by-point analysis on the extracted and processed multiple sets of output signal and voltage data pairs; for each determined scanning voltage amplitude, extracting and confirming the stable, noise-free RF output signal values ​​corresponding to the Majorana zero mode in both even-parity and odd-parity states; defining the absolute difference between the output signals corresponding to the two different parity states at the same scanning voltage amplitude as the signal fluctuation amplitude caused by different parity states under that voltage condition. This fluctuation amplitude directly characterizes the distinguishability of different parity states under the current phase modulation. Following the unified rules described above, the signal fluctuation amplitude corresponding to each voltage point within the entire scanning voltage amplitude range is calculated sequentially. After all calculations are completed, the scanning voltage amplitude is used as the abscissa of a two-dimensional coordinate system, and the corresponding calculated signal fluctuation amplitude is used as the ordinate. The data points consisting of each voltage and fluctuation amplitude are accurately marked in the coordinate system. Then, all discrete data points are connected in an orderly manner through a smooth and distortion-free fitting method to form a continuous, smooth, and clearly trending distribution curve of signal fluctuation amplitude as the scanning voltage changes. This curve fully presents the distribution characteristics of the rising segment, peak segment, and falling segment of the signal fluctuation amplitude during the gradual change of the scanning voltage. It can intuitively reflect the influence of different control voltages on the parity state differentiation effect, providing stable, reliable, and visualized data basis for accurately identifying the optimal phase operating point.

[0028] Step 2.33: Based on the distribution curve of signal fluctuation amplitude as a function of scanning voltage, identify the scanning voltage amplitude corresponding to the maximum value of the fluctuation amplitude as a candidate phase operating point. Specifically, this includes: based on the continuous, complete, and clearly trending distribution curve of signal fluctuation amplitude as a function of scanning voltage obtained through smoothing fitting, conduct a detailed segment-by-segment and point-by-point analysis of the curve's trend, magnitude, and morphological characteristics. First, by comparing the fluctuation amplitude values ​​of each segment of the curve, eliminate non-physical local small peaks caused by environmental interference, circuit noise, or data acquisition errors. Then, among the selected curve feature points, search for wave... The feature point with the largest amplitude, stable position, and a typical peak shape showing an initial rise to a peak and then a fall is identified as the effective peak point that can truly reflect the optimal state of interference. After determining the effective peak point, it is projected vertically downwards onto the horizontal axis in the two-dimensional coordinate system, and the scanning voltage value corresponding to the projection position is read. This value is the scanning voltage amplitude corresponding to the effective peak point. This scanning voltage amplitude, which makes the output signal difference between different fermion parity states most obvious, has the highest distinguishability, and the strongest reading reliability, is used as the candidate phase operating point for subsequent fixed control.

[0029] Step 2.34: Fix the scanning voltage amplitude corresponding to the candidate phase operating point to obtain the electrical phase parameters used for modulation interference conditions. Specifically, this includes: strictly locking and fixing the scanning voltage amplitude corresponding to the effective peak point accurately identified through the distribution curve; first, inputting the scanning voltage amplitude to the precision voltage output module of the gate voltage control circuit; filtering voltage fluctuation interference through the circuit's filtering module to ensure the stability and accuracy of the output voltage; then setting the fixed voltage amplitude as the constant operating voltage of the spin-orbit coupling modulation gate and continuously applying it to the spin-orbit coupling modulation gate, while simultaneously monitoring the two tunneling paths in real time. The relative complex phase difference was determined, confirming that the fixed voltage could keep the relative complex phase difference stable and in the optimal interference state, avoiding phase shift due to voltage fluctuations. Subsequently, the output signal corresponding to the fixed voltage was repeatedly verified to ensure that the difference in output signal under different fermion parity states remained at its maximum and the distinguishability remained stable. Finally, the verified, stable and reliable fixed scanning voltage amplitude was determined as the electrical phase parameter used to modulate the interference conditions in the subsequent interference process. This parameter can be used stably for a long time, providing a stable phase control basis for the accurate reading of the Majorana zero-energy mode parity state, and ensuring the reliability and repeatability of the entire reading process.

[0030] In a preferred embodiment of the present invention, step 3 above may include: Step 3.1: Based on the electrical phase parameters used for modulation interference conditions, the voltage of the spin-orbit coupling modulation gate is fixed at the candidate phase operating point to maintain a defined relative complex phase difference between the tunneling amplitudes of the two tunneling paths, resulting in a readout structure in a parity-sensitive interference state. Specifically, this includes: based on the defined, repeatedly verified, and reliable electrical phase parameters used for modulation interference conditions, the operating voltage of the spin-orbit coupling modulation gate is precisely fixed to the voltage amplitude corresponding to the identified candidate phase operating point through a gate voltage control circuit. The control circuit filters external electromagnetic interference and voltage fluctuations through a built-in filter module to ensure the stability and accuracy of the output voltage, with the error controlled within a preset allowable range. This maintains a defined, stable, and optimal relative complex phase difference between the tunneling amplitudes of the two tunneling paths. The correct mathematical expression for this relative complex phase difference is: ,in The defined relative complex phase difference between the two tunnel paths, in radians. rad , The fixed control voltage corresponding to the candidate phase operating point The inherent phase difference between the two tunneling paths when no control voltage is applied, in radians. radUltimately, a readout structure is obtained that can accurately respond to the parity state of the Majorana zero-energy mode, has stable interference effects, and is free from stray interference, and is in a parity-sensitive interference state.

[0031] Step 3.2: Based on the readout structure in a parity-sensitive interferometric state, utilizing the relative complex phase difference between the two tunneling paths, the effective tunneling amplitude of the closed virtual transition loop exhibits a dependence on the parity state of the fermions formed by the two Majorana zero modes, thus obtaining a parity-dependent tunneling coupling condition. Specifically, based on the readout structure already in a parity-sensitive interferometric state, relying on the established relative complex phase difference between the two tunneling paths, and fully utilizing the tunneling superposition characteristics of the closed virtual transition loop, the electron tunneling processes of the two tunneling paths interact to generate a stable interference effect. This interference effect directly alters the effective tunneling capability of a closed virtual transition loop, causing the effective tunneling amplitude of the loop to no longer be a fixed value. Instead, it undergoes a significant and regular change with the alteration of the fermion parity state formed by the two Majorana zero modes. Specifically, the fermion parity even state corresponds to a fixed effective tunneling amplitude, while the fermion parity odd state corresponds to another effective tunneling amplitude that is significantly different from the even state. The two form a unique and stable correlation. By confirming the specific rules of this correlation, the correspondence criterion between the tunneling coupling effect and the parity state under the current fixed relative complex phase difference can be determined.

[0032] The specific process is as follows: First, through repeated tests, the effective tunneling amplitude values ​​corresponding to the parity even state and parity odd state of fermions are recorded respectively. The one-to-one correspondence between the two parity states and their corresponding amplitudes is confirmed, and deviations caused by random fluctuations are eliminated. Then, the magnitude, stability, and repeatability of the amplitude differences are analyzed to confirm the direction, magnitude, and rate of change of the effective tunneling amplitude value when the parity state switches from an even state to an odd state (or vice versa). The consistency of this change law under the current fixed relative complex phase difference condition is verified. Then, the correspondence criterion between the tunneling coupling effect and the parity state is determined: that is, to determine the range and size of the effective tunneling amplitude value corresponding to the parity even state, and the range and size of the effective tunneling amplitude value corresponding to the parity odd state. At the same time, the applicable conditions, error range, and stability interval of this correspondence are clarified to ensure that the tunneling coupling effect corresponding to different parity states is significantly distinguishable and stable and reliable. Finally, a parity-dependent tunneling coupling condition is obtained in which the tunneling coupling effect clearly depends on the fermion parity state, the change law can be accurately controlled, and the stability and reliability are stable.

[0033] Step 3.3: Based on the parity-dependent tunneling coupling condition, the ground state energy of the quantum dot shifts accordingly with the current parity state, thereby causing the quantum capacitance of the quantum dot to exhibit distinguishable numerical differences under different parity states, resulting in a quantum capacitance signal carrying parity information. Specifically, based on the obtained parity-dependent tunneling coupling condition, the stable coupling characteristics between the quantum dot and the closed virtual transition loop are fully utilized. When the parity state of the fermion composed of two Majorana zero modes changes, the effective tunneling amplitude of the closed virtual transition loop will change accordingly. This change will be directly transmitted to the quantum dot through coupling, causing the ground state energy of the quantum dot to shift accordingly with the current parity state, wherein the parity even state... Corresponding to a stable ground state energy level Parity singularity Corresponding to another stable and with There are significant differences in ground state energy levels The ground-state energy shift of a quantum dot directly alters the distribution of charge carriers within it, thus affecting its quantum capacitance properties. This results in a significant and precisely distinguishable difference in the quantum capacitance of a quantum dot under different parity states. This difference uniquely and accurately reflects the current parity state, ultimately yielding a quantum capacitance signal carrying Majorana zero-mode parity information. The correct mathematical expression for this signal is: ; In the formula The quantum capacitance signal carries parity information and is measured in farads (F). P For fermion parity state. It is an even state. It is a singular state. The intrinsic quantum capacitance of a quantum dot when it is not affected by tunneling coupling is expressed in farads (F). k The proportionality constant is determined by the coupling strength between the quantum dot and the closed virtual transition loop, and is a positive real number. The amplitude of the total effective tunneling amplitude under different parity states, in electron volts. , The relative complex phase difference is fixed in step 3.1.

[0034] In a preferred embodiment of the present invention, step 3.2 above may include: Step 3.21: Based on the readout structure in a parity-sensitive interferometry state, obtain the tunneling amplitude expressions corresponding to the two tunneling paths, including the complex phase factor introduced by spin-orbit coupling, to obtain two path tunneling amplitudes carrying phase information. Specifically, based on the readout structure already in a parity-sensitive interferometry state, combined with the inherent material properties and transmission characteristics of the two tunneling paths, and the precise phase modulation effect introduced after the spin-orbit coupling modulation gate is fixed at the candidate phase operating point, derive and obtain the tunneling amplitude expressions corresponding to the two tunneling paths respectively. Both expressions include the complex phase factor introduced by spin-orbit coupling, thereby obtaining two path tunneling amplitudes carrying complete phase information. The correct mathematical expression for the tunneling amplitude of the first tunneling path is: The correct mathematical expression for the tunneling amplitude of the second tunneling path is: In the formula , These are the path tunneling amplitudes carrying phase information for the two tunneling paths, and are complex values. , These are the inherent tunneling amplitude values ​​of the two tunneling paths without phase modulation, respectively, and are positive real numbers in electron volts (eV). eV ), i The imaginary unit satisfies , , These are the complex phase factors introduced by spin-orbit coupling in the two tunneling paths, in radians. rad ),and , The value is determined by the fixed voltage corresponding to the candidate phase operating point. Precise decision.

[0035] Step 3.22: Based on the tunneling amplitudes of the two paths carrying phase information, and combined with the relative complex phase difference between the two tunneling paths, construct the total effective tunneling amplitude expression of the closed virtual transition loop with the relative complex phase difference as a variable parameter, to obtain a total effective tunneling amplitude function containing the relative complex phase difference parameter. Specifically, this includes: based on the obtained tunneling amplitudes of the two paths carrying phase information... and Combined with the relative complex phase difference between the two determined tunnel paths The correct mathematical relationship is: Based on the principle of electron tunneling superposition in closed virtual transition loops, the tunneling amplitudes of the two paths are vector-superimposed to construct an expression for the total effective tunneling amplitude of the closed virtual transition loop. This expression uses the relative complex phase difference between the two tunneling paths. With the only variable parameter being the total effective tunneling amplitude function, and all other parameters being fixed, a total effective tunneling amplitude function containing the relative complex phase difference parameter is obtained. The correct mathematical expression for this function is: In the formula Let be the total effective tunneling amplitude function including the relative complex phase difference parameter, and be a complex value. , These are the tunneling amplitudes carrying phase information for the two paths, respectively. These are the inherent tunneling amplitude values ​​for the two paths. i The imaginary unit, , For the complex phase factor of the two paths, The relative complex phase difference between the two paths, in radians ( rad ).

[0036] Step 3.23: Based on the total effective tunneling amplitude function, using the fermion parity state composed of two Majorana zero modes as variables, calculate the amplitude of the total effective tunneling amplitude in both parity even and parity odd states to obtain a quantitative correspondence between the parity state and the effective tunneling amplitude. Specifically, this includes: based on the total effective tunneling amplitude function obtained in step 3.22... Using the fermion parity state formed by two Majorana zero-energy modes as the core variable, the fermion parity even state is explicitly denoted as... Fermi parity singularity is denoted as For each of the two parity states, the corresponding parity factor is substituted into the total effective tunneling amplitude function to calculate the amplitude. The correct mathematical expression for the amplitude of the total effective tunneling amplitude under the parity even state is: The correct mathematical expression for the amplitude of the total effective tunneling amplitude under parity singularity is: In the formula , , respectively, represent the amplitudes of the total effective tunneling amplitude in parity even and parity odd states, and are positive real numbers in electron volts (eV). eV ), The total effective tunneling amplitude function, , These are the inherent tunneling amplitude values ​​for the two paths. i The imaginary unit, , For the complex phase factor of the two paths, With a fixed relative complex phase difference, the total effective tunneling amplitude corresponding to the two parity states is obtained through precise calculation, thereby obtaining a clear, unique and repeatable quantitative correspondence between the parity state and the effective tunneling amplitude.

[0037] Step 3.24: Based on the quantitative correspondence between the parity state and the effective tunneling amplitude, determine the variation of the effective tunneling amplitude with the parity state under the current relative complex phase difference condition, and obtain the parity-dependent tunneling coupling condition. Specifically, this includes: based on the obtained quantitative correspondence between the parity state and the effective tunneling amplitude, combined with the fixed relative complex phase difference... Further analysis of the two parity states (even states) strange The specific differences, trends, and stability of the effective tunneling amplitude corresponding to the given conditions were verified through repeated calculations. This clarified that, under the current fixed relative complex phase difference, the effective tunneling amplitude changes from an even state with the parity state. Become a singularity (or from singularity) Transform into an even state The specific variation law of fermion parity is determined to ensure that this variation law is not affected by minor external disturbances and has good repeatability. It is ensured that the effective tunneling amplitude corresponding to different parity states has significant and accurately distinguishable differences, and there are no overlapping or fuzzy areas. Finally, a parity-dependent tunneling coupling condition is obtained in which the tunneling coupling effect is clearly dependent on the fermion parity state, the variation law can be accurately controlled, and it is stable, reliable and repeatable.

[0038] In a preferred embodiment of the present invention, step 4 above may include: Step 4.1: Based on the parity-dependent tunneling coupling condition, the quantum dot is connected to an RF resonant cavity via capacitive coupling, and the RF resonant cavity is connected to an RF readout circuit to obtain a quantum capacitance measurement link in a test state. Specifically, this includes: based on the established and verified effective parity-dependent tunneling coupling condition, the control electrode and sensing electrode of the quantum dot are stably connected to the coupling capacitor node of the RF resonant cavity via a lossless, low-parasitic, and high-linear capacitive coupling method, so that the quantum capacitance of the quantum dot, which changes with the parity state, can directly and sensitively change the overall equivalent resonance parameter of the RF resonant cavity. Then, the signal input port and signal output port of the RF resonant cavity are respectively connected to the RF readout circuit. The RF readout circuit is an integrated, low-noise, and high-sensitivity microwave measurement circuit, mainly composed of a precision microwave signal source, a directional coupler, a low-noise amplifier, a mixer, a filtering module, a quadrature phase detection module, and a data acquisition and processing module.

[0039] The system comprises a precision microwave signal source for outputting a stable probe microwave signal with consistent amplitude and frequency; a directional coupler for separating the incident and reflected signals; a low-noise amplifier for improving the signal-to-noise ratio of weak response signals; a mixer and quadrature phase detection module for down-converting the high-frequency RF signal into a directly acquireable low-frequency baseband signal; a filtering module for suppressing external electromagnetic interference and circuit noise; and a data acquisition and processing module for real-time acquisition, analysis, and output of key characteristic parameters such as reflection coefficients or transmission coefficients. The entire RF readout circuit features wideband response, high isolation, excellent impedance matching characteristics, and high signal acquisition accuracy. Impedance matching structures are incorporated in the connection path to reduce signal reflection and loss. This constructs a complete, stable, and highly resistant quantum capacitance measurement link from the quantum dot and RF resonant cavity to the RF readout circuit, meeting the requirements for precise quantum state detection. The total equivalent capacitance formed between the quantum dot and the RF resonant cavity can be expressed as… ,in This is the total equivalent capacitance of the radio frequency resonant cavity. This refers to the inherent cavity capacitance of the radio frequency resonant cavity itself. For the parity state of fermions P The quantum dot quantum capacitor undergoes significant changes, ultimately resulting in a stable, stray-coupled quantum capacitance measurement link that can be directly used for precise detection of quantum capacitance.

[0040] Step 4.2: Based on the quantum capacitance measurement link in the test state, a probe microwave signal is applied to the RF resonant cavity, while simultaneously monitoring the reflection coefficient or transmission coefficient of the RF resonant cavity to obtain an RF response signal carrying quantum dot state information. Specifically, this includes: based on the fully constructed and impedance-matched quantum capacitance measurement link in a stable test state, a continuous wave single-frequency probe microwave signal with precise frequency, stable amplitude, and stable phase is applied to the RF resonant cavity through the signal source module inside the RF readout circuit. This ensures the probe microwave signal operates near the resonant frequency of the RF resonant cavity to guarantee maximum detection sensitivity. While continuously applying the probe microwave signal, the reflected or transmitted signal at the output of the RF resonant cavity is simultaneously acquired, and the corresponding reflection coefficient or transmission coefficient is calculated in real time. The complete expression for the reflection coefficient is: ,in The reflection coefficient of the radio frequency resonant cavity is denoted as . This represents the load impedance of the RF resonant cavity after the quantum dots are coupled. The standard characteristic impedance set uniformly for the RF readout circuit and the transmission link will cause the calculated reflection coefficient or transmission coefficient to shift significantly with the changes in quantum dot tunneling coupling strength and quantum capacitance, thus obtaining a complete high signal-to-noise ratio RF response signal carrying quantum dot energy level state, tunneling amplitude information and parity state information.

[0041] Step 4.3: Based on the radio frequency response signal carrying quantum dot state information, extract the quantum capacitance value of the quantum dot from the change in reflection coefficient or transmission coefficient to obtain the measured value of the quantum capacitance corresponding to the current parity state. Specifically, this includes: based on the radio frequency response signal with high signal-to-noise ratio and carrying quantum dot state information that has been acquired in real time, performing stable tracking and fine analysis on the trajectory of the change in reflection coefficient or transmission coefficient in the complex plane, extracting key characteristic parameters such as the actual resonant frequency offset, quality factor change, and impedance change of the radio frequency resonant cavity, and then using the standard physical relationship between the inherent resonant frequency and the total equivalent capacitance of the radio frequency resonant cavity. Perform reverse calculation, where This is the actual operating resonant frequency of the radio frequency resonant cavity. For the fixed resonant inductor of the radio frequency resonant cavity, The total equivalent capacitance, including the quantum dot quantum capacitance, can be calculated by subtracting the pre-calibrated inherent resonant capacitance of the radio frequency resonant cavity when there is no quantum dot coupling. This allows for the precise separation and extraction of the current true quantum capacitance value of the quantum dot, which is the measured value of the quantum capacitance corresponding to the current fermion parity state.

[0042] Step 4.4: Compare the measured value of the quantum capacitance corresponding to the current parity state with the pre-calibrated parity-capacitance correspondence to obtain the comparison result. Simultaneously, determine whether the current parity state is a parity even state or a parity odd state based on the comparison result, obtaining a parity state reading result based on pure electrical control. Specifically, this includes: performing a point-by-point, high-precision numerical comparison between the precisely calculated measured value of the quantum capacitance corresponding to the current parity state and a pre-established parity-capacitance standard correspondence data table, established through multiple repeated calibration experiments under the same control voltage, temperature, and microwave power conditions. This standard correspondence has precisely distinguished and calibrated the stable quantum capacitance standard intervals corresponding to parity even states and parity odd states; the two intervals are independent of each other. The method is characterized by non-overlapping, significant distinguishability, and good repeatability. During the comparison process, the deviation between the measured value of quantum capacitance and the center value of two standard intervals is first calculated. Then, the standard interval to which the measured value uniquely belongs is determined. If the measured value falls within the standard interval of quantum capacitance corresponding to the parity even state, the fermion parity state composed of the two Majorana zero modes is determined to be a parity even state. If the measured value falls within the standard interval of quantum capacitance corresponding to the parity odd state, the fermion parity state is determined to be a parity odd state. The entire determination and reading process is achieved solely through electrical control, electrical detection, and electrical calculation, without relying on any external magnetic field, optical reading, or other auxiliary means. Ultimately, a parity state reading result based on pure electrical control, stable reading, strong anti-interference ability, low misjudgment rate, and repeatability is obtained.

[0043] The parity state readout results can be directly applied to the field of topological quantum computing, serving as the core basis for qubit state readout. This enables qubit initialization verification, quantum state evolution monitoring, and the reading and output of quantum computing results. Simultaneously, it can be applied to the stability detection and control optimization of Majorana zero modes, providing reliable electrical readout support for the integrated and miniaturized development of topological quantum devices. It can also be used in the field of quantum sensing, achieving high-sensitivity detection of weak signals through accurate parity state readout.

[0044] The specific implementation of the embodiments of the present invention further includes the following processes and methods: The technical problem to be solved is to achieve interference readout of MZM parity information without the need for external magnetic flux modulation, and to construct a topological qubit readout architecture that can be controlled electrically. Specifically, it aims to solve the following technical problems: First, it replaces the traditional AB flux phase modulation mechanism. Existing interferometric parity readout schemes typically rely on external flux to modulate the phase difference in the interferometric circuit to achieve the difference in measurable signals corresponding to different parity states. This phase modulation method depends on precise magnetic field control and is closely related to the system's magnetic environment. This invention proposes a phase control mechanism that does not require external flux, achieving equivalent phase control through electrical parameter adjustment, thereby reducing dependence on the magnetic field environment.

[0045] Second, parity distinguishability is maintained without introducing external magnetic field modulation. The key to parity readout lies in the ability of different parity states to produce distinguishable differences in the measurement signal. This invention requires the construction of a stable and detectable physical response mechanism for different parity states within an electrical control framework, ensuring sufficient detectability of the readout signal.

[0046] Third, it reduces system complexity caused by magnetic field dependence. In existing technologies, magnetic field generation and control typically require additional current coils, bias circuits, and related stabilization systems. This invention introduces a fully electronically controlled modulation method, reducing or eliminating the need for additional magnetic field control units, thereby simplifying device structure, reducing system design complexity, and providing a more compact implementation path for subsequent integration.

[0047] Fourth, it improves system scalability. In multi-qubit array structures, external magnetic fields can couple to neighboring devices, increasing the difficulty of system-level isolation and optimization. This invention constructs a readout mechanism that does not require magnetic field participation, enabling each qubit unit to operate within a relatively independent electrical control framework. This helps reduce the mutual influence between different readout units caused by magnetic fields, thus providing a more scalable technical foundation for the subsequent large-scale array design of topological qubits.

[0048] Fifth, this embodiment realizes an electrically controlled topological qubit readout architecture that does not require magnetic flux modulation. By utilizing electrically controllable physical mechanisms (such as spin-orbit coupling strength modulation or related electric field control parameters), this embodiment constructs a readout structure that can be precisely controlled by gate voltage or other electrical signals, allowing both parity information modulation and readout to be completed within a unified electrical control system. This approach helps improve the response speed and control accuracy of the readout process and facilitates interface compatibility with existing superconducting quantum circuits or semiconductor electrical control platforms. In summary, the technical objective of this embodiment is not simply to change the measurement method, but rather, while maintaining the feasibility of parity readout, to replace the magnetic flux modulation mechanism with an electrical approach, constructing a topological qubit readout scheme that reduces magnetic field dependence, simplifies the system structure, and has better scalability potential. By solving the above technical problems, a more easily integrated and scalable technical path can be provided for the engineering implementation of topological quantum computing systems.

[0049] To address the issue that existing interferometric parity readout schemes based on external magnetic flux modulation are highly dependent on the magnetic field environment, this embodiment proposes a topological qubit readout architecture that achieves parity interferometric readout without external magnetic flux modulation, based on spin-orbit coupling (SOC, which refers to the interaction between the electron's spin and its direction of motion, which can lead to spin precession).

[0050] The basic technical idea is to utilize spin-orbit coupling to introduce an electrically controllable phase difference, replacing the magnetic flux phase modulation mechanism, to achieve a controllable phase difference between two tunneling paths, thereby constructing a parity-dependent interference modulation effect. In a transmission path containing Rashba-type spin-orbit coupling, the electron's spin rotates around the direction of the equivalent magnetic field during propagation. This spin rotation can introduce phase in a closed path, thus forming a controllable phase difference between paths without the need for external magnetic flux.

[0051] The core understanding of this embodiment is that the key condition for interferometric parity readout is not necessarily the introduction of magnetic flux itself, but rather the establishment of an adjustable relative phase difference between the two tunneling paths. This phase difference can be continuously adjusted under electrical control through spin-orbit coupling modulation.

[0052] Structural design includes the following components: (1) A topological superconducting carrier structure is preferred, preferably using an iron-based superconducting system, such as Fe(Te,Se) nanowires. Spatially separated micro-ZMs can be formed in this structure. The MZMs can exist in a vortex state and remain stable under appropriate conditions. This topological superconducting structure serves as a physical carrier of parity information. Studies have shown that even after the magnetic field is removed, the MZMs in the iron-based superconducting system can still exist for a certain period of time. Therefore, this system has the potential for purely electrically controlled parity readout processes. As an alternative, one-dimensional semiconductor-superconductor nanowires can also be used. This structure requires an external magnetic field to bring the system into the topological phase.

[0053] (2) An interference coupling structure comprising two spatially separated MZMs; a quantum dot structure for realizing electron tunneling coupling; at least two tunneling channels capable of forming closed virtual transition paths; a quantum dot structure with a transmission path having adjustable spin-orbit coupling strength; and a radio frequency quantum capacitor readout circuit or equivalent electrical readout unit. The two MZMs are coupled to the quantum dot, allowing electrons to form effective closed virtual transition loops through different paths. The path includes an adjustable segment with spin-orbit coupling, the SOC strength of which can be adjusted by the gate voltage.

[0054] Working principle: In the interference scheme based on magnetic flux loops, two MZMs are coupled to a quantum dot, and electrons form a closed loop through two paths. An external magnetic flux generates a phase difference. This results in the effective tunneling amplitude having the following form: ; in P For MZM parity ( P = ±1); It is the effective tunneling amplitude, a complex value, and a unitless amplitude characteristic (characterizing the tunneling probability). It is the total tunneling amplitude of an electron passing through two tunneling paths in a closed loop, and its amplitude determines the degree of correction of the quantum dot energy level. The applied magnetic flux is expressed in Weber (Wb), and is related to the Aharonov-Bohm effect formula. The meaning is consistent; , These are the inherent tunneling amplitudes of the two tunneling paths, positive real numbers, dimensionless, representing the electron tunneling capability of a single path; i It is the imaginary unit, satisfying i 2 =-1, used to describe the quantum mechanical properties of complex phase; For the interference phase The introduced complex phase factor, a complex value with a modulus of 1, only changes the phase characteristics of the tunneling amplitude, without changing the amplitude. This represents the interference phase of the Aharonov-Bohm effect, which is dimensionless. Different parities correspond to different interference results, leading to corrections in the quantum dot energy levels and changes in quantum capacitance. ; in, These are the quantum dot quantum capacitances in even and odd parity states, respectively, measured in farads (F). There is a significant and distinguishable numerical difference between the two, which is the direct signal for parity readout. e It is the elementary charge, with a value of approximately 1.602 × 10⁻⁻¹. 19 C This is consistent with the meaning of the magnetic flux quantum formula; The spin-orbit coupling strength is expressed in units of 1. eV · nm The phase difference, which characterizes the strength of the interaction between electron spin and direction of motion in the material, is the core parameter for electrically controlling the phase difference in this embodiment and can be continuously adjusted by the gate voltage. quantum dot detuning ED The second-order partial differential operator, without units, characterizes the second-order rate of change of quantum capacitance with respect to detuning. ED This is the quantum dot detuning quantity, measured in electron volts (eV). eV ); The effective tunneling amplitude is a positive real number with no unit; it is the modulus of the effective tunneling amplitude and determines the magnitude of the quantum dot energy level correction. For the compound operation terms in the formula, the unit is ( eV ) 3 / 2 , is the mathematical correlation term between quantum capacitance and tunneling amplitude and detuning.

[0055] In this embodiment, no external magnetic flux is introduced. Instead, the spin rotation caused by SOC is utilized, which, under spin projection conditions, is equivalent to the complex phase of the tunneling amplitude. Specifically, when SOC exists, the tunneling coupling coefficient can be expressed as a complex number containing spin projection and rotation matrix factors, such that the effective tunneling amplitudes of the two paths... λ 1. λ Both 2 are complex numbers. Because different paths involve different spin rotations, λ 1 and λ There is a naturally adjustable complex phase difference between 2. In the weak coupling limit, electrons form a closed loop through a virtual transition process, and its effective energy correction term can be expressed as... λ 1|、| λ 2|and parity P Related terms. The resulting energy correction and parity. P It is directly proportional, and its magnitude depends on λ 1 and λThe relative complex phase between the two paths. Therefore, as long as there is a non-zero phase difference between the tunneling amplitudes of the two paths, a parity-dependent energy correction effect can be achieved under flux-free conditions, thereby enabling parity differentiation through quantum capacitance or equivalent electrical signals.

[0056] Purely electric control implementation: In this embodiment, the spin-orbit coupling strength It can be adjusted via the gate voltage. The phase approximation introduced by the SOC is similar to... and effective path length L Since they are positively correlated, the phase difference between paths can be continuously controlled by adjusting the gate voltage, thus achieving electrical control of the interference conditions. This control method does not require the introduction of an external magnetic field or flux bias coil, thereby reducing magnetic field-related crosstalk and system complexity, which is beneficial for the integration of multi-qubit array structures.

[0057] Technical Effects: Through the above technical solutions, this invention achieves the construction of a parity-dependent interferometric readout mechanism without the need for external magnetic flux; realizes continuous phase tunability using electrical methods; reduces the system structural complexity caused by magnetic field dependence; improves the scalability and integration compatibility of the qubit readout architecture; and constructs an electrically controlled topological qubit readout framework. In particular, when the topological superconducting carrier is an iron-based superconductor, it enables the realization and readout architecture of topological qubits without any external magnetic field.

[0058] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation, characterized in that, The method includes: A topological qubit readout structure is constructed, the readout structure including at least a topological superconducting carrier for carrying at least two spatially separated Majorana zero modes; and a set of quantum dot structures, each coupled to two spatially separated Majorana zero modes, forming at least two tunneling paths that can constitute closed virtual transition loops, thus obtaining a readout structure with tunable tunneling paths. Based on the readout structure with adjustable tunneling path, the spin-orbit coupling strength in the tunneling path is electrically controlled so that when electrons propagate in different paths, their spin degrees of freedom precess under the action of spin-orbit coupling, thereby introducing a controllable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, and obtaining an electrical phase parameter for modulating the interference condition. According to the electrical phase parameters, the effective tunneling amplitude of the closed virtual transition circuit is made to exhibit a dependence on the parity state of the Majorana zero mode, thereby causing the ground state energy of the quantum dot and its quantum capacitance to undergo a distinguishable shift with the parity state, resulting in a quantum capacitance signal carrying parity information. By using a radio frequency readout circuit coupled to the quantum dot, the change in the quantum capacitance signal carrying parity information is measured, and this change is mapped to the parity information of the Majorana zero mode, thereby obtaining a parity state readout result based on pure electrical control without applying an external magnetic field.

2. The Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation according to claim 1, characterized in that, A topological qubit readout structure is constructed, comprising at least a topological superconducting carrier for carrying at least two spatially separated Majorana zero modes; and a set of quantum dot structures coupled to the two spatially separated Majorana zero modes respectively, forming at least two tunneling paths that can constitute closed virtual transition loops, thereby obtaining a readout structure with tunable tunneling paths, including: A topological superconducting support is prepared, wherein the topological superconducting support is selected from an iron-based superconducting material with intrinsic topological superconducting properties, thereby obtaining a support structure that can be used to support Majorana zero energy modes; Based on the carrier structure, at least two spatially separated Majorana zero modes are induced in the topological superconducting carrier through initialization operations, resulting in a topological superconducting unit containing parity information carrier. On one side of the topological superconducting unit, a set of quantum dot structures is prepared at a distance that forms tunnel coupling with two spatially separated Majorana zero modes. The quantum dots are then tunnel coupled with the two Majorana zero modes to form at least two tunneling paths that can constitute closed virtual transition loops, resulting in a coupled structure containing quantum dots and tunneling paths. Based on the coupling structure, by adjusting the gate voltage applied to the quantum dot, the quantum dot is made to enter a charge degeneracy state, and the tunneling coupling strength of the two tunneling paths tends to be balanced, thus obtaining a readout structure with an adjustable tunneling path in a test state.

3. The Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling and magnetic field-free electronically controlled modulation according to claim 2, characterized in that, By electrically controlling the spin-orbit coupling strength in the tunneling path, the spin degree of freedom of electrons precesses under the spin-orbit coupling effect as they propagate in different paths. This introduces a controllable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, resulting in an electrical phase parameter for modulating the interference condition, including: Based on the readout structure with an adjustable tunneling path in the test state, a spin-orbit coupling modulation gate is set on at least one of the two tunneling paths to obtain a phase modulation structure with an electrical control terminal. Based on a phase modulation structure with electrical control terminals, a scanning voltage is applied to the spin-orbit coupling modulation gate. By changing the amplitude of the scanning voltage, the spin-orbit coupling strength in the tunneling path is continuously controlled. When electrons propagate in different tunneling paths, their spin degrees of freedom precess at different angles under the action of spin-orbit coupling. This introduces a continuously variable relative complex phase difference between the tunneling amplitudes of the two tunneling paths, resulting in an interference parameter scanning result containing different phase conditions. Based on the scanning results of the interference parameters, by simultaneously monitoring the output signal of the radio frequency readout circuit coupled to the quantum dot, the scanning voltage amplitude corresponding to the point where the output signal has the greatest difference due to different parity states is identified, and this is determined as the phase operating point, thus obtaining an electrical phase parameter for modulating the interference conditions.

4. The Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling magnetic field-free electronically controlled modulation according to claim 3, characterized in that, Based on the interference parameter scanning results, by simultaneously monitoring the output signal of the RF readout circuit coupled to the quantum dot, the scanning voltage amplitude corresponding to the point where the output signal exhibits the greatest difference due to parity state is identified and determined as the phase operating point. This yields an electrical phase parameter for modulating the interference conditions, including: Based on the scanning results of interference parameters with different phase conditions, the correspondence between the output signal and the scanning voltage amplitude is extracted from the monitoring data recorded by the radio frequency readout circuit coupled to the quantum dot during the scanning process, and a set of output signal and voltage data pairs is obtained. By analyzing the output signal and voltage data pairs, the fluctuation amplitude of the output signal caused by different parity states under each scanning voltage amplitude is determined, and the distribution curve of the signal fluctuation amplitude as a function of scanning voltage is obtained. Based on the distribution curve of signal fluctuation amplitude as a function of scanning voltage, the scanning voltage amplitude corresponding to the maximum value of fluctuation amplitude is identified as a candidate phase operating point. The scanning voltage amplitude corresponding to the candidate phase operating point is fixed to obtain the electrical phase parameters used for modulation interference conditions.

5. The Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling magnetic field-free electronically controlled modulation according to claim 4, characterized in that, Based on the electrical phase parameters, the effective tunneling amplitude of the closed virtual transition loop exhibits a dependence on the parity state of the Majorana zero mode, thereby causing a distinguishable shift in the ground state energy and quantum capacitance of the quantum dot with respect to the parity state, resulting in a quantum capacitance signal carrying parity information, including: Based on the electrical phase parameters used for modulation interference conditions, the voltage of the spin-orbit coupling modulation gate is fixed at the candidate phase operating point so that a certain relative complex phase difference is maintained between the tunneling amplitudes of the two tunneling paths, resulting in a readout structure in a parity-sensitive interference state. Based on the readout structure in a parity-sensitive interference state, by utilizing the relative complex phase difference between the two tunneling paths, the effective tunneling amplitude of the closed virtual transition loop is made to exhibit a dependence on the parity state of the fermions composed of the two Majorana zero modes, thus obtaining a parity-dependent tunneling coupling condition. Based on the parity-dependent tunneling coupling condition, the ground state energy of the quantum dot shifts accordingly with the current parity state, thereby making the quantum capacitance of the quantum dot exhibit distinguishable numerical differences under different parity states, thus obtaining a quantum capacitance signal carrying parity information.

6. The Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling magnetic field-free electronically controlled modulation according to claim 5, characterized in that, Based on the readout structure in a parity-sensitive interferometric state, and utilizing the relative complex phase difference between the two tunneling paths, the effective tunneling amplitude of the closed virtual transition loop exhibits a dependence on the parity state of the fermions formed by the two Majorana zero-energy modes, thus obtaining a parity-dependent tunneling coupling condition, including: Based on the readout structure in a parity-sensitive interferometric state, the tunneling amplitude expressions corresponding to the two tunneling paths are obtained, including the complex phase factor introduced by spin-orbit coupling, to obtain the tunneling amplitudes of the two paths carrying phase information. Based on the tunneling amplitudes of the two paths carrying phase information, and combined with the relative complex phase difference between the two tunneling paths, an expression for the total effective tunneling amplitude of the closed virtual transition loop with the relative complex phase difference as a variable parameter is constructed, resulting in a total effective tunneling amplitude function containing the relative complex phase difference parameter. Based on the total effective tunneling amplitude function, the fermion parity state composed of two Majorana zero modes is used as a variable to calculate the amplitude of the total effective tunneling amplitude under parity even state and parity odd state, respectively, and obtain the quantitative correspondence between the parity state and the effective tunneling amplitude. Based on the quantitative correspondence between parity state and effective tunneling amplitude, the law of change of effective tunneling amplitude with parity state under the current relative complex phase difference condition is determined, and the parity-dependent tunneling coupling condition is obtained.

7. The Majorana zero-energy mode parity interferometry readout method based on spin-orbit coupling magnetic field-free electronically controlled modulation according to claim 6, characterized in that, By using a radio frequency readout circuit coupled to the quantum dot, the change in the quantum capacitance signal carrying parity information is measured, and this change is mapped to the parity information of the Majorana zero mode. Thus, without applying an external magnetic field, a parity state readout result based on purely electrical control is obtained, including: Based on the parity-dependent tunneling coupling condition, the quantum dot is connected to a radio frequency resonant cavity via capacitive coupling, and the radio frequency resonant cavity is connected to a radio frequency readout circuit to obtain a quantum capacitance measurement link in a state to be measured. Based on the quantum capacitance measurement link in the test state, a probe microwave signal is applied to the radio frequency resonant cavity, and the reflection coefficient or transmission coefficient of the radio frequency resonant cavity is monitored at the same time to obtain a radio frequency response signal carrying quantum dot state information. Based on the radio frequency response signal carrying quantum dot state information, the quantum capacitance value of the quantum dot is extracted from the change in the reflection coefficient or transmission coefficient, and the measured value of the quantum capacitance corresponding to the current parity state is obtained. The measured value of the quantum capacitance corresponding to the current parity state is compared with the pre-calibrated parity-capacitance correspondence to obtain the comparison result. At the same time, the current parity state is determined to be either parity even or parity odd based on the comparison result, thus obtaining a parity state reading result based on pure electrical control.

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