Superconducting-based quantum computing device and method for implementing CNOT gate in superconducting-based quantum computing device

Abstract

The present invention provides a superconducting-based quantum computing device and a method for implementing a CNOT gate in a superconducting-based quantum computing device, wherein the CNOT gate is implemented by using a cross-resonance (CR) pulse in a hybrid system including a transmon and a parity-protected superconducting qubit (PPQ).

Description

Superconductivity-based quantum computing devices and methods for implementing CNOT gates in superconductivity-based quantum computing devices.

[0001] The present invention relates to a technology for implementing a CNOT gate based on a CR pulse in a hybrid system in which a transmon and a PPQ (parity-protected superconducting qubit) are indirectly connected through a resonator, in a superconducting-based quantum computing device and a method for implementing a CNOT gate in a superconducting-based quantum computing device.

[0002] Superconducting qubits are promising candidates for quantum computers. They are based on a Cooper-pair box (CPB) and utilize charge qubits and transmons. Transmons exhibit better tolerance to background charge noise than charge qubits. While a traditional CPB is permeated by a single Cooper pair, a parity-protected superconducting qubit (PPQ) is permeated by two Cooper pairs. Therefore, PPQ represents a superconducting (SC) qubit that preserves the island's parity.

[0003] Previously, a technology was proposed to connect two-qubit gates, transmon and PPQ, via a capacitor. However, this existing technology directly connects the two qubit gates and uses magnetic fields rather than pulses. This resulted in a difference in qubit frequencies between transmon and PPQ, limiting the fabrication of two-qubit gates utilizing cross-resonance.

[0004] The purpose of the present invention is to implement a CNOT gate using CR pulses in a new type of hybrid system in which a transmon and a PPQ are connected through a resonator.

[0005] However, the technical problems to be solved by the present invention are not limited to the above problems, and can be expanded in various ways without departing from the technical spirit and scope of the present invention.

[0006] In a superconducting-based quantum computing device according to an embodiment of the present invention, a CNOT gate is implemented using a cross-resonance pulse (CR pulse) in a hybrid system composed of a transmon and a PPQ (parity-protected superconducting qubit).

[0007] A method for implementing a CNOT gate in a superconducting-based quantum computing device according to an embodiment of the present invention includes a step of applying a CR pulse (cross-resonance pulse) to a hybrid system composed of a transmon and a PPQ (parity-protected superconducting qubit) and a step of implementing a CNOT gate using the CR pulse.

[0008] According to an embodiment of the present invention, a CNOT gate can be implemented with high fidelity by using a CR pulse that can locally apply a pulse only to a specific area in a hybrid system in which a transmon and a PPQ are indirectly connected using a resonator.

[0009] However, the effects of the present invention are not limited to the above effects, and can be expanded in various ways without departing from the technical spirit and scope of the present invention.

[0010] FIG. 1 illustrates the configuration of a superconducting-based quantum computing device using a hybrid system according to an embodiment of the present invention.

[0011] FIG. 2a and FIG. 2b illustrate a pulse protocol for performing a CNOT gate according to an embodiment of the present invention.

[0012] FIG. 3 is a table showing the pulse parameters and average fidelity of CNOTTP in a hybrid system according to an embodiment of the present invention.

[0013] FIG. 4a and FIG. 4b illustrate the gate success probability for the calculation basis state of CNOTTP and the circuit identity for performing CNOTPT according to an embodiment of the present invention.

[0014] FIG. 5 illustrates an operational flowchart of a method for implementing a CNOT gate in a superconducting-based quantum computing device according to an embodiment of the present invention.

[0015] The advantages and features of the present invention, and the methods for achieving them, will become clearer with reference to the embodiments described in detail below together with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but may be implemented in various different forms. These embodiments are provided solely to ensure that the disclosure of the present invention is complete and to fully inform those skilled in the art of the scope of the invention, and the present invention is defined solely by the scope of the claims.

[0016] The terminology used herein is for the purpose of describing embodiments and is not intended to limit the present invention. In this specification, the singular also includes the plural unless specifically stated otherwise. As used herein, the terms "comprises" and / or "comprising" do not exclude the presence or addition of one or more other components, steps, operations, and / or elements.

[0017] Unless otherwise defined, all terms (including technical and scientific terms) used herein may be used in their common sense to those of ordinary skill in the art to which the present invention pertains. Furthermore, terms defined in commonly used dictionaries are not to be interpreted ideally or excessively unless explicitly and specifically defined otherwise.

[0018] Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the attached drawings. Identical components in the drawings are designated by the same reference numerals, and redundant descriptions of identical components are omitted.

[0019]

[0020] The present invention is directed to implementing a new type of CNOT (Controlled NOT) gate by supplying a CR pulse (cross resonance pulse) to a hybrid system formed of a tunable transmon and a parity-protected superconducting qubit (PPQ).

[0021] At this time, the CNOT gate is the most basic among multi-qubit gates, operating on two qubits and receiving two inputs: the control qubit state and the target qubit state. Its role is to apply the X gate to the target qubit only when the control qubit state is in the excited state. Therefore, the CNOT gate is a gate that represents the interdependence of quantum states and performs complex quantum calculations.

[0022] Because the PPQ used in the present invention allows two Cooper pairs to pass through, it is impossible for a single Cooper pair to escape. This makes it possible for PPQ to address the existing problem of Cooper pairs leaking out of the island region of the transmon, causing errors and erroneous signals. Therefore, the present invention can improve the accuracy of quantum computation.

[0023] The present invention provides hardware specifications and pulse parameters for successfully constructing two qubits in a hybrid system, thereby enabling the generation of a CNOT gate with a fidelity greater than 0.998. Therefore, the hybrid system according to an embodiment of the present invention can provide a new platform for quantum computers.

[0024] Hereinafter, the present invention will be described in detail with reference to FIGS. 1 to 5.

[0025]

[0026] FIG. 1 illustrates the configuration of a superconducting-based quantum computing device using a hybrid system according to an embodiment of the present invention.

[0027] Referring to FIG. 1, a superconducting-based quantum computing device (1) according to an embodiment of the present invention may include a hybrid system (10) and a processing unit (20).

[0028] At this time, the hybrid system (10) includes a transmon (100) and a PPQ (parity-protected superconducting qubit, 200), and includes a resonator (300) located between the transmon (100) and the PPQ (200). At this time, the transmon (100) and the PPQ (200) are characterized in that they are indirectly connected and interact with each other based on the resonator (300).

[0029] The resonator (300) has a resonant frequency has. Transmon (100) , It has the charging energy and Josephson energy. At this time, the Josephson energy is the external magnetic flux passing through the shadow. The Josephson energy (E) of the two Josephson junctions that constitute the SQUID structure J1,T , E J2,T ) depends on. And, = E J1,T / E J2,T = 1.01. PPQ(200) is , It has the charging energy and Josephson energy.

[0030] In addition, the transmon (100) and PPQ (200) are capacitively connected. Coupling energy G = G T = G P is G = 2π×0.01 GHz. Transmon (100) and PPQ (200) are n g,T Wow n g,P can be driven.

[0031] A quantum computing device (1) according to an embodiment of the present invention is characterized in that it applies a CR pulse from a target qubit, PPQ (200), to a control qubit, transmon (100), thereby causing a resonance effect in PPQ (200). At this time, the quantum computing device (1) may include a processing unit (20) that applies the CR pulse. Here, the CR pulse is a pulse that vibrates at a target qubit frequency and is an electrical signal applied to the control qubit.

[0032] The processing unit (20) can change the state of the target qubit PPQ (200) where the resonance effect occurs according to the state of the control qubit transmon (100) using a CR pulse. In addition, the processing unit (20) can implement a CNOT gate by applying a CR pulse to the control qubit transmon (100) and then applying an auxiliary pulse to the target qubit PPQ (200) and modifying the phase information of the transmon (100) and PPQ (200). At this time, the processing unit (20) can set the pulse parameters of the CR pulse and the auxiliary pulse to control the application time, amplitude, initial phase, and rising time of each pulse of the CNOT gate.

[0033] More specifically, the processing unit (20) applies a CR pulse to the control qubit, Transmon (100), and applies an auxiliary pulse to the target qubit, PPQ (200), in order to generate a resonance effect of the same structure as the way the CNOT gate operates. In addition, the processing unit (20) can modify the phase information by applying a VZ gate to each of the control qubit and the target qubit.

[0034] To describe in more detail the hybrid system (10) according to an embodiment of the present invention, the total Hamiltonian function of the hybrid system (10) including the transmon (100) and PPQ (200) is as shown in [Mathematical Formula 1] below.

[0035] [Mathematical Formula 1]

[0036] H(t) = H T (t) + H P (t) + H R + H I

[0037]

[0038] At this time, H i , (i = T, P, R) represent the Hamiltonian functions of the transmon (100), PPQ (200), and resonator (300), respectively. HI represents the interaction Hamiltonian function between the resonator (300) and the transmon (100), and between the resonator (300) and PPQ (200). At this time, the energy level of the transmon (100) changes according to the external magnetic flux passing through the SQUID structure.

[0039] The Hamiltonian function HT of transmon (100) is expressed as in [Mathematical Formula 2] below.

[0040] [Equation 2]

[0041]

[0042]

[0043] Here, n T is an operator representing the number of additional Cooper pairs in transmon (100). represents a tunneling operator where a Cooper pair penetrates a Josephson junction. n g,T represents the number of deviations of the transmon (100) and represents the pulse operating in the transmon (100) to configure the gate. E C,Trepresents the charging energy.

[0044] also, is the external magnetic flux function It represents the Josephson energy given by , and is expressed as [Mathematical Formula 3] below. At this time, represents the magnetic flux quantum.

[0045] [Equation 3]

[0046]

[0047]

[0048] Here, is defined as the Josephson energy ratio between two Josephson connections. = E J1,T / E J2,T (>1). At this time, E J1,T Wow E J2,T represents the Josephson energies between the two Josephson connections that make up the SQUID structure. E JΣ,T = E J1,T + E J2,T represents the Josephson energy of the SQUID structure. PPQ(200) is a superconducting qubit, and a pair of Cooper pairs, rather than a single Cooper pair, tunnels to the island of a Cooper-pair box (CPB). At this time, the Hamiltonian function of PPQ(200) is as shown in [Mathematical Formula 4].

[0049] [Equation 4]

[0050]

[0051]

[0052] Here, n P represents the additional Cooper pair number operator in PPQ(200). represents a tunneling operator where a Cooper pair penetrates the Josephson junction. At this time, the Cooper pair in PPQ(200) entering the island moves as a pair, and the tunneling operator is It should be noted that it appears as terms n g,P represents the offset number of PPQ(200) and represents the pulse operating on PPQ(200) to create a gate. E C,P Wow E J,P represent the charging energy and Josephson energy of PPQ(200), respectively.

[0053] Additionally, the Hamiltonian function H of the resonator (300) R is expressed as [Mathematical Formula 5].

[0054] [Equation 5]

[0055]

[0056]

[0057] Here, the present invention = Use as 1. represents the destruction (creation) operator of the resonator (300). w R represents the resonant frequency of the resonator (300).

[0058] The interaction in the hybrid system (10) including the transmon (100) and the PPQ (200) consists of the interaction between the resonator (300) and the transmon (100) and the interaction between the resonator (300) and the PPQ (200). Accordingly, the Hamiltonian function H that follows I is as in [Mathematical Formula 6].

[0059] [Equation 6]

[0060]

[0061]

[0062] Here, G T(P)represents the coupling energy between the resonator (300) - transmon (100) (resonator (300) - PPQ (200)). In addition, the computational basis of the hybrid system (10, C) can be defined as in [Mathematical Formula 7] below.

[0063] [Equation 7]

[0064] C = {ij〉=|k〉|m T =i〉|m P =j-1〉|i=0,1, j=0,1, k=0, m T =0,1, m P =1,2}

[0065]

[0066] Here, |k〉 represents the Fock state of the resonator (300). At this time, since the present invention considers the case where the resonator (300) does not absorb energy, the resonator (300) remains at the bottom energy level. |m T 〉 represents the energy eigenstate of the transmon (100) defined as in [Mathematical Formula 8] below.

[0067] [Equation 8]

[0068]

[0069]

[0070] Here, represents the Hamiltonian function when neither external magnetic flux nor voltage offset exists. Also, |m P 〉 represents the energy eigenstate of PPQ(200) and is defined as in [Mathematical Formula 9].

[0071] [Equation 9]

[0072]

[0073]

[0074] Here, represents the Hamiltonian function when there is no voltage offset. PPQ(200) has Cooper-pairs of different parities in eigenstates. Therefore, the present invention is based on the computation of adjacent energy states with the same parity, which are |m P =1〉 and |m P =2〉. At this time, since the high energy state can affect the cross-resonance (CR), k, m T , m P The case ∈ {0, 1, 2, 3} is included for accurate calculation.

[0075]

[0076] Figures 2a and 2b illustrate a pulse protocol for performing a CNOT gate according to an embodiment of the present invention. In addition, Figure 3 illustrates a CNOT in a hybrid system according to an embodiment of the present invention. TP The pulse parameters and average fidelity of the present invention are shown in a table. In addition, FIG. 4a and FIG. 4b show the CNOT according to an embodiment of the present invention. TP Gate success probability and CNOT for the computational basis state PT It illustrates the circuit identity for performing .

[0077] Referring to Figures 2a and 2b, a CR pulse is applied to the control qubit. After the pulse is applied, an auxiliary pulse is applied to the target qubit. is applied. Here, C= T, T= P indicate that the transmon is the control qubit and PPQ is the target qubit, respectively. The CR pulse is the pulse parameter vector The shape is determined by the auxiliary pulse. The auxiliary pulse is a pulse parameter vector. Its form is determined by .

[0078] In general, single-qubit gates can be easily implemented by injecting frequency pulses into the corresponding qubit. However, fabricating two-qubit gates, such as the CNOT gate, is known to be very difficult. Therefore, the present invention proposes a method for designing a CNOT gate using CR pulses in a hybrid system including transmon and PPQ.

[0079] Pulse is n g,T (t) or n g,P (t) can be applied as the charge bias of each qubit. The general shape of the pulse can be defined as a linear combination of sine functions with a time-varying envelope.

[0080] [Equation 10]

[0081]

[0082]

[0083] Here, the index i∈{T, P} refers to a transmon or PPQ. represents the envelope that changes over time, which is important for gate design. and represent the pulse frequency and initial phase, respectively, which represent the rotation axis on the Bloch sphere.

[0084] When the control qubit is a transmon and the target qubit is a PPQ, the pulse function for creating a CNOT gate is defined as in [Mathematical Formula 11] and [Mathematical Formula 12] below (see FIGS. 2a and 2b).

[0085] [Equation 11]

[0086]

[0087] [Equation 12]

[0088]

[0089]

[0090] Here, n g,T (t) represents the CR pulse applied to the control qubit. n g,P (t) represents the auxiliary pulse applied to the target qubit to complete the CNOT gate. Therefore, and is an envelope defined as [Mathematical Formula 13] and [Mathematical Formula 14] below, respectively.

[0091] [Equation 13]

[0092]

[0093] [Equation 14]

[0094]

[0095]

[0096] Here, Wow T 1(2) are each It represents the pulse amplitude and pulse time of T. rise Is represents the time taken to reach the maximum amplitude. The present invention subsequently describes the pulse parameter e = T rise You can adjust the rising time by setting / T1. T CR represents the time during which the maximum amplitude of the CR pulse is maintained. In addition, Is Indicates the thickness of .

[0097]

[0098] Below, the present invention describes the process of selecting a pulse parameter vector for a CNOT gate. The pulse protocol is as follows:

[0099] In the first step, a CR pulse is injected into the control qubit.

[0100] In the second step, an auxiliary pulse is injected into the target qubit.

[0101] In the third step, a virtual Z (VZ) gate is applied to both qubits.

[0102] In the first step, the pulse parameter vector of the CR pulse is The time evolution operator in the first stage is defined as in [Mathematical Formula 15].

[0103] [Equation 15]

[0104]

[0105]

[0106] Here, H(t) is n g,T (t) and n g,P (t) represents a function. In the second step, the pulse parameters of the auxiliary pulse are . The time evolution operator in the second stage is defined as in [Mathematical Formula 16].

[0107] [Equation 16]

[0108]

[0109]

[0110] Additionally, in the third step, the VZ gate Z represents the z-rotation processed in software.

[0111] [Equation 17]

[0112]

[0113]

[0114] Therefore, the CNOT gate of the present invention includes the following three unitary operators.

[0115] [Equation 18]

[0116]

[0117]

[0118] Here, CNOT ij represents a CNOT gate where the control qubit is i and the target qubit is j. Figure 4b shows a CNOT PT It shows how it can be applied. The performance of the CNOT gate can be evaluated through the average reliability F.

[0119] [Equation 19]

[0120]

[0121]

[0122] Here, |Ψ〉 represents an arbitrary pure state expressed as the computational basis of hybrid systems including transmons and PPQ. CNOT ij,ideal represents an ideal CNOT gate defined as in [Mathematical Formula 20] below.

[0123] [Equation 20]

[0124]

[0125]

[0126] Here, the pulse parameters and average reliability of the CNOT gate are shown in Fig. 3. In addition, Fig. 4a shows the performance of the CNOT gate. This is because the fidelity (F) is improved by using CR pulses in a hybrid system including transmon and PPQ. It tells us that we can build a CNOT gate.

[0127]

[0128] FIG. 5 illustrates an operational flowchart of a method for implementing a CNOT gate in a superconducting-based quantum computing device according to an embodiment of the present invention.

[0129] The CNOT gate implementation method of FIG. 5 is performed by a superconducting-based quantum computing device according to the embodiment of the present invention illustrated in FIG. 1.

[0130] Referring to FIG. 5, in step S510, a cross-resonance pulse (CR pulse) is applied to a hybrid system composed of a transmon and a PPQ (parity-protected superconducting qubit).

[0131] At this time, the hybrid system includes a transmon and a PPQ (parity-protected superconducting qubit), and a resonator located between the transmon and the PPQ. At this time, the transmon and the PPQ are characterized by being indirectly connected and interacting with each other based on the resonator.

[0132] A superconducting-based quantum computing device according to an embodiment of the present invention is characterized in that, in step S510, a CR pulse is applied from a target qubit, PPQ, to a control qubit, transmon, thereby causing a resonance effect in PPQ. Here, the CR pulse is a pulse that vibrates at the target qubit frequency and is an electrical signal applied to the control qubit.

[0133] Accordingly, the superconducting-based quantum computing device can change the state of the target qubit PPQ, where the resonance effect occurs, according to the state of the control qubit transmon using a CR pulse in step S510.

[0134] In step S520, a CNOT gate is implemented using a CR pulse.

[0135] In step S520, the superconducting-based quantum computing device applies a CR pulse to the control qubit, Transmon, and applies an auxiliary pulse to the target qubit, PPQ, to generate a resonance effect having the same structure as the way the CNOT gate operates. In addition, the phase information can be modified by applying a VZ gate to the control qubit, Transmon, and the target qubit, PPQ, respectively. At this time, the superconducting-based quantum computing device can control the application time, amplitude, initial phase, and rising time of each pulse of the CNOT gate by setting the pulse parameters of the CR pulse and the auxiliary pulse.

[0136]

[0137] The systems, devices, or apparatus described above may be implemented as hardware components, software components, and / or a combination of hardware components and software components. For example, the devices and components described in the embodiments may be implemented using one or more general-purpose computers or special-purpose computers, such as, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate array (FPGA), a programmable logic unit (PLU), a microprocessor, or any other device capable of executing instructions and responding to them. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to the execution of the software. For ease of understanding, the processing device is sometimes described as being used alone; however, one of ordinary skill in the art will recognize that the processing device may include multiple processing elements and / or multiple types of processing elements. For example, a processing unit may include multiple processors, or a processor and a controller. Other processing configurations, such as parallel processors, are also possible.

[0138]

[0139] Software may include a computer program, code, instructions, or a combination of one or more of these, which may configure a processing device to perform a desired operation or may, independently or collectively, command the processing device. The software and / or data may be permanently or temporarily embodied in any type of machine, component, physical device, virtual equipment, computer storage medium or device, or transmitted signal wave, for interpretation by the processing device or for providing instructions or data to the processing device. The software may also be distributed over networked computer systems and stored or executed in a distributed manner. The software and data may be stored on one or more computer-readable recording media.

[0140]

[0141] The method according to the embodiment may be implemented in the form of program commands that can be executed through various computer means and recorded on a computer-readable medium. The computer-readable medium may include program commands, data files, data structures, etc., alone or in combination. The program commands recorded on the medium may be those specially designed and configured for the embodiment or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include hardware devices specially configured to store and execute program commands, such as hard disks, magneto-optical media, solid-state drives (SSDs), and ROMs, RAMs, flash memories, etc. Examples of the program commands include not only machine language codes generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter, etc. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiment, and vice versa.

[0142]

[0143] Although the embodiments described above have been described by way of limited examples and drawings, those skilled in the art will appreciate that various modifications and variations can be made based on the above teachings. For example, appropriate results can still be achieved even if the described techniques are performed in a different order than described, and / or components of the described systems, structures, devices, circuits, etc. are combined or combined in a different manner than described, or are replaced or substituted with other components or equivalents.

[0144]

[0145] Therefore, other implementations, other embodiments, and equivalents to the claims also fall within the scope of the claims described below.

Claims

1. A superconducting-based quantum computing device that implements a CNOT gate using a cross-resonance pulse (CR pulse) in a hybrid system composed of a transmon and a parity-protected superconducting qubit (PPQ).

2. In paragraph 1, The above hybrid system It includes a resonator located between the transmon and the PPQ, and the transmon and the PPQ are indirectly connected based on the resonator. A superconducting-based quantum computing device featuring .

3. In paragraph 2, The above transmon and the above PPQ are a superconducting-based quantum computing device with capacitive connection.

4. In paragraph 1, The above CR pulse is A superconducting-based quantum computing device in which a pulse oscillates at the target qubit frequency and is an electrical signal applied to the control qubit.

5. In paragraph 4, The above superconducting-based quantum computing device A processing unit that applies the CR pulse from the target qubit, the PPQ, to the control qubit, the transmon, The above CR pulse causes a resonance effect in the above PPQ. A superconducting-based quantum computing device featuring .

6. In paragraph 5, The above processing unit Changing the state of the PPQ, which is the target qubit where the resonance effect occurs, according to the state of the transmon, which is the control qubit, using the CR pulse. A superconducting-based quantum computing device featuring .

7. In paragraph 6, The above processing unit A superconducting-based quantum computing device that applies the CR pulse to the transmon, which is a control qubit, and applies an auxiliary pulse to the PPQ, which is a target qubit, to generate a resonance effect of the same structure as the way the CNOT gate operates.

8. In paragraph 7, The above processing unit Modifying phase information by applying a VZ gate to each of the above transmon and the above PPQ. A superconducting-based quantum computing device featuring .

9. In paragraph 7, The above processing unit A superconducting-based quantum computing device that controls the application time, amplitude, initial phase, and rising time of each pulse of the CNOT gate by setting the pulse parameters of the CR pulse and the auxiliary pulse.

10. A method for implementing a CNOT gate in a superconducting-based quantum computing device, A step of applying a cross-resonance pulse (CR pulse) to a hybrid system composed of a transmon and a PPQ (parity-protected superconducting qubit); and A step of implementing a CNOT gate using the above CR pulse. A method for implementing a CNOT gate including:

11. In paragraph 10, The above hybrid system It includes a resonator located between the transmon and the PPQ, and the transmon and the PPQ are indirectly connected based on the resonator. A method for implementing a CNOT gate, characterized by:

12. In paragraph 10, The step of applying the above CR pulse is A method for implementing a CNOT gate, wherein the CR pulse is applied to the transmon, which is a control qubit, and the CR pulse causes a resonance effect in the PPQ.

13. In paragraph 12, The step of applying the above CR pulse is Changing the state of the PPQ, which is the target qubit where the resonance effect occurs, according to the state of the transmon, which is the control qubit, using the CR pulse. A method for implementing a CNOT gate, characterized by:

14. In paragraph 13, The steps for implementing the above CNOT gate are In order to generate a resonance effect of the same structure as the way the CNOT gate operates, the CR pulse is applied to the control qubit, the auxiliary pulse is applied to the PPQ, the target qubit, and the VZ gate is applied to the transmon and the PPQ, respectively, to modify the phase information. A method for implementing a CNOT gate, characterized by:

15. In paragraph 14, The steps for implementing the above CNOT gate are A method for implementing a CNOT gate, wherein the pulse parameters of the CR pulse and the auxiliary pulse are set to control the application time, amplitude, initial phase, and rising time of each pulse of the CNOT gate.

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