CN115577779A

CN115577779A - Bare state information determination method and device for multi-body system in superconducting quantum chip layout

Info

Publication number: CN115577779A
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: 2023-01-06
Anticipated expiration: 2042-10-24
Also published as: CN115577779B

Abstract

The invention provides a method and a device for determining naked 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 inductance energy ratio and first symbol information of the M first quantum devices under each intrinsic mode of the first quantum chip based on the structural layout; determining a first transformation matrix based on the first device inductance energy ratio, the first symbol information and a predetermined first relation; 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.

Description

Bare state information determination method and device for 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

With the large-scale development of the superconducting quantum chip, the simulation verification of the chip before the formal flow sheet is also very important besides the higher requirements on the micro-nano processing technology. The purpose of simulation verification is to describe characteristic parameters of the chip as truly as possible, so that researchers can better predict performance indexes of the chip in a design stage, and 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 usually performed by an equivalent circuit method, that is, 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 as to obtain the bare state information of a multi-body system in a superconducting quantum chip layout.

Disclosure of Invention

The disclosure provides a method and a device 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, there is provided a method for determining bare state information of a multi-body system in a superconducting quantum chip layout, 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 greater than 2;

based on the structural layout, determining a first device inductance energy ratio and first symbol information of the M first quantum devices in each eigenmode of the first quantum chip, wherein the first device inductance energy ratio is as follows: a ratio of a first inductive energy stored in the first quantum device in the eigenmode relative to a second inductive energy stored in the first quantum chip in the eigenmode, the first sign information indicating a positive-negative relationship of a current on a josephson junction of the first quantum device in the eigenmode to 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 predetermined first decoration state information of the first quantum chip, wherein the first decoration state information is eigen state information of a multi-body system formed by the first quantum chip, and the first bare state information is eigen state information of the M first quantum devices.

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

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

a first determining module, 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: a ratio of a first inductive energy stored in the first quantum device in the eigenmode relative to a second inductive energy stored in the first quantum chip in the eigenmode, the first sign information indicating a positive-negative relationship of a current on a josephson junction of the first quantum device in the eigenmode to a preset reference direction;

a second determining module, 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 is configured to determine first bare state information of the first quantum chip based on the first transformation matrix and predetermined first decorated state information of the first quantum chip, where the first decorated state information is eigen state information of a multi-body system formed by the first quantum chip, and the first bare state information is eigen state 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 content of the first and second substances,

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 having stored thereon computer instructions for causing a computer to perform any one 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 that the simulation verification effect of the superconducting quantum chip is poor is solved, and the simulation verification effect of the superconducting quantum chip is improved, so that the determination accuracy of the bare state information of a multi-body system in a superconducting quantum chip layout is improved.

It should be understood that the statements in this section do not necessarily identify key or critical features of the embodiments of the present disclosure, nor do they limit the scope of the present disclosure. Other features of the present disclosure will become apparent from the following description.

Drawings

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

fig. 1 is a schematic flow chart 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 schematic flow diagram of a specific example provided by the present disclosure;

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

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

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

fig. 7 is a schematic structural diagram of a bare state information determination 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 with reference to the accompanying drawings, in which various details of the embodiments of the disclosure are included to assist understanding, and which are to be considered as merely exemplary. Accordingly, those 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 the 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 the simulation verification scene of the superconducting quantum chips. The method for determining the bare state information of the multi-body system in the superconducting quantum chip layout according to the embodiment of the disclosure can be executed by the apparatus for determining the bare state information of the multi-body system in the superconducting quantum chip layout according to the embodiment of the disclosure. The bare state information determining device for the multi-body system in the superconducting quantum chip layout of the embodiment of the disclosure may be configured in any electronic device to execute the bare state information determining method for the multi-body system in the superconducting quantum chip layout of the embodiment of the disclosure.

In this step, the first quantum chip may be any one of the quantum chips, and the quantum chip may be a superconducting quantum chip, which is used as a core carrier in a technical scheme of a superconducting circuit, and development of the superconducting quantum chip is very important. Similar to classical chips, superconducting quantum chips also require a complete structural layout before formal production and processing. The structural layout contains 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, M being 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, details will be described by taking the example that all three first quantum devices are qubits, wherein all the three first quantum devices include josephson junctions, and every two first quantum devices are coupled with each other.

Simulation verification of a superconducting quantum chip is an indispensable part in a design stage, in the related technology, a superconducting quantum circuit can be generally subjected to simulation verification by adopting an equivalent circuit method, specifically, a continuous conductor in a quantum chip layout can be regarded as an equipotential body, equivalent circuit modeling is carried out according to a node potential method, and nodes are connected by capacitors or inductors; simulating parameters such as capacitance and inductance between nodes by electromagnetic field simulation software; the equivalent circuit model is quantized to obtain a complete Hamiltonian representing a quantum chip system, and related characteristic parameters in a 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 a large number of approximations, the equivalent circuit method regards a continuous conductor as an equipotential body, and the continuous conductor cannot be regarded as an equipotential body under a high-frequency electromagnetic field, so that the method is different from a real object environment, and a calculation result has a certain difference.

In the related art, for a performance simulation verification task of a quantum chip, a classical Energy Proportion (EPR) method may also be used, which uses high-frequency electromagnetic field simulation and performs post-processing on simulation data to obtain characteristic parameters of the quantum chip. The method is small in application range, can be only used for simulating the condition that the quantum devices are in dispersion coupling (the frequency difference between the quantum devices is far larger than the coupling strength), and cannot solve other conditions such as near resonance (the frequency difference between the quantum devices and the coupling strength are the same in magnitude).

The purpose of this embodiment is: determining a device Inductance Energy Proportion (iEPR) and symbol information of each first quantum device in a superconducting quantum chip layout, wherein the device Inductance Energy Proportion (iEPR) and the symbol information can be used as a bridge for connecting bare state information and decorated state information in a first quantum chip physical system, and a transformation matrix between bare state and decorated state Hamilton quantities can be completely constructed by using the device inductance Energy proportion and the symbol information, so that bare state information of a multi-system in the superconducting quantum chip layout is determined based on the transformation matrix and the decorated state information.

The bare state information may include an eigenfrequency of each quantum device in a 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 practical layouts, qubits are usually composed of coplanar capacitors and josephson junctions together. In practice, a substrate (usually implemented by silicon or sapphire) is designed, an aluminum film is plated on the substrate, qubit capacitors are formed by etching different shapes into the aluminum film, and the nonlinear device josephson junction is designed between two metal plates.

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

The obtaining mode of the structural layout of the first quantum chip includes, 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 a first device inductance energy ratio and first symbol information of the M first quantum devices in each eigenmode of the first quantum chip, wherein the first device inductance energy ratio is as follows: a ratio of a first inductive energy stored in the first quantum device in the eigenmode relative to a second inductive energy stored in the first quantum chip in the eigenmode, the first sign information indicating a positive-negative relationship of a current on a Josephson junction of the first quantum device in the eigenmode with a preset reference direction.

In this step, the first device inductive device fraction is a fraction of a first inductive energy stored in the first quantum device in the eigenmode relative to a second inductive energy stored in the first quantum chip in the eigenmode.

For each first quantum device, the first device inductance energy ratio corresponds to the first quantum device, and the device inductance energy ratio corresponding to the quantum device may include the device inductance energy ratio of the quantum device in each eigenmode of the quantum chip.

Due to the coupling of the quantum devices, the quantum chip may include a plurality of eigenmodes, the number of eigenmodes of which is generally related to the number of the quantum devices, for example, when the quantum chip includes three quantum devices, the quantum chip may generally include three eigenmodes, and the three eigenmodes may correspond to the three quantum devices one to one.

Correspondingly, when the first quantum chip comprises three first quantum devices, the number of the first device inductance energy ratio of the three first quantum devices in each intrinsic mode 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 of the quantum device k in the eigenmode m is as shown in the following formula (1).

Wherein the content of the first and second substances,

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

In another alternative embodiment, the structural layout may be subjected to high-frequency electromagnetic field simulation, that is, eigenmode solution is performed on the input layout to obtain simulation output information, and the simulation output information may include decoration state information of the first quantum chip in the eigenmode of the high-frequency electromagnetic field, and decoration is performedThe state information can be eigen-state information of a quantum system formed by the first quantum chip, and is information representation of the whole quantum system with the mutually coupled first quantum devices. The decoration state information may include frequency of eigenmode of the first quantum chip, electromagnetic field distribution information, etc., and the electromagnetic field distribution information may represent electromagnetic field distribution of the first quantum chip radiated in space under different eigenmodes, for example, the electromagnetic field distribution information may include electric field intensity peak distribution of eigenmode m in space

Peak distribution of magnetic field strength

And surface current density of quantum chip

And the like. Then, the inductance energy ratio of the M first quantum devices in each eigenmode can be determined based on the electromagnetic field distribution information.

The first sign information indicates positive and negative relations between currents on a Josephson junction of the first quantum device in the eigenmode and a preset reference direction. The preset reference direction can be a reference direction in a standard Cartesian coordinate system, the default reference direction is each positive direction of the standard Cartesian coordinate system, and the default reference directions of all the first quantum devices are uniform.

The first sign information indicates that the positive and negative relationship between the current on the josephson junction of the first quantum device in the eigenmode and the preset reference direction includes two conditions, namely the same direction and the reverse direction, and the first sign information is different in the same direction and the reverse direction. In an optional embodiment, when the first sign information is 1, it 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, and when the first sign information is-1, it indicates that the current on the josephson junction of the first quantum device in the eigenmode is in the opposite direction to the preset reference direction.

M can be determined based on electromagnetic field distribution informationAnd the first quantum device is used for providing first symbol information under each eigenmode. Wherein, the sign information of the quantum device k in the eigenmode m can be represented as s _mk When the first quantum chip includes three first quantum devices, the number of the first symbol information of the three first quantum devices in each eigenmode of the first quantum chip is 9, and s is the number of the first symbol information of the three first quantum devices in each eigenmode of the first quantum chip ₁₁ 、s ₁₂ 、s ₁₃ 、s ₂₁ 、s ₂₂ 、s ₂₃ 、s ₃₁ 、s ₃₂ And s ₃₃ 。

Step S103: and 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 the relation between the transformation matrix and first target information, and the first target information comprises the device inductance energy ratio and the symbol information.

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

In the multi-body system, a first relation can be determined by combining the symbol information, the first relation is a relation between a transformation matrix and the device inductance energy ratio and the symbol information, the transformation matrix is represented by U, the transformation matrix can be used as a bridge between decoration state information and bare state information of the multi-body system, and the first relation is represented by the following formula (2).

It can be known that, in order to determine the first transformation matrix, the inductance energy ratio of the first device and the first sign information of the M first quantum devices in each eigenmode need to be obtained, and the first transformation matrix can be obtained by substituting the 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 predetermined first decoration state information of the first quantum chip, wherein the first decoration state information is eigen state information of a multi-body system formed by the first quantum chip, and the first bare state information is eigen state information of the M first quantum devices.

In this step, the first decoration state information may include eigenfrequencies ω 'corresponding to different eigenmodes m of the first quantum chip' _m . May be based on the eigenfrequencies ω 'corresponding to the different eigenmodes m of the first quantum chip' _m Determining a characterization matrix of the Hamiltonian of the first quantum chip in the decorated state, and performing inverse transformation on the characterization matrix of the Hamiltonian in the decorated state by using the first transformation matrix to obtain first naked-state information. The first bare state information may include eigenfrequencies of the M first quantum devices, coupling strength between every two first quantum devices, and the like.

In this embodiment, a structural layout of a first quantum chip is obtained; determining inductance energy ratio and first symbol information of the first devices of the M first quantum devices in each intrinsic mode based on the structural layout; determining a first transformation matrix based on the first device inductance energy ratio, the first symbol information and the first relation; and determining first bare state information of the first quantum chip based on the first transformation matrix and the first decoration state information of the first quantum chip. Therefore, the bare state information of the multi-body system in the quantum chip layout can be determined based on the decorated state information of the multi-body system in the quantum chip layout by utilizing the device inductance energy ratio and the sign information of the quantum device in the intrinsic mode, so that the simulation verification of the quantum chip layout comprising a plurality of quantum devices can be realized, and the design efficiency and the accuracy of the quantum chip layout comprising 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. The method has important practical value for the characteristic parameter verification work in the quantum chip design stage.

Optionally, the step S102 specifically includes:

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

determining the first device inductive energy fraction and the first sign information based on the electromagnetic field distribution information.

In this embodiment, a high-frequency electromagnetic field simulation of a finite element method may be performed on the structural layout, that is, an eigenmode solution may be performed on the input layout 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 can characterize the electromagnetic field distribution of the first quantum chip radiated in the space under different eigenmodes, for example, the electromagnetic field distribution information can comprise the electric field intensity peak distribution of the eigenmode m in the space

Peak distribution of magnetic field strength

And surface current density of the first quantum chip

And so on.

The first device inductive energy fraction may then be determined based on the electromagnetic field distribution information. In the embodiment, the high-frequency electromagnetic field simulation is adopted, the adopted approximation is less, the inductance effect of the conductor caused by a high-frequency electromagnetic field is considered, the actual situation is closer, the accuracy is higher, meanwhile, the method is suitable for 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 the current on the Josephson junction of the first quantum device under each eigenmode can be determined based on the electromagnetic field distribution information, and the positive-negative relation between the direction of the current and the preset reference direction is compared, so that the determination of the first symbol information is realized.

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

determining a current on a Josephson junction of the first quantum device in an intrinsic mode based on the current density;

determining the first symbol information 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, for

And (4) showing.

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

Wherein k is 1,2,.., M,

the length of the Josephson junction of quantum device k when expressed as equivalent lumped inductance in the layout, the integration range of the above equation (25) is

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

Under the condition that the current on the Josephson junction of the first quantum device in each intrinsic mode is determined, the positive and negative relations between the current direction and the preset reference direction can be compared, if the positive and negative relations are the same direction, the first sign information is determined to be 1, if the positive and negative relations are the reverse direction, the first sign information is determined to be-1, the first sign information can also be reversely arranged according to the positive and negative relations, and specific limitation is not carried out, so that the determination of the first sign information can be realized.

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

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

and determining the first symbol information as-1 when the direction of the current indication is opposite to a preset reference direction.

Wherein, I _mk When the current is greater than 0, the direction of the current indication is the same as the preset reference direction, s _mk ＝1，I _mk If < 0, the direction of the current indication is opposite to the preset reference direction, s _mk And (5) keeping the value of-1. In this manner, determination of the first symbol information may be achieved.

Optionally, the inductive energy ratio of the first device is determined as follows:

determining electromagnetic field energy information of the first quantum chip under 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;

determining a ratio of the first inductive energy and the second inductive energy as the first device inductive energy fraction.

In this embodiment, the electric field intensity peak distribution in space based on eigenmode m may be used

Peak distribution of magnetic field intensity

And surface current density of the first quantum chip

And the like, and determining electromagnetic field energy information of the first quantum chip under each eigenmode by combining related parameter information (such as parameter information, electric field radiation information, magnetic field radiation information and the like of a Josephson junction of the first quantum device) of the first quantum chip. Wherein the electromagnetic field energy information may include inductive energy, magnetic field energy, and magnetic field energy of different eigenmodes m at the Josephson junction of the quantum device k,The total electric field energy in space of the different eigenmodes m, the total magnetic field energy in space of the different eigenmodes m, etc.

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

The following describes in detail how the determination of the inductive energy fraction of the device is achieved based on the electromagnetic field distribution information.

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

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

Wherein k is 1,2.

The inductance of the josephson junction of quantum device k,

the length of the Josephson junction of the quantum device k is expressed as equivalent lumped inductance in the layout, and the integral range of the above formula (4) is

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

And electric field radiation information of the first quantum chip, and determining the total electric field energy of the first quantum chip radiation in the space under the eigenmode m, wherein the total electric field energy is shown in the following formula (5).

Wherein the content of the first and second substances,

represents the complex conjugate of the peak distribution of the electric field strength,

the dielectric tensor at different positions in space is expressed, the integral range of the above equation (5) is V, the V represents the space volume, and the above is the electric field radiation information, and the above are all known quantities.

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

The total magnetic field energy of the first quantum chip radiation in the space under 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, and is shown in the following formula (6).

Wherein the content of the first and second substances,

represents the complex conjugate of the peak distribution of the magnetic field strength,

the magnetic permeability tensor at different positions in space is represented, the integral range of the above equation (6) is V, the V represents the space volume, and the above is the magnetic field radiation information, and the above are all known quantities.

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

In an alternative embodiment, the first inductive energy may be determined by proportionally distributing the total magnetic field energy radiated by the first quantum chip in space in the eigenmode to the inductive energy at the josephson junctions of the different quantum devices in the eigenmode. In another alternative embodiment, the magnetic field energy distribution in space may be determined according to the ratio of the inductive energy of the josephson junctions of the quantum device in different eigenmodes, thereby determining the first inductive energy.

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 in space by the first quantum chip in the eigenmode.

The ratio of the first inductive energy and the second inductive energy may then be determined as the first device inductive energy ratio. In this manner, the determination of the first device inductive energy fraction may be achieved based on electromagnetic field distribution information.

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

distributing the first magnetic field energy into M parts based on third inductive energy on Josephson junctions of the M first quantum devices in the eigenmode to obtain second magnetic field energy of the M first quantum devices respectively radiating in space in the eigenmode, wherein 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;

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

In this embodiment, the total magnetic field energy radiated by the first quantum chip in the space in the eigenmode may be proportionally distributed according to 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 equation (4), and the first magnetic field energy is the magnetic field energy determined by the above equation (6), and the total magnetic field energy radiated in the space by the first quantum chip in the eigenmode may be proportionally allocated for each eigenmode based on the third inductive energy on the 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 the inductive energies at the josephson junctions of the M first quantum devices; the energy of the second magnetic field is the product of the energy of the first magnetic field and the percentage.

Wherein the magnetic field energy in the space is distributed proportionally

k1 and k2 respectively represent two different first quantum devices, and the sum of the magnetic field energies distributed on the different quantum devices is equal to the total magnetic field energy of the first quantum chip radiation in the eigenmode m in the space, so that

And (4) showing.

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

And (4) showing. In this way, the determination of the first inductive energy may be achieved.

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

determining the first electric field energy as the second inductive energy.

In this embodiment, the relationship between the inductive energy, the capacitive energy, the electric field energy and the magnetic field energy in the electromagnetic field may be

Representing the total inductive energy stored in eigenmode m,

representing the total stored capacitive energy in eigenmode m,

representing the total electric field energy of the eigenmode m in space,

representing the total magnetic field energy of eigenmode m in space,

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

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

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

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

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

carrying out variable substitution on elements in a 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 The device inductance energy ratio u of the quantum device k in the eigenmode m _mk The elements determined for the rows corresponding to eigenmode m and the columns corresponding to quantum device 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 the relation between the inductive energy stored in the quantum device in the eigenmode and the inductive energy determined based on the inductive parameter of the quantum device in the eigenmode, and the fourth relation is the relation between the inductive energy stored in the quantum chip in the eigenmode and the first Hamiltonian of the quantum chip in a decorated state;

determining a fifth relation between the device inductance energy ratio of the quantum device in the 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 Hamiltonian;

converting the inductance parameter into a secondary quantization operator in a decorated state based on elements in a corresponding column of a quantum device in a transformation matrix, and performing operator operation in a quantum state 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 elements;

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 a decorated state based on elements in a corresponding column of quantum devices 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 naked state;

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

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

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

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

Wherein x is _k For quantum chip in bare statePrimary quantized operator of Hamilton quantity, x' ₁ ，x′ ₂ ，...，x′ _M The method is a primary quantization operator of Hamiltonian of a quantum chip in a decorated state.

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

carrying out secondary quantization on the first Hamiltonian to obtain a secondary quantization operator representation of the first Hamiltonian;

and carrying out quantum state operator operation on the secondary quantization operator representation to obtain a second target parameter.

In this embodiment, a unitary transformation matrix is usually present, and the characterization parameters of the hamiltonian of the first quantum chip in the bare state can be obtained

Characterization parameter converted into Hamiltonian under decorated state

Represented by the following formula (7).

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

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

Wherein the matrix size is 2 Mx 2M, and the submatrix is specific to the diagonal blockThe eigenmode m corresponds to the element u of the row quantum device k corresponding to the column _mk And (4) showing.

Aiming at a quantum device k under an eigenmode m, the target element is u _mk 。

In an alternative embodiment, the second relationship may be

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

According to the principle of quantum mechanics, an expected value of a quantum mechanical quantity may correspond to a classical value, and a third relation and a fourth relation may be obtained, which are expressed by the following expressions (9) and (10), respectively.

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

represents the expected value of the inductance energy of a quantum device k (k is 1,2,.. Multidot.M) under an eigenmode M in quantum mechanics,

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

the total energy expected value of the quantum chip under the eigenmode m in quantum mechanics is represented, the total energy comprises inductive energy and capacitive energy, and the capacitive energy is equal to the inductive energy, so that the total energyThe desired value of the amount is equal to twice the inductive energy,

the Hamiltonian of the quantum chip under the decoration state representation is the first Hamiltonian.

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 equation (11).

Further, a sixth relationship between the inductance parameter and the primary quantization operator of the hamiltonian of the quantum chip in the bare state may be

For the transformation matrix, it can establish the relation between the next quantized Hamiltonian in the naked state representation and the one quantized Hamiltonian in the decorated state representation, as shown in the following equation (12).

Wherein x is ₁ 、x ₂ 、...、x _M 、p ₁ 、p ₂ 、...、p _M For a quantized Hamiltonian in the bare state representation (i.e. a quantized operator of the Hamiltonian in the bare state), x ₁ ′、x ₂ ′、...、x _M ′、p ₁ ′、p ₂ ′、...、p _M ' is a quantized Hamiltonian in the decorated state (i.e. a quantized Hamiltonian in the decorated state).

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

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

Wherein x is _k A primary quantization operator, x ', of Hamiltonian quantity of a quantum chip in a bare state' ₁ ，x′ ₂ ，...，x′ _M A quantization operator for the Hamiltonian of a quantum chip in decorated state u _1k 、u _2k 、...、u _Mk For the k-th column of elements in the sub-matrix of diagonal blocks in the transform matrix.

Further, a relationship (i.e., an eighth relationship) between the hash value operator of next quantization and the hash value operator of second quantization (i.e., the second quantization operator of hash value in decorated state) can be determined.

Then, the inductance parameter, i.e., the inductance parameter, may be set based on the sixth relationship, the seventh relationship, and the eighth relationship

And converting into a secondary quantization operator in a decorated state.

The operator operation of the quantum state can be carried out based on the converted quadratic quantization operator according to the related principle of quantum optics, and the first target parameter is obtained. Wherein the first target parameter is a parameter based on the target element.

The first quantum chip can be subjected to secondary quantization based on the first Hamiltonian in the decorated state, so that a secondary quantization operator representation of the first Hamiltonian can be obtained, and then, the secondary quantization operator representation of the first Hamiltonian can be subjected to quantum-state operator operation based on the quantum optics correlation principle, so that a second target parameter can be obtained.

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 equation (11), as shown in the following equation (14).

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

From the unitarity of the U matrix, iEPR has a normalized characteristic shown in the following equation (15).

∑ _m p _mk ＝∑ _k p _mk ＝1 (15)

I.e. for the submatrix of the diagonal block in U, the sum of the elements in its row is 1 and the sum of the elements in its column is 1.

Then, as can be seen from the above equation (14), iEPR and the transformation matrix U have the correspondence relationship of equation (14), and thus

The transformation matrix U is determined by iEPR, and the sign of the matrix elements is also lacked.

Can introduce symbol information s _mn For representing the signs of the elements in the transformation matrix U, so that the elements in the transformation matrix can be variable-substituted based on the second relation and the sign information to obtain a first relation as shown in the above equation (2), where the first relation is

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

Optionally, the step S104 specifically includes:

determining a first characterization matrix of a Hamiltonian of the first quantum chip after next quantization in the decorated state based on the first decorated state information;

based on the first transformation matrix, performing inverse transformation on the first representation matrix to obtain a second representation matrix of the Hamiltonian of the first quantum chip after quantization for the first time in a naked state;

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

In this embodiment, the first decoration state information may include eigenfrequencies ω 'corresponding to different eigenmodes m of the first quantum chip' _m Based on the eigenfrequency ω' _m Can beTo obtain a first characterization matrix of the hamiltonian of the first quantum chip after next quantization in decorated state, which is represented by the following formula (16).

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

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

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

determining a first eigenfrequency of each first quantum device and first coupling information between every 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 a Hamiltonian quantity of the quantum chip after quantization for the next time in a bare state and third target information, the third target information comprises an 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 an eigenfrequency of the quantum devices;

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

wherein the first bare state information comprises 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, and is a relationship between a characterization parameter of the hamiltonian of the quantum chip in the bare state after the quantum chip is quantized for the first time and the eigenfrequency of the quantum device and the coupling information (i.e., the coupling terms) between the quantum devices.

The ninth relationship is determined as follows:

for a multi-body system with M quantum devices, there is capacitive coupling between each two quantum devices, and the hamiltonian under the naked state representation can be written as shown in equation (18) below.

Wherein Q is _i Is the amount of electric charge, phi _i Is the inductive magnetic flux, C _i 、C _j And C _g，ij Is a capacitance, L _i Is an inductor.

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

wherein, ω is _i Is the bare state frequency, x, of the quantum device _i As new generalized coordinates, p _i For the generalized momentum, the Hamiltonian represented by the following formula (19) is obtained.

Wherein, g _ij Represents the coupling strength between two quantum devices and satisfies 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 of the primary quantization form is quadratic, it can be written in a matrix multiplication form as shown in the following equation (21).

It can be seen that the characterization parameter of the hamiltonian after the quantum chip is quantized once in the bare state is represented by the following formula (22), which characterizes the ninth relationship, and the ninth relationship can be determined.

Then, the second characterization matrix and the characterization parameters in the ninth relationship can be compared to determine the first eigenfrequency ω of each first quantum device _i And first coupling information (i.e., coupling terms) between each two of the M first quantum devices

)。

As can be seen from equation (20) above, the following equation (23) may be used to determine the first coupling strength between different first quantum devices based on the first eigenfrequency and the first coupling information.

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

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

Optionally, the determining, based on the first eigenfrequency and the first coupling information, a first coupling strength between each two quantum devices in the M first quantum devices further includes:

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

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

Wherein, g' ₁₂ Represents the equivalent coupling strength between qubit 1 and qubit 2; g ₁₂ Represents a first coupling strength between qubit 1 and qubit 2; g is a radical of formula _1c Representing a first coupling strength between qubit 1 and a coupler; g is a radical of formula _2c Represents a first coupling strength between qubit 2 and the coupler; omega ₁ Represents the first eigenfrequency of qubit 1; omega ₂ Represents the first eigenfrequency of qubit 2; omega _c Representing the first eigenfrequency of the coupler.

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

Optionally, the method further includes:

and outputting the first bare state information.

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

In an optional embodiment, the overall flow of this embodiment is shown in fig. 3, and the above steps are all described in detail above, and are not described again here. Compared with a related equivalent circuit method, the method is based on high-frequency electromagnetic field simulation, the effect brought by the high-frequency field is considered, the adopted approximation is less, the actual situation is closer, 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 the following 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-qubit device. The layout may include three qubits, wherein the middle qubit is used as a coupler for adjusting the equivalent coupling strength between the left and right qubits. By tuning the magnetic flux of the coupler (the magnetic flux tuning can be simulated by adjusting the inductance of the Josephson junction of the coupler), the coupling disconnection between the qubits (namely, the equivalent coupling strength is 0) can be realized, 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 as follows (setting the inductance of the two qubits to 12nH, and the inductance of the coupler gradually changing from 7nH to 11 nH), with the verification tasks as follows:

verification task 1: calculating bare state information under different coupler inductances by using the method of the embodiment and an equivalent circuit method respectively and comparing the bare state information with the bare state information;

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 the coupling turn-off point and performing data comparison.

The resulting pair of bare-state frequencies for the quantum device at different coupler inductance values for validation task 1 is shown in fig. 4. The data points and the dotted lines represent the result of the bare state frequency obtained by the solution of the method of the embodiment, and the continuous curve represents the result of the bare state frequency obtained by the solution of the equivalent circuit method.

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

In addition, it can be seen that the result of the bare state frequency obtained by the equivalent circuit method is slightly larger than the result of the bare state frequency obtained by the method in this embodiment, because the conductor itself has an inductance effect in the high-frequency electromagnetic field, while the equivalent circuit method takes more approximation because the conductor is regarded 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 verification in this group 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, where data points and dotted lines represent the results of the coupling strengths obtained by the solution of the present embodiment, and the continuous curve represents the results of the coupling strengths obtained by the solution of the equivalent circuit method.

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

In addition, it can be seen that the results of the coupling strengths obtained by the equivalent circuit method are slightly greater than the results of the coupling strengths obtained by the method in this embodiment, because the conductor itself has an inductance effect and there is a mutual inductance effect between different quantum devices in the high-frequency electromagnetic field, and the equivalent circuit method takes more approximation because the conductor is regarded as an equipotential body and does not consider the inductance effect actually existing in the conductor, so the results are slightly greater than the actual situation. The method takes the effect of the high-frequency electromagnetic field into consideration, so that the adopted approximation is less, and the group of data also laterally verifies that the method is closer to the real situation.

For verification task 2: the bare state information obtained by the two methods in the verification task 1 is used, the equivalent coupling strength between the two qubits is determined through the formula (24), data comparison is carried out, and the equivalent coupling strength between the qubits under different coupler inductance values is shown in fig. 6. The data points and the dotted lines are the results of the equivalent coupling strengths obtained by the solution of the present embodiment, and the continuous curve represents the results of the equivalent coupling strengths obtained by the solution of the equivalent circuit method. As can be seen from 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 the method of the embodiment is very close to the result of the equivalent coupling strength obtained by the method of the equivalent circuit, and meanwhile, the coupling turn-off points found by the method of the embodiment and the method of the equivalent circuit are basically consistent, so that the calculation result of the method of the embodiment is proved to be correct.

In addition, it can be seen that the closer the equivalent circuit method is to the coupling turn-off point, the better the equivalent circuit method fits with the method of the present embodiment, because the coupling caused by the inductance effect tends to zero near the coupling turn-off point, and therefore the result of the equivalent circuit also approaches the real situation. In other cases, the equivalent circuit does not consider the influence of the inductance effect of the high-frequency field conductor, so that the absolute values of the equivalent coupling strengths are slightly larger than the absolute value of the equivalent coupling strength obtained by the solution of the method of the embodiment, and therefore, the result of the method of the embodiment is closer to the real situation.

Second embodiment

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

an obtaining module 701, configured to obtain a structure layout of a first quantum chip, where the first quantum chip includes M first quantum devices, each of the first quantum devices includes a josephson junction, 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 symbol information of the M first quantum devices in each eigenmode of the first quantum chip, where the first device inductance energy ratio is: a ratio of a first inductive energy stored in the first quantum device in the eigenmode relative to a second inductive energy stored in the first quantum chip in the eigenmode, the first sign information indicating a positive-negative relationship of a current on a josephson junction of the first quantum device in the eigenmode to 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;

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

Optionally, the first determining module 702 includes:

the solving submodule is used for solving the eigenmode of 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 submodule, configured to determine the first device inductive energy fraction and the first sign information based on the electromagnetic field distribution information.

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

a first determination unit for determining a current on a josephson junction of the first quantum device in an intrinsic mode based on the current density;

a second determination 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 sub-module 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 for determining the first inductive energy and the second inductive energy based on the electromagnetic field energy information;

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

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

distributing the first magnetic field energy into M parts based on third inductive energy on the Josephson junctions of the M first quantum devices in the eigenmode to obtain second magnetic field energy of the M first quantum devices respectively radiating in the space in the eigenmode, wherein 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;

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

determining the first electric field energy as the second inductive energy.

Optionally, the apparatus further comprises:

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 eigen mode of the quantum chip and a target element in a pre-constructed transformation matrix, and the target element is an element determined by a row corresponding to the eigen mode and a column corresponding to the quantum device;

and the variable substitution module is used for performing 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 inductive energy stored in the quantum device in the eigenmode and inductive energy determined based on an inductive parameter of the quantum device in the eigenmode, and the fourth relation is a relation between the inductive energy stored in the quantum chip in the eigenmode and the first Hamiltonian quantity of the quantum chip in a decorated state;

a third determining submodule, configured to determine a fifth relationship between a device inductance energy ratio of the quantum device in an eigenmode and second target information based on the third relationship and the fourth relationship, where the second target information includes the inductance parameter and the first hamilton quantity;

the first operator operation sub-module is used for converting the inductance parameter into a secondary quantization operator in a decoration state based on elements in a corresponding column of a quantum device in a transformation matrix, and performing operator operation of a quantum state 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;

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

and the transformation sub-module 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 operation sub-module is specifically configured to:

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

Wherein x is _k A primary quantization operator, x ', of Hamiltonian quantity of a quantum chip in a bare state' ₁ ，x′ ₂ ，...，x′ _M The method is a primary quantization operator of Hamiltonian of a quantum chip in a decorated state.

Optionally, the second operator operation sub-module is specifically configured to:

Optionally, the third determining module 704 includes:

the fourth determining submodule is used for determining a first characterization matrix of the Hamiltonian of the first quantum chip after next quantization in the decorated state based on the first decorated state information;

the inverse transformation submodule is used for carrying out inverse transformation on the first representation matrix based on the first transformation matrix to obtain a second representation matrix of the Hamiltonian of the first quantum chip after quantization for the first time in a naked state;

and the fifth determining submodule is used for determining the first bare state information based on the second characterization matrix.

Optionally, the fifth determining submodule is specifically configured to:

determining a first eigenfrequency of each first quantum device and first coupling information between every 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 a Hamiltonian quantity of a quantum chip after quantization for the next time in a naked state and third target information, the third target information comprises the eigenfrequency of the quantum devices and the coupling information between the quantum devices, and the coupling information is determined based on the coupling strength between the quantum devices and the eigenfrequency of the quantum devices;

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

a fifth determining module for determining an equivalent coupling strength between the two qubits based on the first eigenfrequency and the first coupling strength, the first bare state information further comprising the equivalent coupling strength.

Optionally, the apparatus further comprises:

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

The device 700 for determining bare state information of a multi-body system in a superconducting quantum chip layout provided by the disclosure can implement each process implemented by the method for determining bare state information of a multi-body system in a superconducting quantum chip layout, and can achieve the same beneficial effects, and is not repeated here.

In the technical scheme of the disclosure, the collection, storage, use, processing, transmission, provision, disclosure and other processing of the personal information of the related user are all in accordance with the regulations of related laws and regulations and do not violate the good customs of the public order.

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

FIG. 8 shows 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 phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be examples 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 calculation 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 bus 804.

A number of components in the device 800 are connected to the I/O interface 805, including: an input unit 806, such as a keyboard, a mouse, or the like; 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, or the like; and a communication unit 809 such as a network card, modem, wireless communication transceiver, etc. 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.

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

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuitry, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), system on a 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 that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, receiving data and instructions from, and transmitting data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for implementing the 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/acts specified in the flowchart and/or block diagram to be performed. 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. A 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 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 a pointing device (e.g., a mouse or a 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 can 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, speech, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a back-end 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 back-end, 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 clients and servers. A client and server are generally 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 combining a blockchain.

It should be understood that various forms of the flows shown above may be used, with steps reordered, added, or deleted. For example, the steps described in the present disclosure may be executed in parallel or sequentially or in different orders, and are not limited herein as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved.

The above detailed description should not be construed as limiting the scope of the disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions may be made, depending on design requirements and other factors. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present disclosure should be included in the scope of protection of the present disclosure.

Claims

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

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 the relation between the transformation matrix and first target information, and the first target information comprises the device inductance energy ratio and the symbol information;

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

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

determining the first symbol information 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 inductive energy fraction is determined by:

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

determining the first electric field energy as the second inductive energy.

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

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

wherein p is _mk The component inductance energy ratio u of the quantum component k in the eigenmode m _mk The elements determined for the rows corresponding to eigenmode m and the columns corresponding to quantum device k in the transformation matrix.

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

determining a fifth relation between the device inductance energy ratio of the quantum device in the 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 quantity;

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

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;

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

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

Wherein x is _k A primary quantization operator, x ', of Hamiltonian quantity of a quantum chip in a bare state' ₁ ，x′ ₂ ，…，x′ _M The method is a primary quantization operator of Hamiltonian of a quantum chip in a decorated state.

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

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

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

17. The method of claim 1, further comprising:

and outputting the first bare state information.

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

the acquisition module is used for acquiring 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 greater than 2;

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

19. The apparatus of claim 18, wherein the first determining means comprises:

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

21. The apparatus according to 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 an eigenmode, the first quantum chip radiates a first magnetic field energy in space and a third inductive energy at josephson junctions of the M first quantum devices, and the fourth determining unit is 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:

determining the first electric field energy as the second inductive energy.

25. The apparatus of claim 18, further comprising:

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

26. The garment of claim 25Wherein the second relationship is:

27. The apparatus of claim 26, wherein the fourth determining means comprises:

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.

28. The apparatus of claim 27, wherein the first operator computation submodule is further configured to:

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

Wherein x is _k A primary quantization operator, x ', of the Hamiltonian of the quantum chip in the bare state' ₁ ，x′ ₂ ，…，x′ _M The method is a primary quantization operator of Hamiltonian of a quantum chip in a decorated state.

30. The apparatus of claim 27, wherein the second operator operation submodule is further configured to:

31. The apparatus of claim 18, wherein the third determining means comprises:

32. The apparatus according to claim 31, wherein the fifth determining submodule is specifically 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 having stored thereon computer instructions for causing the computer to perform the method of any one of claims 1-17.

37. A computer program product comprising a computer program which, when executed by a processor, implements the method according to any one of claims 1-17.