CN115577779B

CN115577779B - Method and device for determining bare state information of multi-body system in superconducting quantum chip layout

Info

Publication number: CN115577779B
Application number: CN202211304939.8A
Authority: CN
Inventors: 余轲辉; 付元豪; 焦晓杨; 晋力京
Original assignee: Beijing Baidu Netcom Science and Technology Co Ltd
Current assignee: Beijing Baidu Netcom Science and Technology Co Ltd
Priority date: 2022-10-24
Filing date: 2022-10-24
Publication date: 2023-06-27
Anticipated expiration: 2042-10-24
Also published as: CN115577779A

Abstract

The disclosure provides a method and a device for determining bare state information of a multi-body system in a superconducting quantum chip layout, relates to the technical field of quantum computing, and particularly relates to the technical field of superconducting quantum chips. The specific implementation scheme is as follows: obtaining a structural layout of a first quantum chip, wherein the first quantum chip comprises M first quantum devices; determining first device inductance energy duty ratio and first symbol information of M first quantum devices under each intrinsic mode of a first quantum chip based on a structural layout; determining a first transformation matrix based on the first device inductance energy ratio, the first sign information, and a predetermined first relationship; first bare state information of the first quantum chip is determined based on the first transformation matrix and first decoration state information of the first quantum chip, which is determined in advance.

Description

Method and device for determining bare state information of multi-body system in superconducting quantum chip layout

Technical Field

The disclosure relates to the technical field of quantum computing, in particular to the technical field of superconducting quantum chips, and specifically relates to a method and a device for determining bare state information of a multi-body system in a superconducting quantum chip layout.

Background

Along with the large-scale development of superconducting quantum chips, the simulation verification of the chips before formal flow is also important besides providing higher requirements for micro-nano processing technology. The simulation verification aims to describe the characteristic parameters of the chip as truly as possible, so that researchers can better predict the performance index of the chip in the design stage, and the trial-and-error cost of micro-nano processing of the quantum chip is reduced.

At present, the simulation verification of the superconducting quantum chip is generally performed by an equivalent circuit method, namely the superconducting quantum chip is equivalent to a circuit model, and the simulation verification of the superconducting quantum chip is performed based on the equivalent circuit model, so that the bare state information of the multi-body system in the superconducting quantum chip layout is obtained.

Disclosure of Invention

The present disclosure provides a method and an apparatus for determining bare state information of a multi-body system in a superconducting quantum chip layout.

According to a first aspect of the present disclosure, a method for determining bare state information of a multi-body system in a superconducting quantum chip layout is provided, including:

obtaining a structural layout of a first quantum chip, wherein the first quantum chip comprises M first quantum devices, the first quantum devices comprise Josephson junctions, and M is an integer larger than 2;

Based on the structural layout, determining first device inductance energy duty ratios and first symbol information of the M first quantum devices in each intrinsic mode of the first quantum chip, wherein the first device inductance energy duty ratios are as follows: the ratio of the first inductive energy stored in the first quantum device in the eigenmode to the second inductive energy stored in the first quantum chip in the eigenmode, wherein the first symbol information indicates the positive-negative relation between the current on the Josephson junction of the first quantum device in the eigenmode and a preset reference direction;

determining a first transformation matrix based on the first device inductance energy ratio, the first symbol information and a predetermined first relation, wherein the first relation is a relation between the transformation matrix and first target information, and the first target information comprises the device inductance energy ratio and the symbol information;

and determining first bare state information of the first quantum chip based on the first transformation matrix and the predetermined first decoration state information of the first quantum chip, wherein the first decoration state information is the eigenstate information of a multi-body system formed by the first quantum chip, and the first bare state information is the eigenstate information of the M first quantum devices.

According to a second aspect of the present disclosure, there is provided a bare state information determining apparatus of a multi-body system in a superconducting quantum chip layout, including:

the device comprises an acquisition module, a first quantum chip and a second quantum chip, wherein the acquisition module is used for acquiring a structural layout of the first quantum chip, the first quantum chip comprises M first quantum devices, the first quantum devices comprise Josephson junctions, and M is an integer larger than 2;

the first determining module is configured to determine, based on the structural layout, a first device inductance energy ratio and first symbol information of the M first quantum devices in each eigenmode of the first quantum chip, where the first device inductance energy ratio is: the ratio of the first inductive energy stored in the first quantum device in the eigenmode to the second inductive energy stored in the first quantum chip in the eigenmode, wherein the first symbol information indicates the positive-negative relation between the current on the Josephson junction of the first quantum device in the eigenmode and a preset reference direction;

a second determining module, configured to determine a first transformation matrix based on the first device inductance energy duty ratio, the first symbol information, and a predetermined first relationship, where the first relationship is a relationship between the transformation matrix and first target information, and the first target information includes the device inductance energy duty ratio and the symbol information;

The third determining module is configured to determine first bare state information of the first quantum chip based on the first transformation matrix and predetermined first decoration state information of the first quantum chip, where the first decoration state information is eigenstate information of a multi-body system formed by the first quantum chip, and the first bare state information is eigenstate information of the M first quantum devices.

According to a third aspect of the present disclosure, there is provided an electronic device comprising:

at least one processor; and

a memory communicatively coupled to the at least one processor; wherein, the liquid crystal display device comprises a liquid crystal display device,

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform any one of the methods of the first aspect.

According to a fourth aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform any of the methods of the first aspect.

According to a fifth aspect of the present disclosure, there is provided a computer program product comprising a computer program which, when executed by a processor, implements any of the methods of the first aspect.

According to the technology disclosed by the invention, the problem of relatively poor simulation verification effect of the superconducting quantum chip is solved, and the simulation verification effect of the superconducting quantum chip is improved, so that the accuracy of determining the bare state information of the multi-body system in the superconducting quantum chip layout is improved.

It should be understood that the description in this section is not intended to identify key or critical features of the embodiments of the disclosure, nor is it intended to be used to limit the scope of the disclosure. Other features of the present disclosure will become apparent from the following specification.

Drawings

The drawings are for a better understanding of the present solution and are not to be construed as limiting the present disclosure. Wherein:

FIG. 1 is a flow diagram of a method for determining bare state information of a multi-body system in a superconducting quantum chip layout according to a first embodiment of the present disclosure;

FIG. 2 is a layout of a QCQ structure containing three qubits;

FIG. 3 is a flow diagram of a specific example provided by the present disclosure;

FIG. 4 is a graph comparing the results of bare state frequencies of quantum devices at different coupler inductance values;

FIG. 5 is a graph of the coupling strength between different quantum devices at different coupler inductance values;

FIG. 6 is a graph of equivalent coupling strength between qubits at different coupler inductance values;

Fig. 7 is a schematic structural diagram of a bare state information determining apparatus of a multi-body system in a superconducting quantum chip layout according to a second embodiment of the present disclosure;

fig. 8 is a schematic block diagram of an example electronic device used to implement embodiments of the present disclosure.

Detailed Description

Exemplary embodiments of the present disclosure are described below in conjunction with the accompanying drawings, which include various details of the embodiments of the present disclosure to facilitate understanding, and should be considered as merely exemplary. Accordingly, one of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

First embodiment

As shown in fig. 1, the present disclosure provides a method for determining bare state information of a multi-body system in a superconducting quantum chip layout, including the following steps:

step S101: obtaining a structural layout of a first quantum chip, wherein the first quantum chip comprises M first quantum devices, and the first quantum devices comprise Josephson junctions.

Wherein M is an integer greater than 2.

In this embodiment, the method for determining the bare state information of the multi-body system in the superconducting quantum chip layout relates to the technical field of quantum computing, in particular to the technical field of superconducting quantum chips, and can be widely applied to simulation verification scenes of superconducting quantum chips. The method for determining the bare state information of the multi-body system in the superconducting quantum chip layout of the embodiment of the disclosure can be executed by the device for determining the bare state information of the multi-body system in the superconducting quantum chip layout of the embodiment of the disclosure. The bare state information determining device of the multi-body system in the superconducting quantum chip layout of the embodiment of the disclosure can be configured in any electronic equipment to execute the bare state information determining method of the multi-body system in the superconducting quantum chip layout of the embodiment of the disclosure.

In the step, the first quantum chip can be any quantum chip, the quantum chip can be a superconducting quantum chip, and the development of the superconducting quantum chip is important as a core carrier of a superconducting circuit technical scheme. Similar to classical chips, superconducting quantum chips also require a complete structural layout prior to formal production and processing. The structural layout comprises information of all core devices, control lines, reading lines and the like of the quantum chip.

The first quantum chip may include M first quantum devices, where M is an integer greater than 2, such as three first quantum devices (e.g., three qubits), four first quantum devices, which correspond to a multi-body system. In the following embodiments, three first quantum devices are taken as examples of qubits, wherein each of the three first quantum devices includes a josephson junction, and every two first quantum devices are coupled to each other.

The simulation verification of the superconducting quantum chip is an indispensable ring in the design stage, in the related technology, the superconducting quantum circuit can be generally simulated and verified by adopting an equivalent circuit method, and particularly, a continuous conductor in the quantum chip layout can be regarded as an equipotential body, and the equivalent circuit modeling is carried out according to a node potential method, and the nodes are connected by using capacitance or inductance; then simulating parameters such as capacitance, inductance and the like among the nodes through electromagnetic field simulation software; the equivalent circuit model is quantized to obtain the complete Hamiltonian quantity representing the quantum chip system, and the relevant characteristic parameters under the bare state can be obtained at the same time, so that simulation verification of the superconducting quantum chip is realized. However, the equivalent circuit method adopts more approximation, the equivalent circuit method regards the continuous conductor as an equipotential body, and the continuous conductor cannot be regarded as an equipotential body under the high-frequency electromagnetic field, so that the method is different from the real object environment, and the calculation result has a certain gap.

In the related art, for the performance simulation verification task of the quantum chip, a classical energy duty ratio (Energy Participation Ratio, EPR) method can be adopted, high-frequency electromagnetic field simulation is adopted, and after-treatment is carried out on simulation data to obtain characteristic parameters of the quantum chip, although the method considers the influence of the high-frequency electromagnetic field, the obtained characteristic parameters are not comprehensive enough, only the characteristic parameters (such as decoration state frequency and nonlinear parameters) corresponding to the decoration state can be obtained, and the characteristic parameters in the bare state can not be obtained. The method has a small application range, and can be only used for simulating the situation that all quantum devices are in dispersion coupling (the frequency difference between the quantum devices is far greater than the coupling strength), and can not solve other situations such as near resonance (the frequency difference between the quantum devices is the same as the coupling strength).

The purpose of this embodiment is to: and determining the device inductance energy duty ratio (inductance Energy Participation Ratio, iEPR) and symbol information of each first quantum device in the superconducting quantum chip layout, wherein the device inductance energy duty ratio (iEPR) and symbol information can be used as a bridge for connecting the bare state information and the decoration state information in the first quantum chip physical system, and a transformation matrix between the Hamiltonian quantities of the bare state and the decoration state can be completely constructed by utilizing the device inductance energy duty ratio and the symbol information, so that the bare state information of the multi-body system in the superconducting quantum chip layout is determined based on the transformation matrix and the decoration state information.

The bare state information may include an eigenfrequency of each quantum device in the bare state, a coupling strength between every two quantum devices, and the like.

Among the core devices, one of the most important devices is the qubit. In a practical layout, the qubits are typically composed of co-planar capacitances and josephson junctions. In practice, a substrate (typically realized by silicon or sapphire) is designed, an aluminum film is plated on the substrate, the qubit capacitance is formed by etching different shapes on the aluminum film, and a nonlinear device josephson junction is designed between two metal plates.

The basic structure of the superconducting quantum chip is described below, and as shown in fig. 2, a layout of a "qubit-coupler-qubit" structure is shown, in which the cross structure represents the self-capacitance part of the device, the black square below the cross structure represents the josephson junction, and the simulation can be performed by a lumped inductor. The structures on the left side and the right side are quantum bits, the cross in the middle is a coupler (also a quantum bit), and a three-body quantum bit multi-body system is formed together.

The obtaining mode of the structural layout of the first quantum chip comprises, but is not limited to, obtaining a pre-stored layout and obtaining a quantum chip layout input by a user.

Step S102: based on the structural layout, determining first device inductance energy duty ratios and first symbol information of the M first quantum devices in each intrinsic mode of the first quantum chip, wherein the first device inductance energy duty ratios are as follows: the first symbol information indicates the positive-negative relation between the current on the josephson junction of the first quantum device in the eigenmode and a preset reference direction, and the first symbol information indicates the positive-negative relation between the first inductive energy stored in the first quantum device in the eigenmode and the second inductive energy stored in the first quantum chip in the eigenmode.

In this step, the first device inductance device duty cycle is the duty cycle of the first inductance energy stored in the first quantum device in the eigenmode relative to the second inductance energy stored in the first quantum chip in the eigenmode.

Wherein for each first quantum device, there is a corresponding first device inductance energy ratio, and the device inductance energy ratio corresponding to the quantum device may include a device inductance energy ratio of the quantum device in each eigenmode of the quantum chip.

Due to the coupling of the individual quantum devices, the quantum chip may comprise a plurality of eigenmodes, the number of which is typically related to the number of quantum devices, e.g. when the quantum chip comprises three quantum devices, three eigenmodes may typically be comprised, which may correspond one-to-one to the three quantum devices.

Correspondingly, when three first quantum devices are included in the first quantum chip, the number of the first device inductance energy ratios of the three first quantum devices in each eigenmode of the first quantum chip is 9, and p is respectively ₁₁ 、p ₁₂ 、p ₁₃ 、p ₂₁ 、p ₂₂ 、p ₂₃ 、p ₃₁ 、p ₃₂ And p ₃₃ 。

The device inductance energy ratio of the quantum device k in the eigenmode m can be expressed as p _mk The device inductance energy ratio of the quantum device k in the eigenmode m is shown in the following formula (1).

Wherein, the liquid crystal display device comprises a liquid crystal display device,

first inductive energy stored in quantum device k in eigenmode m, +.>

The second inductive energy stored in the quantum chip in eigenmode m.

In an alternative embodiment, the structural layout may be placed in an electromagnetic field simulation environment to perform simulation of the first quantum chip, so as to obtain simulation output information, where the simulation output information may include relevant parameter information, such as capacitance information, inductance information, and the like, of an equivalent circuit model of the first quantum chip. The first device inductance energy duty ratio of the M first quantum devices in each eigenmode can be determined by adopting a Hamiltonian modeling mode based on related parameter information of an equivalent circuit model of the first quantum chip.

In another optional implementation manner, the structure layout can be subjected to high-frequency electromagnetic field simulation, namely, the input layout is subjected to eigenmode solution to obtain simulation output information, the simulation output information can comprise decoration state information of the first quantum chip under the eigenmode of the high-frequency electromagnetic field, the decoration state information can be eigenstate information of a quantum system formed by the first quantum chip, and the decoration state information is information representation of an integral quantum system formed by mutually coupling all the first quantum devices. The decoration state information can comprise frequency of the intrinsic mode of the first quantum chip, electromagnetic field distribution information and the like, the electromagnetic field distribution information can characterize the electromagnetic field distribution of the first quantum chip radiated in space under different intrinsic modes, for example, the electromagnetic field distribution information can comprise the electric field intensity peak value distribution of the intrinsic mode m in space

Magnetic field peak distribution->

Surface current Density of Quantum chip +.>

Etc. Thereafter, M first quantum devices may be determined to be in the semiconductor device based on the electromagnetic field distribution informationThe first device inductance energy ratio in each eigenmode.

The first sign information indicates a positive-negative relationship between a current on the josephson junction of the first quantum device in the eigenmode and a preset reference direction. The preset reference direction may be a reference direction under a standard cartesian coordinate system, the default reference direction is each positive direction of the standard cartesian coordinate system, and the default reference directions are uniform for all the first quantum devices.

The positive and negative relation between the current on the Josephson junction of the first quantum device and the preset reference direction in the eigenmode is indicated by the first symbol information, wherein the positive and negative relation comprises two conditions, namely the same direction and the opposite direction, and the first symbol information is different when the same direction and the opposite direction are respectively adopted. In an alternative embodiment, the first sign information indicates that the current on the josephson junction of the first quantum device in the eigenmode is in the same direction as the preset reference direction when the first sign information is 1, and the first sign information indicates that the current on the josephson junction of the first quantum device in the eigenmode is opposite to the preset reference direction when the first sign information is-1.

First sign information of the M first quantum devices in respective eigenmodes may be determined based on the electromagnetic field distribution information. Wherein the sign information of the quantum device k in the eigenmode m can be expressed as s _mk When three first quantum devices are included in the first quantum chip, the number of first sign information of the three first quantum devices in each eigenmode of the first quantum chip is 9, respectively s ₁₁ 、s ₁₂ 、s ₁₃ 、s ₂₁ 、s ₂₂ 、s ₂₃ 、s ₃₁ 、s ₃₂ Sum s ₃₃ 。

Step S103: a first transformation matrix is determined based on the first device inductance energy duty cycle, the first symbol information, and a predetermined first relationship, the first relationship being a relationship of the transformation matrix to first target information, the first target information including the device inductance energy duty cycle and the symbol information.

In the following steps, the first bare state information of the first quantum chip may be determined using the data obtained by the simulation, the iEPR, and the first symbol information.

In the multi-body system, symbol information can be combined to determine a first relation, the first relation is a relation between a transformation matrix and the symbol information, the transformation matrix is represented by U and can serve as a bridge between the decoration state information and the bare state information of the multi-body system, and the first relation is represented by the following formula (2).

It is known that, in order to determine the first transformation matrix, the first device inductance energy ratio and the first sign information of the M first quantum devices in each eigenmode need to be obtained, and the first transformation matrix may be obtained by substituting the first inductance energy ratio and the first sign information into the first relationship.

Step S104: and determining first bare state information of the first quantum chip based on the first transformation matrix and the predetermined first decoration state information of the first quantum chip, wherein the first decoration state information is the eigenstate information of a multi-body system formed by the first quantum chip, and the first bare state information is the eigenstate information of the M first quantum devices.

In this step, the first decoration state information may include an eigenfrequency ω corresponding to a different eigenmode m of the first quantum chip ^′ _m . Can be based on the eigenfrequency omega corresponding to the different eigenmodes m of the first quantum chip ^′ _m Determining a characterization matrix of the Hamiltonian quantity of the first quantum chip in the decorated state, and carrying out inverse transformation on the characterization matrix of the Hamiltonian quantity in the decorated state by utilizing the first transformation matrix to obtain first bare state information. The first bare state information may include an eigenfrequency of the M first quantum devices, a coupling strength between every two first quantum devices, and the like.

In the embodiment, the structural layout of the first quantum chip is obtained; determining first device inductance energy duty ratio and first symbol information of M first quantum devices in each eigenmode based on the structure layout; determining a first transformation matrix based on the first device inductance energy duty cycle, the first symbol information, and the first relationship; based on the first transformation matrix and the first decoration state information of the first quantum chip, first bare state information of the first quantum chip is determined. Therefore, the determination of the bare state information of the multi-body system in the quantum chip layout can be realized based on the decoration state information of the multi-body system in the quantum chip layout by utilizing the device inductance energy duty ratio and the symbol information of the quantum device in the intrinsic mode, so that the simulation verification of the quantum chip layout containing a plurality of quantum devices can be realized, and the design efficiency and the accuracy of the quantum chip layout containing a plurality of quantum devices are improved. In addition, the frequency interval of the quantum device can be not limited in the quantum chip layout, and the application range is wider. Has important practical value for the characteristic parameter verification work in the quantum chip design stage.

Optionally, the step S102 specifically includes:

Carrying out eigenmode solving on the structural layout to obtain electromagnetic field distribution information of the first quantum chip in each eigenmode of the high-frequency electromagnetic field;

the first device inductance energy ratio and the first sign information are determined based on the electromagnetic field distribution information.

In this embodiment, the high-frequency electromagnetic field simulation of the finite element method may be performed on the structural layout, that is, the input layout is subjected to eigenmode solution, so as to obtain first decoration state information of the first quantum chip in each eigenmode of the high-frequency electromagnetic field, where the first decoration state information may include electromagnetic field distribution information of the first quantum chip in each eigenmode of the high-frequency electromagnetic field.

The electromagnetic field distribution information may characterize the electromagnetic field distribution of the first quantum chip radiated in space under different eigenmodes, e.g., the electromagnetic field distribution information may include the peak distribution of the electric field intensity of eigenmode m in space

Magnetic field peak distribution->

First amount ofSurface Current Density of the chiplet->

Etc.

Thereafter, a first device inductance energy ratio may be determined based on the electromagnetic field distribution information. In the embodiment, the high-frequency electromagnetic field simulation is adopted, so that the approximation is less, the inductance effect of the conductor caused by the high-frequency electromagnetic field is considered, the method is closer to the actual situation, the accuracy is higher, the method is applicable to the coupling situation of a full-frequency interval (the frequency difference between different devices can be in any interval), and the method has important practical value for the design and simulation of the superconducting quantum chip.

And, can confirm the electric current on Josephson junction of the first quantum device under each eigenmode on the basis of the electromagnetic field distribution information, compare the direction of the electric current with the positive and negative relation of the reference direction of the default, realize the determination of the first symbol information.

Optionally, the electromagnetic field distribution information includes a current density on the surface of the first quantum chip in the eigenmode, and the first sign information is determined by:

determining a current on the josephson junction of the first quantum device in eigenmode based on the current density;

the first sign information is determined based on the current.

In this embodiment, the electromagnetic field distribution information may include a current density on the surface of the first quantum chip in the eigenmode

And (3) representing.

Based on the current density, the current I on the Josephson junction of the quantum device k in eigenmode m is determined using the following formula (3) _mk 。

Wherein k is 1,2, …, M,

for the length of the josephson junction of quantum device k, expressed in layout as equivalent lumped inductance, the integration range of equation (25) above is +.>

The integral area is the area of the equivalent inductance of the Josephson junction in the layout, and the parameter information of the Josephson junction is known.

Under the condition that the current on the Josephson junction of the first quantum device under each eigenmode is determined, the forward and reverse relation between the current direction and the preset reference direction can be compared, if the forward and reverse relation is the same direction, the first symbol information is determined to be 1, if the forward and reverse relation is reverse, the first symbol information is determined to be-1, the first symbol information can also be reversely arranged according to the forward and reverse relation, the specific limitation is not carried out, and the determination of the first symbol information can be realized.

Optionally, the determining the first symbol information based on the current includes:

under the condition that the direction indicated by the current is in the same direction as a preset reference direction, determining the first symbol information as 1;

and determining the first symbol information to be-1 under the condition that the direction indicated by the current is opposite to a preset reference direction.

Wherein I is _mk When the current is more than 0, the direction indicated by the current is the same as the preset reference direction, s _mk ＝1，I _mk When less than 0, the direction of current indication is opposite to the preset reference direction, s _mk = -1. In this way, determination of the first symbol information can be achieved.

Optionally, the first device inductance energy ratio is determined by:

determining electromagnetic field energy information of the first quantum chip in each eigenmode based on the electromagnetic field distribution information;

Determining the first inductive energy and the second inductive energy based on the electromagnetic field energy information;

and determining the ratio of the first inductance energy and the second inductance energy as the first device inductance energy ratio.

In the present embodiment, the peak distribution of the electric field intensity in space can be based on the eigenmode m

Magnetic field peak distribution->

And surface current density of the first quantum chip +.>

And the like, and combining relevant parameter information (such as parameter information of a Josephson junction, electric field radiation information, magnetic field radiation information and the like of the first quantum device) of the first quantum chip to determine electromagnetic field energy information of the first quantum chip in each intrinsic mode. The electromagnetic field energy information may include, among others, the inductive energy of the different eigenmodes m on the josephson junction of the quantum device k, the total electric field energy of the different eigenmodes m in space, the total magnetic field energy of the different eigenmodes m in space, etc.

On the basis of obtaining the electromagnetic field energy information, the first device inductance energy duty ratio of each first quantum device in the first quantum chip under different eigenmodes can be determined based on the electromagnetic field energy information. Thus, the determination of the inductance energy ratio of the device can be realized based on the high-frequency electromagnetic field simulation mode.

How the determination of the device inductance energy ratio is achieved based on the electromagnetic field distribution information is described in detail below.

The electromagnetic field distribution information may include a surface current density of the first quantum chip

The inductive energy at the josephson junction of the quantum device k in eigenmode m may be determined based on the current density and parametric information of the josephson junction of the first quantum device,represented by the following formula (4).

Wherein k is 1,2, …, M,

inductance of josephson junction for quantum device k +.>

For the length of the josephson junction of quantum device k, expressed in layout as equivalent lumped inductance, the integration range of equation (4) above is +.>

The electromagnetic field distribution information may include a peak distribution of electric field intensity of the first quantum chip radiation in the space under the eigenmode, and may be based on the peak distribution of electric field intensity

And the electric field radiation information of the first quantum chip, determining the total electric field energy of the first quantum chip radiation in the space under the intrinsic mode m, and using the following formula (5).

complex conjugate representing peak electric field intensity distribution, +.>

Representing the dielectric tensor at different positions in space, the integral range of the above formula (5) V and V represent the space volume, and the above are the electric field radiation information, which are all known quantities.

In addition, the electromagnetic field distribution information may include a peak distribution of magnetic field intensity of the first quantum chip radiation in the space in the eigenmode

The total magnetic field energy radiated by the first quantum chip in the space in the eigenmode m can be determined based on the magnetic field intensity peak distribution and the magnetic field radiation information of the first quantum chip, as shown in the following formula (6).

complex conjugate representing peak distribution of magnetic field strength, +.>

The integral range of the above formula (6) is V, V represents the volume of the space, and the above is the radiation information of the magnetic field, which are all known quantities.

The first inductive energy and the second inductive energy may then be determined based on the electromagnetic field energy information, e.g. the first inductive energy and the second inductive energy may be determined based on the inductive energy on the josephson junction of the quantum device k in eigenmode m, the total electric field energy radiated by the first quantum chip in space in eigenmode m and the total magnetic field energy radiated by the first quantum chip in space in eigenmode m.

In an alternative embodiment, the first inductive energy may be determined by dividing the total magnetic field energy radiated by the first quantum chip in space in the eigenmode by the ratio of the inductive energies on the josephson junctions of different quantum devices in the eigenmode. In a further alternative embodiment, the first inductive energy may be determined by spatially distributing the magnetic field energy in accordance with the inductive energy duty cycle of the josephson junctions of the quantum device in different eigenmodes.

In an alternative embodiment, the second inductive energy may be determined as the total capacitive energy stored by the first quantum chip in the eigenmode. In another alternative embodiment, the second inductive energy may be determined as the total electric field energy radiated by the first quantum chip in space in the eigenmode.

Thereafter, a ratio of the first inductive energy to the second inductive energy may be determined as a first device inductive energy ratio. In this manner, determination of the first device inductance energy ratio may be achieved based on the electromagnetic field distribution information.

Optionally, the electromagnetic field energy information includes: in eigenmode, the first quantum chip radiates a first magnetic field energy in space and a third inductive energy on josephson junctions of the M first quantum devices, the first inductive energy being determined by:

based on the third inductive energy on the Josephson junctions of the M first quantum devices in the eigenmode, the first magnetic field energy is distributed into M parts, so that the second magnetic field energy which is respectively radiated in space by the M first quantum devices in the eigenmode is obtained, the magnetic field energy of each part is the second magnetic field energy, and the ratio of the second magnetic field energy of any two first quantum devices is equal to the ratio of the third inductive energy on the Josephson junctions of the two first quantum devices;

And for each first quantum device, adding the second magnetic field energy radiated by the first quantum device in space and the third inductance energy on the Josephson junction of the first quantum device to obtain the first inductance energy.

In this embodiment, the total magnetic field energy radiated by the first quantum chip in the eigenmode in space can be distributed according to the ratio of the inductance energy on the josephson junctions of different quantum devices in the eigenmode. Specifically, the third inductive energy is the inductive energy determined by the above formula (4), the first magnetic field energy is the magnetic field energy determined by the above formula (6), and for each eigenmode, the total magnetic field energy radiated by the first quantum chip in space in the eigenmode can be allocated according to the ratio based on the third inductive energy on josephson junctions of the M first quantum devices in the eigenmode.

As for each first quantum device, the second magnetic field energy of each portion may be determined as a percentage of the third inductive energy in the sum of inductive energies on josephson junctions of the M first quantum devices; the second magnetic field energy is the product of the first magnetic field energy and the percentage.

Wherein the magnetic field energy distribution ratio in the space is

k1 and k2 each represent no

The sum of the magnetic field energy distributed on the same two first quantum devices and different quantum devices is equal to the total magnetic field energy radiated by the first quantum chip in the intrinsic mode m in space, and

and (3) representing.

Then, for each first quantum device, adding the inductance energy of the first quantum device on Josephson junction in the eigenmode and the distributed magnetic field energy to obtain the first inductance energy stored in the first quantum device in the eigenmode, using

And (3) representing. In this way, a determination of the first inductive energy may be achieved.

Optionally, the electromagnetic field energy information includes: in the eigenmode, the first quantum chip radiates a first electric field energy in space, and the second inductive energy is determined by:

the first electric field energy is determined as the second inductive energy.

In the present embodiment, the relationship among the inductance energy, capacitance energy, electric field energy, and magnetic field energy in the electromagnetic field may be

Representing the total inductive energy stored in eigenmode m, < >>

Representing the total stored capacitance energy in eigenmode m, < >>

Indicating the total electric field energy of eigenmode m in space,/->

Representing the total magnetic field energy of eigenmode m in space,/- >

The equivalent lumped inductance of the josephson junction is attributed to the kinetic inductance, representing the energy stored by the eigenmode m in the kinetic inductance.

It is known that the total inductance energy stored in the eigenmode m is equal to the total electric field energy of the eigenmode m in space, and thus, the first electric field energy can be determined as the second inductance energy, and the determination of the second inductance energy is achieved.

Correspondingly, according to the electric field energy in the electromagnetic field energy information, the device inductance energy duty ratio of the quantum device k in the intrinsic mode is determined by adopting the formula (1),

optionally, before the step S103, the method further includes:

determining a second relation, wherein the second relation is a relation between the device inductance energy ratio of the quantum device under the intrinsic mode of the quantum chip and a target element in a pre-constructed transformation matrix, and the target element is an element determined by the corresponding row of the intrinsic mode and the corresponding column of the quantum device;

performing variable substitution on elements in the transformation matrix based on the second relation and the symbol information to obtain the first relation;

the transformation matrix is a block diagonal matrix, and the sub-matrices of two diagonal blocks in the transformation matrix are equal.

Optionally, the second relationship is:

wherein p is _mk Device inductance energy duty cycle for quantum device k in eigenmode m, u _mk Elements determined for the rows corresponding to eigenmodes m and the columns corresponding to quantum devices k in the transformation matrix.

Optionally, the determining the second relationship includes:

determining a third relation and a fourth relation, wherein the third relation is a relation between the inductance energy stored in the quantum device in the eigenmode and the inductance energy determined based on the inductance parameter of the quantum device in the eigenmode, and the fourth relation is a relation between the inductance energy stored in the quantum chip in the eigenmode and the first Hamiltonian of the quantum chip in the decoration state;

determining a fifth relation between a device inductance energy ratio of the quantum device in an eigenmode and second target information based on the third relation and the fourth relation, wherein the second target information comprises the inductance parameter and the first hamilton;

converting the inductance parameter into a secondary quantization operator in a decoration state based on elements of a corresponding column of the quantum device in the transformation matrix, and performing quantum state operator operation based on the converted secondary quantization operator to obtain a first target parameter, wherein the first target parameter is a parameter based on the target element;

Performing quantum state operator operation on the first Hamiltonian quantity to obtain a second target parameter;

and transforming the fifth relation based on the first target parameter and the second target parameter to obtain a second relation.

Optionally, the converting the inductance parameter into a secondary quantization operator in the decoration state based on elements of a corresponding column of the quantum device in the transformation matrix includes:

determining a sixth relation between the inductance parameter and a primary quantization operator of the Hamiltonian quantity of the quantum chip in a bare state;

based on elements of a corresponding column of the quantum device in the transformation matrix, determining a seventh relation between a primary quantization operator of the Hamiltonian quantity of the quantum chip in a bare state and a primary quantization operator of the Hamiltonian quantity of the quantum chip in a decorated state;

determining an eighth relation between a primary quantization operator and a secondary quantization operator of the Hamiltonian quantity of the quantum chip in the decoration state;

and converting the inductance parameter into a secondary quantization operator in the decoration state based on the sixth relation, the seventh relation and the eighth relation.

Optionally, the seventh relationship includes: x is x _k ＝u _1k x ₁ ′+u _2k x ₂ ′+…+u _Mk x′ _M ，k∈{1,2,…,M}；

Wherein x is _k One-time quantization operator for Hamiltonian quantity of quantum chip in bare state, x ₁ ′，x ₂ ′，…，x′ _M The method is a once quantized operator of Hamiltonian quantity of the quantum chip in a decoration state.

Optionally, the performing quantum state operator operation on the first hamiltonian to obtain a second target parameter includes:

performing secondary quantization on the first Hamiltonian quantity to obtain a secondary quantization operator representation of the first Hamiltonian quantity;

and performing quantum state operator operation on the secondary quantized operator representation to obtain a second target parameter.

In this embodiment, there is generally a unitary transformation matrix, and the characteristic parameters of the hamiltonian of the first quantum chip in the bare state can be obtained

Characterization parameter converted into Hamiltonian quantity under decoration state +.>

Represented by the following formula (7).

Wherein ω' ₁ 、ω′ ₂ 、…、ω′ _M For the eigenfrequencies corresponding to different eigenmodes, U is a transformation matrix, which is known to be a block diagonal matrix, in order to satisfy

The sub-matrices of the two diagonal blocks are equal, and thus, the pre-constructed transformation matrix can be expressed by the following equation (8).

Wherein the matrix size is 2M multiplied by 2M, and the element of the row quantum device k corresponding to the eigenmode M is u for the submatrix of the diagonal block _mk And (3) representing.

For the quantum device k under the eigenmode m, the target element is u _mk 。

In an alternative embodiment, the second relationship may be

The determination of the second relationship is explained in detail below.

According to the principle of quantum mechanics, the expected value of the quantum mechanical quantity can correspond to the classical value, and a third relationship and a fourth relationship can be obtained, which are represented by the following formulas (9) and (10), respectively.

Wherein, in the above formulas (9) and (10),

represents the expected inductance energy value of a quantum device k (k is 1, 2, … and M) under an intrinsic mode M in quantum mechanics, < >>

The capacitance energy of the quantum chip is equal to the electric field energy in the space>

Representing the total energy expected value of the quantum chip in the intrinsic mode m in quantum mechanics, wherein the total energy comprises inductance energy and capacitance energy, and the capacitance energy is equal to the inductance energy, so that the total energy expected value is equal to the inductance energy which is doubled, ">

The first Hamiltonian amount is the Hamiltonian amount of the quantum chip under the decoration state.

Based on the definition of iEPR at the quantum theory level, a fifth relationship can be obtained based on the third relationship and the fourth relationship, as shown in the following formula (11).

Further, the sixth relation between the inductance parameter and the primary quantization operator of the Hamiltonian amount of the quantum chip in the bare state may be

For the transformation matrix, it can build the Hamiltonian arithmetic and decoration state of the next quantization of the bare state representationThe relationship between the once quantized hamiltonian under the representation is shown in the following formula (12).

Wherein x is ₁ 、x ₂ 、…、x _M 、p ₁ 、p ₂ 、…、p _M Hamiltonian operator for one time quantization under bare state (i.e. one time quantization operator of Hamiltonian amount under bare state), x ₁ ′、x ₂ ′、…、x _M ′、p ₁ ′、p ₂ ′、…、p _M ' is a once quantized hamiltonian in the decorated state representation (i.e., a once quantized hamiltonian in the decorated state).

From the above expression (12), the relationship (i.e., seventh relationship) between the hamiltonian of the next quantization of the bare state representation and the hamiltonian of the next quantization of the decorated state representation can be obtained, as shown in the following expression (13).

x _k ＝u _1k x ₁ ′+u _2k x ₂ ′+…+u _Mk x′ _M ，k∈{1,2,…,M} (13)

Wherein x is _k One-time quantization operator for Hamiltonian quantity of quantum chip in bare state, x ₁ ′，x ₂ ′，…，x′ _M One-time quantization operator for Hamiltonian quantity of quantum chip in decoration state, u _1k 、u _2k 、…、u _Mk Is the kth column element in the submatrix of the diagonal block in the transformation matrix.

Further, a relationship (i.e., an eighth relationship) between the hamiltonian of the next quantization of the decorated state representation and the hamiltonian of the secondary quantization (i.e., the secondary quantization of the hamiltonian in the decorated state) may be determined.

Then, the inductance parameter, namely, can be based on the sixth relation, the seventh relation and the eighth relation

Conversion toThe secondary quantization operator in the decorated state.

The operator operation of the quantum state can be performed based on the converted secondary quantized operator according to the related principle of quantum optics, so as to obtain a first target parameter. Wherein the first target parameter is a parameter based on the target element.

The second quantized operator representation of the first hamiltonian can be obtained by performing secondary quantization on the first hamiltonian from the first hamiltonian of the first quantum chip under the decoration state, and then the second target parameter can be obtained by performing quantum operator operation on the second quantized operator representation of the first hamiltonian according to the quantum optical correlation principle.

Accordingly, based on the first target parameter and the second target parameter, the relationship (i.e., the second relationship) between the device inductance energy ratio of the quantum device k and the target element in the eigenmode m can be obtained by using the above formula (11), as shown in the following formula (14).

In this way, determination of the second relationship may be achieved.

From the uniproperty of the U matrix, iEPR has normalized characteristics represented by the following formula (15).

∑ _m p _mk ＝∑ _k p _mk ＝1(15)

I.e. for a sub-matrix of diagonal blocks in U, the sum of the elements in its rows is 1 and the sum of the elements in its columns is 1.

From the above equation (14), since iEPR and the transformation matrix U have a correspondence as in equation (14), the following equation (14)

To determine the transformation matrix U using iEPR, the judgment of the signs of the matrix elements is also lacking.

Symbol information s can be introduced _mn For representing the signs of the elements in the transformation matrix U, and therefore, the transformation matrix may be modified based on the second relationship and the sign informationPerforming variable substitution on the intermediate elements to obtain a first relation shown in the formula (2), wherein the first relation is

In this way, the determination of the first relationship may be achieved.

Optionally, the step S104 specifically includes:

determining a first characterization matrix of the Hamiltonian amount of the first quantum chip after one-time quantization in the decoration state based on the first decoration state information;

based on the first transformation matrix, carrying out inverse transformation on the first characterization matrix to obtain a second characterization matrix of Hamiltonian quantity of the first quantum chip after primary quantization in a bare state;

and determining the first bare state information based on the second characterization matrix.

In this embodiment, the first decoration state information may include an eigenfrequency ω corresponding to different eigenmodes m of the first quantum chip ^′ _m Based on eigenfrequency omega ^′ _m A first characterization matrix of the hamiltonian amount of the first quantum chip after the primary quantization in the decorated state can be obtained, and is represented by the following formula (16).

The first characterization matrix is inverse transformed based on the first transformation matrix, represented by the following equation (17).

Based on the above formula (17), a second characterization matrix of the hamiltonian amount of the first quantum chip after the primary quantization in the bare state can be obtained, and correspondingly, the first bare state information can be determined based on the second characterization matrix. In this way, the determination of the first bare state information may be implemented based on the first transformation matrix.

Optionally, the determining, based on the second characterization matrix, the first bare state information includes:

determining first eigenfrequency of each first quantum device and first coupling information between each two quantum devices in the M first quantum devices based on the second characterization matrix and a predetermined ninth relation, wherein the ninth relation is a relation between a characterization parameter of Hamiltonian amount of the quantum chip after primary quantization in a bare state and third target information, the third target information comprises the eigenfrequency of the quantum devices and coupling information between the quantum devices, and the coupling information is determined based on coupling strength between the quantum devices and the eigenfrequency of the quantum devices;

Determining a first coupling strength between each two quantum devices of the M first quantum devices based on the first eigenfrequency and the first coupling information;

wherein the first bare state information includes at least one of the first eigenfrequency and the first coupling strength.

In this embodiment, a ninth relationship may be first determined, where the ninth relationship is used to determine a characterization matrix of the hamiltonian of the quantum chip in the bare state, where the characterization matrix is a relationship between a characterization parameter of the hamiltonian of the quantum chip after being quantized once in the bare state and coupling information (i.e., a coupling term) between an eigenfrequency of the quantum device and the quantum device.

The determination of the ninth relationship is as follows:

for a multi-body system with M quantum devices, capacitive coupling exists between every two quantum devices, and the Hamiltonian quantity in a bare state can be written as shown in the following formula (18).

Wherein Q is _i Is the charge quantity phi _i For inductive magnetic flux, C _i 、C _j And C _g,ij Is a capacitor L _i Is an inductance.

The hamiltonian amount represented by the above formula (18) is quantized once, and the following variables may be substituted:

wherein omega _i Is the bare state frequency, x of the quantum device _i For new generalized coordinates, p _i The hamiltonian amount represented by the following formula (19) is obtained as the generalized momentum.

/>

Wherein g _ij Representing the coupling strength between two quantum devices, satisfying g _ij ＝g _ji 。

Determining a coupling term based on coupling strength and frequency between two quantum devices

Represented by the following formula (20).

Since the hamiltonian amount in the primary quantized form is quadratic, it can be written in a matrix-multiplied form as shown in the following equation (21).

It is known that, the characterization parameter of the hamiltonian amount of the quantum chip after the primary quantization in the bare state is shown in the following formula (22), and the characterization parameter is the ninth relationship, so that the determination of the ninth relationship can be realized.

Thereafter, the second characterization matrix and the ninth relationship may be alignedCharacterization parameters, determining the first eigenfrequency omega of each first quantum device _i And first coupling information (i.e., coupling terms) between each two quantum devices of the M first quantum devices

)。

From the above equation (20), the first coupling strength between different first quantum devices can be determined using the following equation (23) based on the first eigenfrequency and the first coupling information.

The first bare state information may include at least one of a first eigenfrequency and the first coupling strength, and in addition, the first bare state information may further include characteristic parameters such as a dispersion ratio, non-harmonic property, and equivalent coupling strength.

In this way, the determination of the first bare state information may be implemented based on the second characterization matrix. Therefore, based on the first transformation matrix, the bare state information can be restored from the decoration state information of the multi-body system, and the bare state information is helpful for researchers to better evaluate the performance of the quantum chip in the design stage, so that the method has important practical value for the simulation verification work in the quantum chip design stage.

Optionally, the M first quantum devices include two qubits and a coupler for coupling the two qubits, and after determining the first coupling strength between each two quantum devices in the M first quantum devices based on the first eigenfrequency and the first coupling information, the method further includes:

and determining the equivalent coupling strength between the two qubits based on the first eigenfrequency and the first coupling strength, wherein the first bare state information further comprises the equivalent coupling strength.

The M first quantum devices may be a qubit-coupler-qubit (qubit-coupler-qubit, QCQ) structure, and on the basis of obtaining the first eigenfrequency and the first coupling strength, an equivalent coupling strength between two qubits may be further determined, which is represented by the following formula (24).

Wherein g ^′ ₁₂ Representing the equivalent coupling strength between qubit 1 and qubit 2; g ₁₂ Representing a first coupling strength between qubit 1 and qubit 2; g _1c Representing a first coupling strength between qubit 1 and the coupler; g _2c Representing a first coupling strength between qubit 2 and the coupler; omega ₁ A first eigenfrequency representing qubit 1; omega ₂ A first eigenfrequency representing qubit 2; omega _c Representing the first eigenfrequency of the coupler.

In this way, determination of the equivalent coupling strength between two qubits in the QCQ structure can be achieved.

Optionally, the method further comprises:

outputting the first bare state information.

The first bare state information can be output for corresponding application, for example, the first bare state information is output to researchers to better evaluate the performance of the quantum chip in a design stage, and the first bare state information is output to the researchers to perform further simulation verification work.

In an alternative implementation, the overall flow of this embodiment is shown in fig. 3, and the above steps are already described in detail, which is not described herein again. Compared with the related equivalent circuit method, the method has the advantages that based on high-frequency electromagnetic field simulation, the effect brought by the high-frequency field is considered, the adopted effect is approximate to less and is closer to the actual condition, and the method has important practical value for the design and verification work of the superconducting quantum chip.

The correctness of the scheme of the present embodiment is verified by a specific example. The QCQ structural layout taking fig. 2 as an example is subjected to simulation verification, and is the structural layout of a three-quantum bit device. The layout can comprise three quantum bits, wherein the middle quantum bit is used as a coupler for adjusting the equivalent coupling strength between the quantum bits at the left end and the right end. By tuning the magnetic flux of the coupler (here, the magnetic flux tuning can be simulated by adjusting the inductance of the josephson junction of the coupler), the coupling turn-off between the qubits can be realized (i.e. the equivalent coupling strength is 0), thereby suppressing the influence of parasitic coupling, crosstalk and the like and greatly improving the performance of the quantum chip.

The equivalent coupling strength tuning of the QCQ structure can be simulated (set the inductance of two qubits to 12nH, the inductance of the coupler gradually changes from 7nH to 11 nH), and the verification task is as follows:

verification task 1: the bare state information under different coupler inductances is calculated and compared by the method of the embodiment and the equivalent circuit method respectively;

verification task 2: and calculating the equivalent coupling strength between the quantum bits under different coupler inductances by using the bare state information, verifying the existence of a coupling switching point and comparing data.

For verification task 1, the resulting pair of bare state frequencies of quantum devices at different coupler inductance values is shown in fig. 4. Wherein, the data points and the dotted lines represent the results of the bare state frequency obtained by solving the method in the embodiment, and the continuous curve represents the results of the bare state frequency obtained by solving the equivalent circuit method.

As can be seen from fig. 4, the bare state frequency variation trend of the coupler obtained under different coupler inductance values is consistent with the equivalent circuit, and the bare state frequency values of the quantum bit 1 and the quantum bit 2 are almost unchanged, because the change of the coupler inductance value does not affect the bare state frequency of the quantum bit, the result accords with the actual situation, which indicates that the bare state frequency calculated by the method of the embodiment is correct.

In addition, the result of the bare state frequency obtained by solving the equivalent circuit method is slightly larger than the result of the bare state frequency obtained by solving the equivalent circuit method, because the conductor has an inductance effect under the high-frequency electromagnetic field, and the equivalent circuit method adopts more approximation because the conductor is regarded as an equipotential body and the inductance effect actually existing by the conductor is not considered, so that the result is slightly larger than the actual situation. The group of verification can prove the effectiveness of the method of the embodiment, and is closer to the real situation in theory.

The coupling strength pairs between different quantum devices under different coupler inductance values are shown in fig. 5, wherein data points and dotted lines represent the result of the coupling strength obtained by solving the method in this embodiment, and continuous curves represent the result of the coupling strength obtained by solving the equivalent circuit method.

As can be seen from fig. 5, the bare state coupling strength between the qubits obtained under different coupler inductance values is almost unchanged, which accords with the theory of QCQ structure, and meanwhile, the solved qubit 1 and qubit 2 are respectively matched with the bare state coupling strength of the coupler and the change trend of the equivalent circuit method, and the data value is close, so that the bare state coupling strength calculated by the method in the embodiment is correct.

In addition, the result of the coupling strength obtained by solving the equivalent circuit method is slightly larger than the result of the coupling strength obtained by solving the equivalent circuit method, because the conductor has an inductance effect and mutual inductance effects among different quantum devices under the high-frequency electromagnetic field, and the equivalent circuit method adopts more approximation by regarding the conductor as an equipotential body and does not consider the inductance effect actually existing in the conductor, so that the result is slightly larger than the actual situation. The method of the embodiment considers the effect of the high-frequency electromagnetic field, so that the method adopts less approximation, and the data of the embodiment also laterally verifies that the method of the embodiment is more similar to the real situation.

For verification task 2: and (3) determining the equivalent coupling strength between two qubits by using the bare state information obtained by the two methods in the verification task 1 through the formula (24), and comparing data, wherein the equivalent coupling strength between the qubits under different coupler inductance values is shown in a graph like that shown in fig. 6. The data points and the dotted lines are the results of the equivalent coupling strength obtained by solving the method in the embodiment, and the continuous curve represents the results of the equivalent coupling strength obtained by solving the equivalent circuit method. As can be seen from this fig. 6, the method of this embodiment can simulate the process of tuning the equivalent coupling strength of the qubit by the coupler and find the coupling Guan Duandian (i.e., the equivalent coupling strength is 0).

The result of the equivalent coupling strength obtained by solving the method in the embodiment is very close to the result of the equivalent coupling strength obtained by solving the equivalent circuit method, and meanwhile, the coupling turn-off point found by the method in the embodiment is basically consistent with the coupling turn-off point found by the equivalent circuit method, so that the calculation result of the method in the embodiment is proved to be correct.

In addition, the equivalent circuit method is better matched with the method in the embodiment when approaching the coupling off point, because the coupling caused by the inductance effect is also close to zero near the coupling off point, and the result of the equivalent circuit is closer to the real situation. Under other conditions, the equivalent circuit does not consider the influence of the self inductance effect of the high-frequency field conductor, so that the absolute value of the equivalent coupling strength is slightly larger than that obtained by solving the method in the embodiment, and the result of the method in the embodiment is more close to the real situation.

Second embodiment

As shown in fig. 7, the present disclosure provides a bare state information determining apparatus 700 of a multi-body system in a superconducting quantum chip layout, including:

an obtaining module 701, configured to obtain a structural layout of a first quantum chip, where the first quantum chip includes M first quantum devices, the first quantum devices include josephson junctions, and M is an integer greater than 2;

a first determining module 702, configured to determine, based on the structural layout, a first device inductance energy ratio and first sign information of the M first quantum devices in each eigenmode of the first quantum chip, where the first device inductance energy ratio is: the ratio of the first inductive energy stored in the first quantum device in the eigenmode to the second inductive energy stored in the first quantum chip in the eigenmode, wherein the first symbol information indicates the positive-negative relation between the current on the Josephson junction of the first quantum device in the eigenmode and a preset reference direction;

a second determining module 703, configured to determine a first transformation matrix based on the first device inductance energy ratio, the first symbol information, and a predetermined first relationship, where the first relationship is a relationship between the transformation matrix and first target information, and the first target information includes the device inductance energy ratio and the symbol information;

The third determining module 704 is configured to determine first bare state information of the first quantum chip based on the first transformation matrix and predetermined first decoration state information of the first quantum chip, where the first decoration state information is eigenstate information of a multi-body system formed by the first quantum chip, and the first bare state information is eigenstate information of the M first quantum devices.

Optionally, the first determining module 702 includes:

the solving submodule is used for carrying out eigenmode solving on the structural layout to obtain electromagnetic field distribution information of the first quantum chip under each eigenmode of the high-frequency electromagnetic field;

a first determining sub-module for determining the first device inductance energy ratio and the first sign information based on the electromagnetic field distribution information.

Optionally, the electromagnetic field distribution information includes a current density on a surface of the first quantum chip in an eigenmode, and the first determining submodule includes:

a first determining unit for determining a current on a josephson junction of the first quantum device in eigenmode based on the current density;

and a second determining unit configured to determine the first symbol information based on the current.

Optionally, the second determining unit is specifically configured to:

Optionally, the first determining submodule includes:

a third determining unit configured to determine electromagnetic field energy information of the first quantum chip in each eigenmode based on the electromagnetic field distribution information;

a fourth determination unit configured to determine the first inductive energy and the second inductive energy based on the electromagnetic field energy information;

and a fifth determining unit, configured to determine a ratio of the first inductive energy and the second inductive energy as the first device inductive energy duty ratio.

Optionally, the electromagnetic field energy information includes: in eigenmode, the first quantum chip radiates a first magnetic field energy in space and a third inductive energy on josephson junctions of the M first quantum devices, the fourth determining unit being specifically configured to:

Optionally, the electromagnetic field energy information includes: in the eigenmode, the first quantum chip radiates a first electric field energy in space, and the fourth determining unit is specifically configured to:

the first electric field energy is determined as the second inductive energy.

Optionally, the apparatus further includes:

a fourth determining module, configured to determine a second relationship, where the second relationship is a relationship between a device inductance energy ratio of the quantum device in an eigenmode of the quantum chip and a target element in a pre-configured transformation matrix, where the target element is an element determined by an eigenmode corresponding row and a quantum device corresponding column;

and the variable substitution module is used for carrying out variable substitution on elements in the transformation matrix based on the second relation and the symbol information to obtain the first relation.

Optionally, the second relationship is:

Optionally, the fourth determining module includes:

the second determining submodule is used for determining a third relation and a fourth relation, the third relation is a relation between the inductance energy stored in the quantum device in the eigenmode and the inductance energy determined based on the inductance parameter of the quantum device in the eigenmode, and the fourth relation is a relation between the inductance energy stored in the quantum chip in the eigenmode and the first Hamiltonian of the quantum chip in the decoration state;

a third determining submodule, configured to determine a fifth relation between a device inductance energy duty cycle of the quantum device in an eigenmode and second target information based on the third relation and the fourth relation, where the second target information includes the inductance parameter and the first hamiltonian amount;

the first operator module is used for converting the inductance parameter into a secondary quantized operator in a decoration state based on elements of a corresponding column of the quantum device in the transformation matrix, and performing quantum state operator operation based on the converted secondary quantized operator to obtain a first target parameter, wherein the first target parameter is a parameter based on the target element;

The second operator module is used for carrying out quantum state operator operation on the first Hamiltonian quantity to obtain a second target parameter;

and the transformation submodule is used for transforming the fifth relation based on the first target parameter and the second target parameter to obtain a second relation.

Optionally, the first operator module is specifically configured to:

Optionally, the seventh relationship includes: x is x _k ＝u _1k x ₁ ^′ +u _2k x ₂ ^′ +…+u _Mk x ^′ _M ，k∈{1,2,…,M}；

Wherein x is _k One-time quantization operator for Hamiltonian quantity of quantum chip in bare state, x ₁ ^′ ，x ₂ ^′ ，…，x ^′ _M The method is a once quantized operator of Hamiltonian quantity of the quantum chip in a decoration state.

Optionally, the second operator module is specifically configured to:

Optionally, the third determining module 704 includes:

a fourth determining submodule, configured to determine, based on the first decoration state information, a first characterization matrix of a hamiltonian amount of the first quantum chip after being quantized once in the decoration state;

the inverse transformation submodule is used for carrying out inverse transformation on the first characterization matrix based on the first transformation matrix to obtain a second characterization matrix of Hamiltonian quantity of the first quantum chip after primary quantization in a bare state;

and a fifth determining sub-module, configured to determine the first bare state information based on the second characterization matrix.

Optionally, the fifth determining submodule is specifically configured to:

Optionally, the M first quantum devices include two qubits and a coupler for coupling the two qubits, and the apparatus further includes:

and a fifth determining module, configured to determine an equivalent coupling strength between the two qubits based on the first eigenfrequency and the first coupling strength, where the first bare state information further includes the equivalent coupling strength.

Optionally, the apparatus further includes:

and the output module is used for outputting the first bare state information.

The device 700 for determining the bare state information of the multi-body system in the superconducting quantum chip layout provided by the disclosure can realize each process realized by the embodiment of the method for determining the bare state information of the multi-body system in the superconducting quantum chip layout, and can achieve the same beneficial effects, and for avoiding repetition, the description is omitted here.

In the technical scheme of the disclosure, the related processes of collecting, storing, using, processing, transmitting, providing, disclosing and the like of the personal information of the user accord with the regulations of related laws and regulations, and the public order colloquial is not violated.

According to embodiments of the present disclosure, the present disclosure also provides an electronic device, a readable storage medium and a computer program product.

FIG. 8 illustrates a schematic block diagram of an example electronic device that may be used to implement embodiments of the present disclosure. Electronic devices are intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular telephones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the disclosure described and/or claimed herein.

As shown in fig. 8, the apparatus 800 includes a computing unit 801 that can perform various appropriate actions and processes according to a computer program stored in a Read Only Memory (ROM) 802 or a computer program loaded from a storage unit 808 into a Random Access Memory (RAM) 803. In the RAM 803, various programs and data required for the operation of the device 800 can also be stored. The computing unit 801, the ROM 802, and the RAM 803 are connected to each other by a bus 804. An input/output (I/O) interface 805 is also connected to the bus 804.

Various components in device 800 are connected to I/O interface 805, including: an input unit 806 such as a keyboard, mouse, etc.; an output unit 807 such as various types of displays, speakers, and the like; a storage unit 808, such as a magnetic disk, optical disk, etc.; and a communication unit 809, such as a network card, modem, wireless communication transceiver, or the like. The communication unit 809 allows the device 800 to exchange information/data with other devices via a computer network such as the internet and/or various telecommunication networks.

The computing unit 801 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 801 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various specialized Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, etc. The calculation unit 801 performs the respective methods and processes described above, for example, a bare state information determination method of a multi-body system in a superconducting quantum chip layout. For example, in some embodiments, the method of determining bare state information for a multi-body system in a superconducting quantum chip layout may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as storage unit 808. In some embodiments, part or all of the computer program may be loaded and/or installed onto device 800 via ROM 802 and/or communication unit 809. When a computer program is loaded into RAM 803 and executed by computing unit 801, one or more steps of the bare state information determination method of the multi-body system in the superconducting quantum chip layout described above may be performed. Alternatively, in other embodiments, the computing unit 801 may be configured to perform the bare state information determination method of the multi-body system in the superconducting quantum chip layout in any other suitable way (e.g. by means of firmware).

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuit systems, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), systems On Chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs, the one or more computer programs may be executed and/or interpreted on a programmable system including at least one programmable processor, which may be a special purpose or general-purpose programmable processor, that may receive data and instructions from, and transmit data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for carrying out methods of the present disclosure may be written in any combination of one or more programming languages. These program code may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus such that the program code, when executed by the processor or controller, causes the functions/operations specified in the flowchart and/or block diagram to be implemented. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.

In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. The machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and pointing device (e.g., a mouse or trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such background, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), and the internet.

The computer system may include a client and a server. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server may be a cloud server, a server of a distributed system, or a server incorporating a blockchain.

It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps recited in the present disclosure may be performed in parallel, sequentially, or in a different order, provided that the desired results of the disclosed aspects are achieved, and are not limited herein.

The above detailed description should not be taken as limiting the scope of the present disclosure. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present disclosure are intended to be included within the scope of the present disclosure.

Claims

1. A method for determining bare state information of a multi-body system in a superconducting quantum chip layout comprises the following steps:

2. The method of claim 1, wherein the determining, based on the structural layout, first device inductance energy duty cycles and first sign information for the M first quantum devices in respective eigenmodes of the first quantum chip comprises:

3. The method of claim 2, wherein the electromagnetic field distribution information comprises a current density on the first quantum chip surface in eigenmodes, the first sign information determined by:

the first sign information is determined based on the current.

4. The method of claim 3, wherein the determining the first symbol information based on the current comprises:

5. The method of claim 2, wherein the first device inductance energy ratio is determined by:

6. The method of claim 5, wherein the electromagnetic field energy information comprises: in eigenmode, the first quantum chip radiates a first magnetic field energy in space and a third inductive energy on josephson junctions of the M first quantum devices, the first inductive energy being determined by:

7. The method of claim 5, wherein the electromagnetic field energy information comprises: in the eigenmode, the first quantum chip radiates a first electric field energy in space, and the second inductive energy is determined by:

the first electric field energy is determined as the second inductive energy.

8. The method of claim 1, the determining a first transformation matrix based on the first device inductance energy ratio, the first sign information, and a predetermined first relationship, further comprising, prior to:

9. The method of claim 8, wherein the second relationship is:

10. The method of claim 9, wherein the determining the second relationship comprises:

11. The method of claim 10, wherein the converting the inductance parameter into a secondary quantization operator in a decorated state based on elements of a corresponding column of quantum devices in a transformation matrix comprises:

12. The method of claim 11, wherein the seventh relationship comprises: x is x _k ＝u _1k x′ ₁ +u _2k x′ ₂ +…+u _Mk x′ _M ，k∈{1，2，...，M}；

Wherein x is _k Is one-time quantization operator of Hamiltonian quantity of quantum chip in bare state, x' ₁ ，x′ ₂ ，…，x′ _M The method is a once quantized operator of Hamiltonian quantity of the quantum chip in a decoration state.

13. The method of claim 10, wherein the performing the quantum state operator operation on the first hamiltonian quantity to obtain a second target parameter comprises:

14. The method of claim 1, wherein the determining the first bare state information of the first quantum chip based on the first transformation matrix and the predetermined first decorated state information of the first quantum chip comprises:

15. The method of claim 14, wherein the determining the first bare state information based on the second characterization matrix comprises:

16. The method of claim 15, wherein the M first quantum devices comprise two qubits and a coupler for coupling the two qubits, the determining a first coupling strength between each two of the M first quantum devices based on the first eigenfrequency and the first coupling information further comprising:

17. The method of claim 1, further comprising:

outputting the first bare state information.

18. A bare state information determining device of a multi-body system in a superconducting quantum chip layout comprises:

19. The apparatus of claim 18, wherein the first determination module comprises:

20. The apparatus of claim 19, wherein the electromagnetic field distribution information comprises a current density on a surface of the first quantum chip in eigenmodes, the first determination submodule comprising:

21. The apparatus of claim 20, wherein the second determining unit is specifically configured to:

22. The apparatus of claim 19, wherein the first determination submodule comprises:

23. The apparatus of claim 22, wherein the electromagnetic field energy information comprises: in eigenmode, the first quantum chip radiates a first magnetic field energy in space and a third inductive energy on josephson junctions of the M first quantum devices, the fourth determining unit being specifically configured to:

24. The apparatus of claim 22, wherein the electromagnetic field energy information comprises: in the eigenmode, the first quantum chip radiates a first electric field energy in space, and the fourth determining unit is specifically configured to:

the first electric field energy is determined as the second inductive energy.

25. The apparatus of claim 18, further comprising:

26. The apparatus of claim 25, wherein the second relationship is:

27. The apparatus of claim 26, wherein the fourth determination module comprises:

28. The apparatus of claim 27, wherein the first operator module is specifically configured to:

29. The garment of claim 28Wherein the seventh relationship comprises: x is x _k ＝u _1k x′ ₁ +u _2k x′ ₂ +…+u _Mk x′ _M ，k∈{1，2，...，M}；

Wherein x is _k Is one-time quantization operator of Hamiltonian quantity of quantum chip in bare state, x' ₁ ，x′ ₂ ，...，x′ _M The method is a once quantized operator of Hamiltonian quantity of the quantum chip in a decoration state.

30. The apparatus of claim 27, wherein the second operator module is specifically configured to:

31. The apparatus of claim 18, wherein the third determination module comprises:

32. The apparatus of claim 31, wherein the fifth determination submodule is configured to:

33. The apparatus of claim 32, wherein the M first quantum devices comprise two qubits and a coupler for coupling the two qubits, the apparatus further comprising:

34. The apparatus of claim 18, further comprising:

and the output module is used for outputting the first bare state information.

35. An electronic device, comprising:

at least one processor; and

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-17.

36. A non-transitory computer readable storage medium storing computer instructions for causing the computer to perform the method of any one of claims 1-17.