CN113065251A - Method and device for acquiring propagation amplitude of strongly coupled waveguide - Google Patents

Method and device for acquiring propagation amplitude of strongly coupled waveguide Download PDF

Info

Publication number
CN113065251A
CN113065251A CN202110353000.XA CN202110353000A CN113065251A CN 113065251 A CN113065251 A CN 113065251A CN 202110353000 A CN202110353000 A CN 202110353000A CN 113065251 A CN113065251 A CN 113065251A
Authority
CN
China
Prior art keywords
energy
equation
bare
initial value
waveguide
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110353000.XA
Other languages
Chinese (zh)
Other versions
CN113065251B (en
Inventor
王冲
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Environmental Features
Original Assignee
Beijing Institute of Environmental Features
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Environmental Features filed Critical Beijing Institute of Environmental Features
Priority to CN202110353000.XA priority Critical patent/CN113065251B/en
Publication of CN113065251A publication Critical patent/CN113065251A/en
Application granted granted Critical
Publication of CN113065251B publication Critical patent/CN113065251B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/60—Superconducting electric elements or equipment; Power systems integrating superconducting elements or equipment

Abstract

The invention relates to a strong coupling waveguide propagation amplitude acquisition technology, and aims to solve the problem of low initial calculation accuracy in a simulation process in the strong coupling waveguide propagation amplitude acquisition process. The method for acquiring the propagation amplitude of the strongly coupled waveguide comprises the following steps: measuring a waveguide structure parameter; splitting a summation term of an energy intrinsic equation into two parts, wherein one part is the sum of all naked eigenvalues close to a to-be-solved variable of the energy intrinsic equation, and the other part is the sum of all naked eigenvalues far away from the to-be-solved variable of the energy intrinsic equation; substituting the new summation item into an energy eigen equation to solve, and substituting the obtained solution serving as an iteration initial value into an eigen value and an eigenvector in the energy eigen equation; and obtaining the propagation amplitude of the strong coupling waveguide according to the eigenvalue and the eigenvector. The invention discloses a strong coupling waveguide propagation amplitude acquisition device which comprises a summation item splitting module, an initial value acquisition module, an eigenvalue and eigenvector acquisition module and a propagation amplitude acquisition module.

Description

Method and device for acquiring propagation amplitude of strongly coupled waveguide
Technical Field
The invention relates to a strong coupling waveguide propagation amplitude acquisition technology, in particular to a semi-analytic simulation method for a superconducting qubit system in a strong coupling waveguide.
Background
The preparation and evolution of superconducting qubits is one of the core problems in the field of quantum information and quantum computing. The superconducting qubit system is arranged in the strong coupling waveguide, so that the interaction strength of the superconducting qubit and photons can be remarkably improved, the operation and the coherence of the superconducting qubit can be maintained, the superconducting qubit system is widely concerned by related researches, and the superconducting qubit system has guiding significance for the simulation of the superconducting qubit system in the strong coupling waveguide and the development of related equipment. The key to this simulation is solving the energy eigenproblems of the system, including calculating the corresponding eigenvalues and eigenvectors, and thus the propagation amplitudes characterizing the evolution of the system.
At present, in the process of simulating the propagation amplitude of the strongly coupled waveguide, the bare eigenvalue (including the bare continuous eigenvalue and the bare discrete eigenvalue, both of which are known) of the system is mostly used as the iteration initial value of the energy eigen equation to numerically solve the energy eigen equation of the system. Because the interval between adjacent bare continuous eigenvalues is extremely small (inversely proportional to the linearity of the system), when the equation to-be-solved variable is positioned near the bare continuous eigenvalue, the energy eigen equation changes violently, so that the first calculation accuracy of the simulation process is low, the iteration initial value needs to be adjusted frequently according to the first calculation result for recalculation, and the calculation efficiency of the propagation amplitude of the strong coupling waveguide is greatly reduced.
Therefore, in view of the above disadvantages, it is desirable to provide a new technique for obtaining the propagation amplitude of the strongly coupled waveguide.
Disclosure of Invention
The invention aims to solve the technical problem that in the strong coupling waveguide propagation amplitude obtaining process, the first calculation accuracy of the simulation process is low, and provides a method and a device for obtaining the strong coupling waveguide propagation amplitude aiming at the defects in the prior art.
In order to solve the above technical problem, the present invention provides a method for obtaining propagation amplitude of a strongly coupled waveguide, including:
a measurement step: measuring waveguide linearity L and obtaining omegakAnd ωaValue of (a), ωaAnd ωkRespectively representing a state of dispersion from bare and a momentum of
Figure BDA0003001650670000027
Corresponding to the bare eigenvalues of the state vector of the bare continuous state,
Figure BDA0003001650670000021
n＝±1，±2，…；
and a summation item splitting step: splitting a summation term of an energy intrinsic equation into two parts, wherein one part is the sum of all naked eigenvalues close to a to-be-solved variable of the energy intrinsic equation, and the other part is the sum of all naked eigenvalues far away from the to-be-solved variable of the energy intrinsic equation, so as to obtain a new summation term of the energy intrinsic equation;
an initial value acquisition step: substituting the waveguide linearity L and the new summation item into the energy eigen equation to solve, and taking the obtained solution as an iteration initial value;
and an eigenvalue and eigenvector acquisition step: substituting the iteration initial value into the energy eigen equation to calculate an eigenvalue and an eigenvector of the energy eigen equation;
a propagation amplitude acquisition step: and obtaining the propagation amplitude of the strong coupling waveguide according to the eigenvalue and the eigenvector.
Optionally, the expression of the energy eigen equation is:
Figure BDA0003001650670000022
wherein Ω represents a variable to be solved, | a, of the energy eigen equation>And
Figure BDA0003001650670000023
respectively representing a bare discrete state and a momentum of
Figure BDA0003001650670000024
The state vector of the bare continuous state of,
Figure BDA0003001650670000025
n＝±1，±2，…，
Figure BDA0003001650670000026
gkthe interaction of superconducting qubits with photons is characterized.
Optionally, the new summation term of the energy eigen equation in the summation term splitting step is:
Figure BDA0003001650670000031
where P represents the principal value integral.
Optionally, the initial value obtaining step includes:
substituting the waveguide linearity L and the new summation term into the energy eigen equation;
limit omega to omegaq＜Ω＜ωq+2π/L；
Obtaining unique solutions by numerical methods
Figure BDA0003001650670000032
Will be described in
Figure BDA0003001650670000033
As the sum of the bare eigenvalues omegaqThe corresponding iteration initial value.
Optionally, the eigenvalue and eigenvector obtaining step includes:
substituting the iteration initial value into the energy eigen equation to calculate an eigen value of the energy eigen equation;
according to Hamiltonian
Figure BDA0003001650670000034
Obtaining an eigenvector equation set;
and substituting the eigenvalue into the eigenvector equation set to obtain an eigenvector.
Optionally, in the propagation amplitude obtaining step, the propagation amplitude p (t) is calculated by the following formula:
Figure BDA0003001650670000035
where < a > represents the dual state vector corresponding to | a >.
The invention also provides a strong coupling waveguide propagation amplitude acquisition device, which comprises:
a summation item splitting module configured to split a summation item of an energy eigen equation into two parts, wherein one part is the sum of all the bare eigenvalues close to the to-be-solved variable of the energy eigen equation, and the other part is the sum of all the bare eigenvalues far away from the to-be-solved variable of the energy eigen equation, so as to obtain a new summation item of the energy eigen equation;
an initial value acquisition module configured to substitute the waveguide linearity L and the new summation term into the energy eigen equation for solution, and take the obtained solution as an iteration initial value;
an eigenvalue and eigenvector acquisition module configured to calculate eigenvalues and eigenvectors of an energy eigen equation by substituting the iteration initial value into the energy eigen equation; and
a propagation amplitude acquisition module configured to obtain a propagation amplitude of the strongly coupled waveguide from the eigenvalues and eigenvectors.
Optionally, the expression of the energy eigen equation is:
Figure BDA0003001650670000041
wherein Ω represents a variable to be solved, | a, of the energy eigen equation>And
Figure BDA0003001650670000042
respectively representing a bare discrete state and a momentum of
Figure BDA0003001650670000043
The state vector of the bare continuous state of,
Figure BDA0003001650670000044
n＝±1，±2，…，
Figure BDA0003001650670000045
ωaand ωkRespectively represent and | a>And
Figure BDA0003001650670000046
corresponding bare eigenvalue, gkCharacterizing superconducting quantaBit-to-photon interactions.
Optionally, the new summation term of the energy eigen equation in the summation term splitting module is:
Figure BDA0003001650670000047
where P represents the principal value integral.
Optionally, the initial value obtaining module includes:
a substitution submodule configured to substitute the waveguide linearity L and the new summation term into the energy eigen equation;
a limit submodule configured to limit omega to omegaq＜Ω＜ωq+2π/L；
An iteration initial value obtaining submodule configured to obtain a unique solution by a numerical method
Figure BDA0003001650670000048
And combining the above
Figure BDA0003001650670000049
As the sum of the bare eigenvalues omegaqThe corresponding iteration initial value.
The implementation of the method and the device for acquiring the propagation amplitude of the strongly coupled waveguide has the following beneficial effects: and a proper iteration initial value is calculated by using a semi-analytic method, so that for each bare continuous eigenvalue, the corresponding continuous eigenvalue can be obtained by only one iteration calculation, and the simulation efficiency of the propagation amplitude of the strong coupling waveguide is greatly improved.
Drawings
Fig. 1 is a schematic flow chart of a strong coupling waveguide propagation amplitude acquisition method according to a first embodiment of the present invention;
fig. 2 is a schematic structural diagram of a strong coupling waveguide propagation amplitude obtaining apparatus according to a first embodiment of the present invention;
fig. 3 is a schematic structural diagram of an initial value obtaining module according to a first embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Example one
As shown in fig. 1, an embodiment of the present invention provides a method for obtaining a propagation amplitude of a strongly coupled waveguide, where the method includes the following steps S1 to S5.
Step S1, measurement step:
measuring structural parameters of the strong coupling waveguide, including waveguide linearity L and the like, and acquiring omega according to the structural parameters of the waveguidekAnd ωaThe value of (c).
Step S2, a summation item splitting step:
the root of the difficulty in numerical solution of the energy eigen equation is that the equation contains a summation term for a bare eigenvalue, the embodiment first approximately calculates an analytical expression of the summation term, specifically, the summation term is split into two parts, the first part contains summation for all bare eigenvalues close to a to-be-solved variable of the equation, the second part contains summation for all bare eigenvalues far away from the to-be-solved variable of the equation, then the upper and lower summation limits of the first part are respectively expanded to positive and negative infinity and the infinite number of the summation is performed, the second part is replaced by corresponding principal value integrals, and the sum of the two parts is the analytical expression of the summation term.
Taking the case of superconducting qubits as two-level atoms and no dissipation in the system as an example, the dynamics of the system are represented by Hamiltonian
Figure BDA0003001650670000061
Description, in its general form:
Figure BDA0003001650670000062
where L is the system (waveguide) linearity, ωaAnd
Figure BDA0003001650670000063
respectively, a bare discrete eigenvalue (characterizing the superconducting qubit excited state energy) and a bare continuous eigenvalue (characterizing the photon energy). | a>(characterizing the excited state of a superconducting qubit) and
Figure BDA0003001650670000064
(characteristic photons) are respectively related to omegaaAnd ωkCorresponding state vector, ωaTaking a real number, ωkIs a real analytic function of k, is a continuous state,<a | and
Figure BDA0003001650670000065
are the corresponding dual state vectors, gkCharacterizing the interaction of superconducting qubits with photons, ωkAnd gkThe dependency on k is given by the actual system.
The energy eigenequation for the system is written as:
Figure BDA0003001650670000066
where Ω is the variable to be solved for the energy eigenequation. When L is large, the energy eigen equation contains a summation term
Figure BDA0003001650670000067
In omega-omegaq
Figure BDA0003001650670000068
Near (i.e. omega at omega)qNearby) changes dramatically, making equation solution difficult, so the present invention first approximates the analytical expression for the summation term. Specifically, the summation term is split into two parts: the first part comprises the summation of the naked continuous eigenvalues of all variables to be solved for the approach equation, and the second part comprises the summation of all variables to be solved for the departure equationSumming the bare continuous eigenvalues of the quantities; expanding the upper and lower summation limits of the first part into positive and negative infinity respectively, summing the infinite series, and replacing the second part with corresponding main value integrals; the sum of the two parts is an analytical expression of a summation term, because omegaaDo not correspond to a continuum, and are therefore not considered here. Each bare eigenvalue ωkAnalytical expressions each corresponding to a summation term:
Figure BDA0003001650670000071
g characterizes the interaction of the superconducting qubit with photons, and the lower subscript q corresponds to a particular value of k.
Step S3, initial value acquisition step:
substituting the analytical expressions of the waveguide linearity L and the summation term into an energy eigen equation to obtain a new energy eigen equation:
Figure BDA0003001650670000072
limit omega to omegaq＜Ω＜ωq+2π/LInsofar, the above equations can be uniquely solved by numerical methods (e.g., invoking Mathematica or MATLAB-ready functions)
Figure BDA0003001650670000073
Figure BDA0003001650670000074
I.e. the sum of the bare eigenvalues omegaqThe corresponding iteration initial value.
Step S4, eigenvalue and eigenvector acquisition step:
to be provided with
Figure BDA0003001650670000075
Substituting the initial value of iteration into energy eigen equation to carry out numerical solution (such as calling Mathemica or MATLAB ready-made function) to obtain the value of ωqCorresponding continuous eigenvalue omegaq. Due to intrinsic energy equation in
Figure BDA0003001650670000076
The change of the neighborhood is gentle, and omega can be obtained through one-time calculationq. For each one
Figure BDA0003001650670000077
Repeating the above process to obtain all continuous eigenvalues.
Ω＜min{ωkDirectly solving an energy eigen equation by using the region numerical value of the equation to obtain a discrete eigen value omegaa。
For each eigenvalue Ω, the corresponding eigenvector | Ω > is given by:
Figure BDA0003001650670000081
step S5, propagation amplitude acquisition step: obtaining the propagation amplitude P (t) of the strongly coupled waveguide from the eigenvalues and eigenvectors:
Figure BDA0003001650670000082
as shown in fig. 2, this embodiment further provides an apparatus for obtaining a propagation amplitude of a strongly coupled waveguide, where the apparatus includes:
a summation item splitting module 1 configured to split a summation item of an energy eigen equation into two parts, one part being a sum of all bare eigenvalues close to a to-be-solved variable of the energy eigen equation, and the other part being a sum of all bare eigenvalues far away from the to-be-solved variable of the energy eigen equation, so as to obtain a new summation item of the energy eigen equation;
an initial value obtaining module 2 configured to substitute the waveguide linearity L and the new summation term into the energy eigen equation to solve, and use the obtained solution as an iteration initial value;
an eigenvalue and eigenvector acquisition module 3 configured to calculate eigenvalues and eigenvectors of an energy eigen equation by substituting the iteration initial value into the energy eigen equation; and
a propagation amplitude obtaining module 4 configured to obtain a propagation amplitude of the strongly coupled waveguide from the eigenvalues and eigenvectors.
As a preferred embodiment of the present application, the expression of the energy eigen equation is:
Figure BDA0003001650670000083
wherein Ω represents a variable to be solved, | a, of the energy eigen equation>And
Figure BDA0003001650670000084
respectively representing a bare discrete state and a momentum of
Figure BDA0003001650670000085
The state vector of the bare continuous state of,
Figure BDA0003001650670000086
n＝±1，±2，…，
Figure BDA0003001650670000091
ωaand ωkRespectively represent and | a>And
Figure BDA0003001650670000092
corresponding bare eigenvalue, gkRepresenting the interaction of the bare discrete state with the bare continuous state.
As a preferred embodiment of the present application, the new summation term of the energy eigen equation in the summation term splitting module 1 is:
Figure BDA0003001650670000093
where P represents the principal value integral.
As shown in fig. 3, as a preferred embodiment of the present application, the initial value obtaining module 2 includes:
a substitution submodule 21 configured to substitute the waveguide linearity L and the new summation term into the energy eigen equation;
a limit submodule 22 configured to limit omega to omegaq＜Ω＜ωq+2π/L(ii) a And
an iteration initial value obtaining submodule 23 configured to obtain a unique solution by a numerical method
Figure BDA0003001650670000094
And combining the above
Figure BDA0003001650670000095
As the sum of the bare eigenvalues omegaqThe corresponding iteration initial value.
The strong-coupling waveguide propagation amplitude obtaining apparatus according to the embodiment of the present application can implement steps S2 to S5 of the strong-coupling waveguide propagation amplitude obtaining method according to the embodiment of the present application, and the principle and effect thereof are not described herein again.
In summary, the method and the device for obtaining the propagation amplitude of the strongly coupled waveguide improve the semi-analytic simulation process of the superconducting qubit system in the strongly coupled waveguide, and solve the problem that the prior method has low calculation efficiency because the iteration initial value of the energy eigen equation needs to be frequently adjusted, the semi-analytic method is used for calculating the proper iteration initial value, so that for each bare continuous eigenvalue, the corresponding continuous eigenvalue can be obtained only by one-time iteration calculation, and the simulation efficiency of the propagation amplitude of the strongly coupled waveguide is greatly improved.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A method for obtaining propagation amplitude of a strongly coupled waveguide is characterized by comprising the following steps:
a measurement step: measuring waveguide linearity L and obtaining omegakAnd ωaValue of (a), ωaAnd ωkRespectively representing a state of dispersion from bare and a momentum of
Figure FDA0003001650660000011
Corresponding to the bare eigenvalues of the state vector of the bare continuous state,
Figure FDA0003001650660000012
and a summation item splitting step: splitting a summation term of an energy intrinsic equation into two parts, wherein one part is the sum of all naked eigenvalues close to a to-be-solved variable of the energy intrinsic equation, and the other part is the sum of all naked eigenvalues far away from the to-be-solved variable of the energy intrinsic equation, so as to obtain a new summation term of the energy intrinsic equation;
an initial value acquisition step: substituting the waveguide linearity L and the new summation item into the energy eigen equation to solve, and taking the obtained solution as an iteration initial value;
and an eigenvalue and eigenvector acquisition step: substituting the iteration initial value into the energy eigen equation to calculate an eigenvalue and an eigenvector of the energy eigen equation;
a propagation amplitude acquisition step: and obtaining the propagation amplitude of the strong coupling waveguide according to the eigenvalue and the eigenvector.
2. The method of claim 1, wherein the energy eigenequation is expressed as:
Figure FDA0003001650660000013
wherein Ω represents a variable to be solved, | a, of the energy eigen equation>And
Figure FDA0003001650660000014
respectively representing a bare discrete state and a momentum of
Figure FDA0003001650660000015
The state vector of the bare continuous state of,
Figure FDA0003001650660000016
Figure FDA0003001650660000017
gkthe interaction of superconducting qubits with photons is characterized.
3. The method of claim 2, wherein the new summation term of the energy eigen equation in the summation term splitting step is:
Figure FDA0003001650660000021
where P represents the principal value integral.
4. The method according to claim 3, wherein the initial value obtaining step comprises:
substituting the waveguide linearity L and the new summation term into the energy eigen equation;
limit omega to omegaq＜Ω＜ωq+2π/L；
Obtaining unique solutions by numerical methods
Figure FDA0003001650660000022
Will be described in
Figure FDA0003001650660000023
As the sum of the bare eigenvalues omegaqThe corresponding iteration initial value.
5. The method of claim 4, wherein the eigenvalue and eigenvector acquisition step comprises:
substituting the iteration initial value into the energy eigen equation to calculate an eigen value of the energy eigen equation;
according to Hamiltonian
Figure FDA0003001650660000025
Obtaining an eigenvector equation set;
and substituting the eigenvalue into the eigenvector equation set to obtain an eigenvector.
6. The method according to claim 2, wherein in the propagation amplitude obtaining step, the propagation amplitude p (t) is calculated by the following formula:
Figure FDA0003001650660000024
where < a > represents the dual state vector corresponding to | a >.
7. A strongly coupled waveguide propagation amplitude acquisition apparatus, comprising:
a summation item splitting module configured to split a summation item of an energy eigen equation into two parts, wherein one part is the sum of all the bare eigenvalues close to the to-be-solved variable of the energy eigen equation, and the other part is the sum of all the bare eigenvalues far away from the to-be-solved variable of the energy eigen equation, so as to obtain a new summation item of the energy eigen equation;
an initial value acquisition module configured to substitute the waveguide linearity L and the new summation term into the energy eigen equation for solution, and take the obtained solution as an iteration initial value;
an eigenvalue and eigenvector acquisition module configured to calculate eigenvalues and eigenvectors of an energy eigen equation by substituting the iteration initial value into the energy eigen equation; and
a propagation amplitude acquisition module configured to obtain a propagation amplitude of the strongly coupled waveguide from the eigenvalues and eigenvectors.
8. The apparatus of claim 7, wherein the energy eigenequation is expressed as:
Figure FDA0003001650660000031
wherein Ω represents a variable to be solved, | a, of the energy eigen equation>And
Figure FDA0003001650660000032
respectively representing a bare discrete state and a momentum of
Figure FDA0003001650660000037
The state vector of the bare continuous state of,
Figure FDA0003001650660000033
Figure FDA0003001650660000034
ωaand ωkRespectively represent and | a>And
Figure FDA0003001650660000035
corresponding bare eigenvalue, gkThe interaction of superconducting qubits with photons is characterized.
9. The apparatus of claim 7, wherein the new summation term of the energy eigen equation in the summation term splitting module is:
Figure FDA0003001650660000036
where P represents the principal value integral.
10. The apparatus of claim 7, wherein the initial value obtaining module comprises:
a substitution submodule configured to substitute the waveguide linearity L and the new summation term into the energy eigen equation;
a limit submodule configured to limit omega to omegaq＜Ω＜ωq+2π/L；
An iteration initial value obtaining submodule configured to obtain a unique solution by a numerical method
Figure FDA0003001650660000041
And combining the above
Figure FDA0003001650660000042
As the sum of the bare eigenvalues omegaqThe corresponding iteration initial value.
CN202110353000.XA 2021-03-31 2021-03-31 Method and device for obtaining propagation amplitude of strong coupling waveguide Active CN113065251B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110353000.XA CN113065251B (en) 2021-03-31 2021-03-31 Method and device for obtaining propagation amplitude of strong coupling waveguide

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110353000.XA CN113065251B (en) 2021-03-31 2021-03-31 Method and device for obtaining propagation amplitude of strong coupling waveguide

Publications (2)

Publication Number Publication Date
CN113065251A true CN113065251A (en) 2021-07-02
CN113065251B CN113065251B (en) 2023-04-25

Family

ID=76565038

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110353000.XA Active CN113065251B (en) 2021-03-31 2021-03-31 Method and device for obtaining propagation amplitude of strong coupling waveguide

Country Status (1)

Country Link
CN (1) CN113065251B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113656983A (en) * 2021-08-31 2021-11-16 北京环境特性研究所 Complex target quantum imaging simulation method and device, computing equipment and medium

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140028112A1 (en) * 2011-01-14 2014-01-30 City University Of Hong Kong Apparatus and method for wireless power transfer
US20170206461A1 (en) * 2016-01-15 2017-07-20 Wisconsin Alumni Research Foundation System and Method for Quantum Computation Using Symmetrical Charge Qubits
US20170262765A1 (en) * 2016-03-09 2017-09-14 Socpra Sciences Et Génie S.E.C. Periodical modulation of longitudinal coupling strength for quantum non-demolition qubit readout
CN111046333A (en) * 2019-12-09 2020-04-21 嘉兴学院 Method and system for accurately and effectively solving eigenstates of large sparse matrix
CN112231947A (en) * 2020-09-16 2021-01-15 华中科技大学 Simulation method and system of double-anisotropic waveguide

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140028112A1 (en) * 2011-01-14 2014-01-30 City University Of Hong Kong Apparatus and method for wireless power transfer
US20170206461A1 (en) * 2016-01-15 2017-07-20 Wisconsin Alumni Research Foundation System and Method for Quantum Computation Using Symmetrical Charge Qubits
US20170262765A1 (en) * 2016-03-09 2017-09-14 Socpra Sciences Et Génie S.E.C. Periodical modulation of longitudinal coupling strength for quantum non-demolition qubit readout
CN111046333A (en) * 2019-12-09 2020-04-21 嘉兴学院 Method and system for accurately and effectively solving eigenstates of large sparse matrix
CN112231947A (en) * 2020-09-16 2021-01-15 华中科技大学 Simulation method and system of double-anisotropic waveguide

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
GERASSIMOS A. ATHANASSOULIS 等: "A FAST-CONVERGENT SPECTRAL METHOD FOR WAVE PROPAGATION AND SCATTERING IN NON-UNIFORM WAVEGUIDES" *
唐学辉: "波动力学中线性谐振子的能量本征值" *
邱昕: "多模磁光耦合理论研究" *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113656983A (en) * 2021-08-31 2021-11-16 北京环境特性研究所 Complex target quantum imaging simulation method and device, computing equipment and medium

Also Published As

Publication number Publication date
CN113065251B (en) 2023-04-25

Similar Documents

Publication Publication Date Title
CN113496285B (en) Quantum circuit-based data processing method and device, electronic equipment and medium
Alonso et al. A geometric formulation of Higgs effective field theory: measuring the curvature of scalar field space
Sen Soft theorems in superstring theory
Liu et al. Gradient optimization of finite projected entangled pair states
Gugenberger et al. Comparison of phase-field models for surface diffusion
WO2018074006A1 (en) Simulation device, computer program, and simulation method
Twamley Bures and statistical distance for squeezed thermal states
Akinyemi Shallow ocean soliton and localized waves in extended (2+ 1)-dimensional nonlinear evolution equations
Odot et al. DeepPhysics: A physics aware deep learning framework for real‐time simulation
CN113158527B (en) Method for calculating frequency domain electromagnetic field based on implicit FVFD
CN114580647B (en) Quantum system simulation method, computing device, device and storage medium
Yu et al. Complex dynamics in biological systems arising from multiple limit cycle bifurcation
Wu et al. Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment
CN113065251A (en) Method and device for acquiring propagation amplitude of strongly coupled waveguide
Alexandridis Studying state convergence of input-to-state stable systems with applications to power system analysis
Douglas Calabi–Yau metrics and string compactification
Campos et al. Quantum mechanics on phase space: the hydrogen atom and its Wigner functions
Li et al. Efficient quantum simulation of electron-phonon systems by variational basis state encoder
Peng Qualitative analysis on a diffusive and ratio-dependent predator–prey model
Du et al. Super Resolution Generative Adversarial Networks for Multi-Fidelity Pressure Distribution Prediction
Bergner et al. Integrable supersymmetric fluid mechanics from superstrings
Saito et al. An iterative improvement method for HHL algorithm for solving linear system of equations
Meng et al. Primal-dual hybrid gradient algorithms for computing time-implicit Hamilton-Jacobi equations
Chen et al. Traveling Wave Solution of the Kaup–Boussinesq System with Beta Derivative Arising from Water Waves
Clisby Endless self-avoiding walks

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant