CN114444016A - Method for realizing Yixin model - Google Patents
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Abstract
The invention relates to a method for realizing an Esin model. And driving the Kerr nonlinear optical parametric oscillator by using an external pump so as to obtain the Hamilton quantity based on the Kerr nonlinear optical parametric oscillator. And converting the Hamiltonian based on the Kerr nonlinear optical parametric oscillator into an evolution model with generalized coordinates and generalized momentum. And carrying out iterative evolution on the generalized coordinates and the generalized momentum, and obtaining the numerical value of the preset parameter in the Hamilton quantity based on the Kerr nonlinear optical parametric oscillator according to the iterative evolution of the generalized coordinates and the generalized momentum. Based on the quantity of the IshHamilton and a value according to the predetermined parameter, the evolution result of the evolution model is made to correspond to the ground state result of the IshHamilton.
Description
Technical Field
The invention mainly relates to the technical field of an Esinon model, in particular to a method for realizing the Esinon model.
Background
The problem of combination optimization occurs in various situations of society and industry, and the efficiency of society and industry can be improved by rapidly solving the problem of combination optimization. However, these problems are notorious difficulties because of combinatorial explosion, and the number of candidate solutions grows exponentially depending on the scale of the problem. Therefore, new computational methods are expected to be available for combinatorial optimization hardware devices for these problems have recently been developed by various methods, and in particular, an yixin machine designed to find the ground state of the yixin spin model has recently attracted a lot of attention because many combinatorial optimization problems can be mapped to yixin problems, such as very large scale integrated circuit design and drug design, and financial portfolio management. Notable examples include, for example: quantum annealing furnace and interference network based on quantum annealing and its superconducting circuit, coherent laser machine and coherent laser pulse.
However, the machinery of yixin is complex, and the use of harsh conditions such as a quantum annealing furnace based on a superconducting circuit is often required to provide an ultra-low operating temperature, and complete connection between qubits cannot be achieved. The feedback control part of the coherent yixin machine is allowed to be realized by a digital circuit, such as a field programmable gate array and other similar circuits, and a large amount of operations and corresponding speed in the feedback control based on the classical computer principle limit the solving efficiency of the machine. Meanwhile, the clock synchronization rate with the coupler and the interference contrast of light greatly influence the accuracy of the understanding. The industry has begun to look again at building software-based solution algorithms by reproducing the principles of this type of hardware model solution.
The Issin spin dynamics model is originally a model describing the magnetic properties of a crystal. An yincisco machine, also known as an annealing furnace, is a special purpose computer capable of solving a particular class of combinatorial optimization problems very quickly and efficiently, and such a special purpose computing architecture can provide orders of magnitude acceleration in solving combinatorial optimization problems. Given an initial input configuration, which the yincinder evolves into an output configuration that minimizes the total energy of the system, the input is typically configured as a two-dimensional matrix of two spins (e.g., +1 and-1, 0 or 1 or spin up and spin down). The method is widely used in the fields of condensed state physics, material science, magnetic theory, statistical physics, mechanics and the like, and can describe and research phenomena such as properties of a uniaxial anisotropic magnetic system, properties of a public transport command system or a glass substance, active properties of protein molecules, phase change of binary solution and the like.
Classical computers can solve some combinatorial optimization problems of lower complexity, but for some combinatorial optimization problems that are more difficult to handle, such as the max-cut problem, the temporal complexity is often unacceptable for classical computers. The emerging quantum computer has strong computing power on parallel operation based on a computing mode of hardware natural evolution, and can quickly complete certain computations which cannot be completed by a classical computer. The itaxin model is originally a model providing aspects of physical content for describing a plurality of physical phenomena, and the development is now that problems such as combinatorial optimization and non-deterministic polynomial can be solved, and when the problems are mapped to the itaxin hamilton, the optimal solution of the problems can be found by solving the ground state of the hamilton.
Optimization is the process of finding the best or near-best solution from a set of many possible solutions. Combinatorial optimization is then some subset of optimization that involves finding the best or near-best object in a limited set of objects. Examples of portfolio optimization problems are task scheduling, vehicle routing, portfolio optimization, and the like. The main doubt is that most combinatorial optimization problems are very difficult to solve in the sense that it takes an impractical time dimension, such as years or more, to obtain an accurate optimal solution. As such, many have been designed to achieve close proximity within practical time scales such as seconds, minutes, or hours or days. Examples of such approximation techniques are simulated annealing or evolutionary optimization.
With the help of traditional resources, the yinxin model can be constructed by using hardware resources such as traditional computers and various processors to solve or attempt to solve the yinxin problem, and the yinxin problem and other combined problems are solved on the basis of traditional hardware and software resources.
Disclosure of Invention
The application discloses a method for realizing an Exin model, which comprises the following steps:
driving the Kerr nonlinear optical parametric oscillator by using an external pump so as to obtain a Hamilton quantity based on the Kerr nonlinear optical parametric oscillator;
converting the Hamiltonian based on Kerr nonlinear optical parametric oscillator into an evolution model with generalized coordinates and generalized momentum;
iteratively evolving the generalized coordinates and the generalized momentum to obtain values of predetermined parameters in the Hamiltonian based on a Kerr nonlinear optical parametric oscillator according to the iterative evolution of the generalized coordinates and the generalized momentum;
and enabling the evolution result of the evolution model to correspond to the ground state result of the inching Hamiltonian based on the inching Hamiltonian and the value according to the preset parameter.
The above method is characterized in that:
the Hamiltonian H under Kerr nonlinear optical parametric oscillator conditions is expressed as:
where K is the nonlinear Kerr coefficient and the detuning frequency DeltaiRepresenting the difference between the resonance frequency of the ith resonator of the N resonators and half the pump frequency, epsilon0Is the coupling strength, JijA coupling term corresponding to the quantity of the Isuzhamiltonian;
and
and aiThe generation operator and annihilation operator of the ith harmonic oscillator are provided, and P is the pumping speed.
The above method is characterized in that:
the evolution model H (x, p) with generalized coordinates x and generalized momentum p is expressed as:
wherein
And aiThe relation between the generalized coordinate x and the generalized momentum p satisfies the following conditions:
the above method is characterized in that:
the process of iterating the dynamic evolution of the generalized coordinate x and the generalized momentum p includes:
where f represents a white gaussian noise term, t is time, and n represents a transform factor.
The above method is characterized in that:
and setting the initial values of the generalized coordinates and the generalized momentum to be equal to zero.
The above method is characterized in that:
and comparing the ground state result obtained by the generalized coordinates and the generalized momentum in the previous iteration with the ground state result obtained by the generalized momentum in the next iteration while the generalized coordinates and the generalized momentum undergo multiple iterative evolutions, and if the ground state results obtained by the previous iteration and the next iteration are the same, determining that the ground state result at the moment is a correct ground state result.
The above method is characterized in that:
and when the generalized coordinates and the generalized momentum undergo multiple iterative evolution, comparing the ground state result obtained by the generalized coordinates and the generalized momentum in the previous iteration with the ground state result obtained by the generalized momentum in the next iteration, and if the ground state results obtained by the previous iteration and the ground state result obtained by the next iteration are different, readjusting the numerical value of the preset parameter and continuing the iterative evolution until the ground state results are the same.
The above method is characterized in that:
the isooctane hamilton is expressed as:
wherein sigmaiThe result of the ground state of the pauli corresponding to the ith harmonic oscillator is represented by ± 1 of the spin state of isooctyl.
The above method is characterized in that:
the predetermined parameter includes at least a detuning frequency ΔiAnd a transform factor n.
The above method is characterized in that:
and if the ground state results obtained by the previous iteration and the next iteration are the same, defining the value of the preset parameter at the moment as the final value after the iterative optimization.
The existing software resources and hardware resources can be used in the method, so that the problem of Yixin under a multi-spin full-connection system is solved, and an Yixin model is realized. The problem of yixin can be solved without using any yixin machine with complex structure and without using harsh conditions such as a quantum annealing furnace based on a superconducting circuit, and without needing ultralow operation temperature. Compared with the existing implementation mode of the Itanium model, the algorithm has high calculation speed and low error rate, and avoids complex hardware operation.
Drawings
To make the above objects, features and advantages more comprehensible, embodiments accompanied with figures are described in detail below, and features and advantages of the present application will become apparent upon reading the following detailed description and upon reference to the following figures.
Fig. 1 is a schematic diagram of a general architecture for driving a kerr nonlinear optical parametric oscillator with an external pump.
FIG. 2 is a flow chart of a method for implementing the Exin model by performing evolution iteration using an evolution model.
FIG. 3 is a step of optimization incorporating predetermined parameters in a process flow for implementing the Esin model.
Fig. 4 is an example of continuous parametric optimization of predetermined parameters by comparison of ground state results.
FIG. 5 shows the final parameters obtained by comparing the ground state results and making the ground state results consistent.
Detailed Description
The present invention will be described more fully hereinafter with reference to the accompanying examples, which are intended to illustrate and not to limit the invention, but those skilled in the art, on the basis of which they may obtain without inventive faculty, without departing from the scope of the invention.
Referring to fig. 1, with the continuous development and improvement of nonlinear optics, the pumping mode of the optical parametric oscillator is also continuously changed, and on one hand, the properties of the nonlinear crystal gradually develop towards a high damage threshold, a wide transparent region, a low absorption loss and a large size; on the other hand, the pumping light source itself is also developing, and the characteristics of high peak value, narrow line width, high average power and the like are appearing in pumping. KERR Non-linear Optical Parametric oscillators (KERR Non-linear OPOs) are a class of Optical Parametric oscillators (Optical Parametric oscillators) known in the industry. In the field, it is important to improve the conversion efficiency of the optical parametric oscillator, reduce the pumping threshold of the parametric oscillation, and control the line width of the parametric light. Its main purposes are two: the optical parametric oscillator OPO with high conversion efficiency can generate parametric light with better indexes such as beam quality and the like, and meanwhile, if the pumping threshold value is successfully reduced, the strict requirements on a pumping source, a nonlinear crystal and a cavity film can be relaxed; in addition, the wide application of parametric light provides more strict indexes of the quality of the parametric light, such as narrower line width, and the like, and also promotes the research on various operating parameters of the optical parametric oscillator.
Referring to fig. 1, for KERR nonlinear optical parametric oscillator (KERR OPO): the external pumping PU can be used for driving the Kerr nonlinear optical parametric oscillator to obtain the Hamilton quantity based on the Kerr nonlinear optical parametric oscillator. The external pump is most typically a laser pump source. The optical superlattice material which is rapidly developed in recent years presents various brand new quasi-phase matching optical parametric oscillation theories, and because the optical superlattice material has the advantages which are not possessed by a plurality of intrinsic crystals, the optical superlattice material provides a wider application prospect for the optical parametric oscillator. The operation modes of the optical parametric oscillator at the current stage include various oscillation operation modes such as pulse, continuous and mode-locked operation, etc., and the operation modes of the optical parametric oscillator also include a single-mode operation mode in multimode, and the pump PU or the pump source is distributed in solid, gas, dye and even excimer laser types, etc. The optical coupling device CP may couple the light beam provided by the pump into an optical transmission medium such as an optical fiber used by the kerr nonlinear optical parametric oscillator.
Referring to fig. 1, regarding an Optical Parametric Oscillator (OPO): two beams with different frequencies are incident on the nonlinear crystal to generate polarized traveling waves with different frequencies. If the speed of propagation of the polarized travelling wave in the crystal is the same as or similar to the speed of free propagation of the electromagnetic wave, an accumulative increase will be caused. The two incident beams may be termed "pump" and "signal" and the third beam that is concomitantly produced may be termed "idler" which, under the appropriate conditions, may be mixed with the pump to produce a polarized traveling wave having a signal frequency whose phase substantially reinforces the signal light. This process continues as both the signal and idler light are intensified and the pump light decays as the propagation distance in the crystal increases and this process is parametric amplification and is parametric oscillation as it progresses through the resonator. Optical parametric oscillation is the only way to achieve tunable coherent light in some optical bands, or is the most efficient one.
Referring to fig. 1, regarding an Optical Parametric Oscillator (OPO): as a wide tuning coherent light source, it overcomes the limitation of output wavelength of solid and gas laser, and can generate ultraviolet to far infrared laser. A laser beam of relatively high frequency and intensity is passed through the same nonlinear medium as a beam of relatively low frequency and intensity, with the result that the signal wave is amplified and a third light wave is generated. The frequency of idle wave is exactly equal to that of non-pumping light, and this nonlinear optical phenomenon, i.e. optical parametric amplification, is a very important optical characteristic: if a nonlinear medium is placed in an optical resonator and the pump light wave and the signal light wave and the idle light wave are repeatedly passed back and forth through some kind of nonlinear medium many times, once the gain of the signal light wave and the idle light wave due to optical parametric amplification is larger than the loss of the signal light wave and the idle light wave in the resonator, laser oscillation can be formed in the resonator, and at the same time, in an actual optical parametric oscillator, it is not required to input a signal wave of a certain intensity from the outside because it can also be generated by spontaneous radiation in the nonlinear medium.
Referring to fig. 1, the optical parametric oscillator is mainly characterized in that: the tuning range is wide, the laser can be very compact, and high-power and narrow-linewidth output can be realized. One of the conditions of the optical parametric oscillator: the threshold pump power condition is that after the pump power reaches a certain value, the gain of the signal light waves is equal to or greater than the optical loss of the signal light waves in the cavity, and if the pump light intensity exceeds the threshold, the energy of the pump light is mainly converted into coherent signal light or idle light waves to be output. Second condition of the optical parametric oscillator: the energy conservation condition is that in the parametric amplification process, when one photon is added to the signal light wave and the idle light wave, the corresponding pumping light wave loses one photon, so that the three waves should meet the energy conservation condition. Third condition of the optical parametric oscillator: the condition that the respective phases match should be reached.
Referring to fig. 1, because of the relationship of characteristic frequencies of working substances, a certain laser can only output laser with a fixed wavelength, which brings great limitations to its application, and expanding the coverage of laser wavelengths generally utilizes the nonlinear effect of tunable lasers and nonlinear optical crystals, which has become a common concern in the physical, optical, material and technical fields. In recent years, many solid-state tunable lasers with advanced technology are successively available, and especially all-solid-state tunable lasers can represent the development direction in this field. It can be understood that the optical parametric laser is a device that performs frequency conversion on laser light to generate tunable laser light, such as a nonlinear optical crystal, and belongs to a coherent optical parametric process with a laser mixing technology, such as a frequency doubling or sum frequency or difference frequency technology. The Optical Parametric Oscillator (OPO) is widely applied to the fields of new materials, biology, resonance spectroscopy, chemistry, distance measurement, radar and the like due to the advantages and irreplaceability of the OPO, such as wide tuning range, compact structure, convenient use, high power, wide wavelength coverage range, higher energy conversion efficiency and the like.
Referring to fig. 1, various technical solutions and technical features of the optical parametric laser (OPO) described above and below or disclosed in the conventional art are also applicable to the present application, and therefore, the present application is not repeated herein.
Referring to fig. 2, the present application discloses a method for implementing an izod model, or a bifurcation algorithm for solving the izod model based on the optical parametric oscillator principle. In an alternative embodiment, the method comprises: the process 10 mainly utilizes an external pump to drive the KERR nonlinear optical parametric oscillator (KERR OPO) so as to obtain a hamilton based on the KERR nonlinear optical parametric oscillator; the process 11 mainly converts the Hamiltonian based on the Kerr nonlinear optical parametric oscillator into an evolution model with generalized coordinates and generalized momentum; the process 12 mainly includes performing iterative evolution on the generalized coordinate and the generalized momentum, for example, obtaining values of some predetermined parameters in the hamiltonian based on the kerr nonlinear optical parametric oscillator according to the iterative evolution of the generalized coordinate and the generalized momentum; the process 13 mainly extracts a ground state result based on the quantity of the evans hamiltonian and according to the value of the predetermined parameter, for example, the evolution result of the evolution model is made to correspond to the ground state result of the evans hamiltonian. The above is the main workflow.
Referring to fig. 3, the present application discloses another method for implementing the izod model, or the present application discloses another bifurcation algorithm for solving the izod model based on the optical parametric oscillator principle. Based on fig. 2 but additionally including: the process 14 mainly compares the ground state results obtained from multiple iterations. If the ground state results obtained by performing multiple iterative evolutions on the generalized coordinates and the generalized momentum are consistent or the same, that is, if the comparison result is YES, executing the workflow 15, that is, outputting the ground state results, and then, outputting the correct ground state results; if the ground state results obtained by performing the multiple iterative evolutions on the generalized coordinates and the generalized momentum are inconsistent or different, and if the comparison result is NO, the workflow 12 is executed, that is, the subsequent iterative evolutions on the generalized coordinates and the generalized momentum are continued for multiple times, it is noted that the workflow 12 further includes a step of parametric optimization and the parametric optimization process is to readjust the values of the predetermined parameters in the hamilton quantity. The ground state results are difficult to be consistent provided that the values of some predetermined parameters in the hamiltonian are not optimal final values.
Referring to fig. 3, in addition to the example of fig. 2, the hamiltonian H of the KERR nonlinear optical parametric oscillator (KERR) under the rotation representation can be expressed in the following manner.
See fig. 3, in addition to the example of fig. 2. In Hamiltonian H: k is a nonlinear Kerr coefficient; deltaiIs the detuning frequency and represents the difference between the resonance frequency of the ith resonator and half of the pump frequency; epsilon0Is the coupling strength and the amount of Hamiltonian H corresponding to the amount of Ocimum HamiltonianIsingCoupling term J ofijAnd so on.
See fig. 3, in addition to the example of fig. 2. Where P (upper case) is the pumping rate. When the pumping rate gradually and slowly rises to a larger value from zero, the energy state with the lowest threshold (ground state) firstly appears in the optical parametric oscillator or the Kerr nonlinear optical parametric oscillator, and the high energy state is restrained by mode competition. It is also worth noting that the state energy split of each harmonic oscillator is close to the following equation:
the state energy of harmonic oscillator related to pumping rate is expressed as
See fig. 3, in addition to the example of fig. 2. Wherein sigmaiThe intrinsic energy of the Paul operator corresponding to the ith harmonic oscillator and under the self-expression is +/-1. Wherein a is similar tojThe intrinsic energy of the Paul operator corresponding to the j harmonic oscillator and under the self-expression is +/-1. The final evolution result of the KERR nonlinear parametric oscillator (KERR OPO) thus corresponds to the ground state solution of the quantity of isoocthamiltonian.
See fig. 3, in addition to thisThe example of fig. 2. Wherein
And aiRespectively, the generation and annihilation operators of the ith harmonic oscillator and can also be transformed into generalized coordinates x and generalized momentum p (lower case).
With respect to generating and annihilating operators may be represented as
See fig. 3, in addition to the example of fig. 2. The Hamiltonian of a Kerr nonlinear parametric oscillator (KERR OPO) can be represented as an evolution model H (x, p) by a generalized coordinate x and a generalized momentum p.
According to the Hamiltonian regular equation, the generalized coordinate, the generalized momentum and the like can meet the following conditions:
see fig. 3, in addition to the example of fig. 2. The evolution of the generalized coordinates and generalized momentum can be converted into the form of a classical system of differential equations, noting that the pumping rate is capital letters and the generalized momentum is lower case letters:
see fig. 3, in addition to the example of fig. 2. The kinetic evolution of generalized coordinates and generalized momentum allows iteration using the explicit Chouiola method, noting that the pumping rate is capital letters and the generalized momentum is lower case letters:
see fig. 3, in addition to the example of fig. 2. In an alternative embodiment, where the values of the initial generalized coordinate and the generalized momentum are both zero, in order to ensure the formation of the bifurcation evolution, a gaussian white noise term f may be added in the iteration so as to avoid a situation where the specific generalized coordinate and the initial value of the generalized momentum cause the bifurcation to have a unique result. Making the divergence of the generalized coordinates and generalized momentum naturally uncertain. The white gaussian noise term can have a given value in alternative embodiments or be a tunable parameter in other embodiments. The pumping rate P is a time-varying parameter that can slowly increase from zero and, when the pumping rate is above the ground state threshold, classical systems develop a tendency toward a bifurcation of the ground state stability if they cannot exceed the separation of the ground and excited states. The above mainly introduces an evolution iteration process of the evolution model. The initial values of the generalized coordinates and the generalized momentum, namely the initial values of the generalized coordinates and the generalized momentum are related to a white gaussian noise term, so that the evolution is very important.
Referring to fig. 3, the pumping characteristics of the Optical Parametric Oscillator (OPO): when the pump exceeds the threshold, the conversion efficiency increases with increasing pump intensity, and after reaching the maximum, the conversion efficiency decreases with increasing pump intensity, i.e. there is an optimum pump value. In addition, the optimal pump values corresponding to different output transmittances are different, that is, the optimal coupling transmittances are different under different pump intensities. The basis of the method is to solve the bifurcation algorithm of the Escissoring model based on the Kerr nonlinear optical parametric oscillator principle, so that the algorithm naturally and adaptively follows the characteristics.
Referring to fig. 3, the application discloses a bifurcation algorithm for solving an ixing model based on an oscillator principle, which mainly comprises the following algorithm scheme: according to the Hamilton quantity of the Kerr oscillator under the drive of an external pump, giving an evolution equation of a generalized coordinate and a generalized momentum in a corresponding classical system; performing feed-forward iteration on generalized coordinates and momentum bifurcation evolution; and automatically optimizing parameters in the algorithm based on the calculation result of the generalized coordinate. And converting the final optimized result such as a ground state or a parameter into a corresponding solution result of the IshIn spin. The method can solve the problem of Yixin of the multi-spin full-connection system. Compared with the existing Itanium machine mode, the software solving algorithm based on the traditional hardware resources has high calculation speed and low error rate, avoids complicated hardware operation and avoids harsh working conditions required by the Itanium machine mode. The method and the device are suitable for solving the combined optimization problem which can be converted into the solving of the Yixin Hamiltonian. In an alternative embodiment, a Hamiltonian canonical equation, such as a differential form resulting in generalized coordinates and generalized momentum, is used in converting the Hamiltonian of a Kerr nonlinear optical parametric oscillator to a model in the classical theoretical physics category. And (3) carrying out iterative evolution of a differential equation set by using an explicit Chorre method on the generalized coordinate and momentum bifurcation evolution. And according to the iteration result of the generalized coordinate, optimizing internal preset parameters by adopting a self-circulation mode so as to solve when outputting accurate result parameters, wherein the gradient descent idea and iteration updating are combined in the optimization process.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: this is where the generalized coordinate diverges when the pump rate P reaches a certain value, and the generalized momentum oscillates with a small amplitude around the origin in any case.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: due to the fact that
And
presence of some non-linear terms, at different JijAn overflow of the evolving final result value may occur at the input.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: to avoid overflow of the output result value in a high number of spins regime, in an alternative embodiment, the parametersThe initialization can be performed on the coupling strength J between spins in the Yixin problemijThe matrix J of (a) is subjected to multiplication transformation of an identity smaller number.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: even for the coupling strength J between spins in the problem of reflection of YixinijThe matrix J of (a) does not affect the final result of the ground state solution. And mapping the final evolution result of the generalized coordinate to the value of the Ixin spin state +/-1.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: for the solution of the quantity of isoocthamiltonian with a degenerate ground state, the result of the solution is in two specific cases, with a probability of occurrence of 50% each.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: amount of detuning ΔiThat is, the detuning frequency reflects the resonance mode of the system itself, and the value thereof affects the branching position of the generalized coordinate.
Referring to fig. 3, with respect to the bifurcated evolution of generalized coordinates and momentum, in the iterative evolution: for the solution of multiple self-selection system Yixin problems, the situation that the energy interval between the ground state and the excited state is too close is considered, and the generalized coordinate crosses the ground state and is directly subjected to bifurcation evolution towards the excited state when the pumping rate reaches a certain degree, so that the misconvergence is obtained. The self-loop approach to optimizing the internal predetermined parameters is equivalent to providing a solution to the misinterpretation.
Referring to fig. 3, parameters are optimized by means of an iteration result of generalized coordinates and the like and a self-loop: in which the bifurcation and evolution of the generalized coordinate according to the exact solution are determined, in an alternative embodiment, the bifurcation point of the generalized coordinate or the final evolution result of the generalized coordinate may be set to a suitable interval (e.g., set to an interval)
Nearby). The result of the solution at this point is highly accurate and less prone to error. Therefore, the accuracy of the state result is high when the generalized coordinate bifurcation point is selected in the interval.
See fig. 3, by iterative junctions of generalized coordinates, etcOptimizing parameters in a fruit and self-circulation mode: this utilizes the idea of gradient descent and the amount of detuning ΔiThat is, the magnitude of the detuning frequency is positively correlated with the bifurcation position of the generalized coordinate.
Referring to fig. 3, parameters are optimized by means of an iteration result of generalized coordinates and the like and a self-loop: this is where the pair reflects the strength of the coupling J between spins in the Ixin problemijThe matrix J is subjected to constant multiplication transformation, the transformation factor is n, and the size of n is positively correlated with the final evolution result of the generalized coordinate.
Referring to fig. 3, parameters are optimized by means of an iteration result of generalized coordinates and the like and a self-loop: wherein the heterogeneity of the time evolution result is solved according to multiple cycles, and the detuning quantity delta is adjustediAnd carrying out iterative optimization by using the transformation factor n.
Referring to fig. 3, parameters are optimized by means of an iteration result of generalized coordinates and the like and a self-loop: this outputs the ground state result with consistency for multiple loop solutions.
Referring to fig. 1, in an alternative embodiment, the present application discloses a substitution algorithm for solving an izod model or a substitution method for implementing the izod model based on the kerr nonlinear optical parametric oscillator principle, including the steps of: converting a Hamilton quantity of a Kerr nonlinear optical parametric oscillator under the driving of a pump into a corresponding evolution equation or an evolution model with generalized coordinates and generalized momentum, such as an evolution equation in a classical system; step two: performing bifurcation evolution on the generalized coordinates and the generalized momentum and using feedforward iteration; step three: based on the calculation result of the generalized coordinate, automatically optimizing and calculating a preset parameter; and step four, converting the finally optimized ground state result into a corresponding solution result of the IshIn spin. Note that the approaches described in the foregoing for implementing the izod model are equally applicable to this alternate embodiment. The present alternative example is slightly different from fig. 3.
Referring to fig. 1, in an alternative embodiment, the present application discloses a substitution algorithm for solving an izod model or a substitution method for implementing the izod model based on the kerr nonlinear optical parametric oscillator principle, including the steps of: step one, driving the Harr by a Kerr nonlinear optical parametric oscillator under the drive of a pumpThe Milton quantity is converted into a corresponding evolution model with generalized coordinates and generalized momentum; step two, setting a coupling term J of the Exin Hamiltonian related to the evolution modelij(ii) a Step three: setting the values of part of the predetermined parameters in the evolution model of the Hamiltonian; step four: performing iteration on the dynamics evolution of the generalized coordinates and the generalized momentum by using an explicit Euler method; step four: calculating the ground state result of each harmonic oscillator according to the solution of the explicit Euler method; step five: after the generalized coordinates and the generalized momentum are evolved for multiple times, comparing the ground state results of each harmonic oscillator before and after iteration, judging whether the ground state results before and after iteration are the same, if the ground state results obtained by the previous iteration and the next iteration are different, readjusting the numerical value of the preset parameter (re-executing the step three) and continuing iterative evolution until the ground state results of each harmonic oscillator before and after iteration are the same; and in the fifth step, if the ground state results obtained by the previous iteration and the next iteration are the same, directly outputting the ground state result of each harmonic oscillator. Note that the approaches described in the foregoing for implementing the izod model are equally applicable to this alternate embodiment. The present alternative example is slightly different from fig. 3.
Referring to fig. 3, in an alternative embodiment, the hamilton quantity based on the kerr nonlinear optical parametric oscillator is converted into an evolution model with a generalized coordinate and a generalized momentum, the generalized coordinate and the generalized momentum need to be iteratively evolved in the evolution model, and a value of a predetermined parameter in the hamilton quantity based on the kerr nonlinear optical parametric oscillator is obtained according to the iterative evolution of the generalized coordinate and the generalized momentum; if the predetermined parameter comprises at least the detuning frequency ΔiAnd the transformation factor n and the predetermined parameters may also comprise further parameters of a further type such as a hamiltonian function and/or in an evolution model. Based on the quantity of evans hamiltonian and depending on the value of a predetermined parameter, for example combining an evolution model based on the hamiltonian under a kerr nonlinear optical parametric oscillator condition with a conventional expression of the evans hamiltonian, the evolution result of the evolution model corresponds to the ground state result of the evans hamiltonian. In an alternative example, the evolution model and the Esinhamiltonian are commonAnd thereby implementing a ground state solution. In an alternative example, the values of the predetermined parameters in the evolution model are optimized and finally determined, and the evolution result of the evolution model is equivalent to solving the respective ground state results, so that the evolution result of the evolution model corresponds to the ground state result of the quantity of the Ishamiltonian. The optimization procedure of the predetermined parameters will be described further below.
Referring to FIG. 3, in an alternative embodiment, a method of implementing the Esin model has been taught: the process 14 mainly compares the ground state results obtained from multiple iterations. If the ground state results obtained by performing the iterative evolution of the generalized coordinates and the generalized momentum for a plurality of times are identical or identical, i.e. the comparison result is YES, the work flow 15 is executed, i.e. the ground state result is output and is now the correct ground state result. If the ground state results obtained by performing the multiple iterative evolutions on the generalized coordinates and the generalized momentum are inconsistent or different, that is, if the comparison result is NO, the workflow 12 is executed, that is, the generalized coordinates and the generalized momentum are continuously subjected to the subsequent multiple iterative evolutions. Readjusting predetermined parameters (such as detuning frequency delta) in the evolution model before performing subsequent iterative evolution on the generalized coordinates and the generalized momentum for multiple timesiAnd transforming the value of the factor n, etc.) so that the ground state result obtained in the previous iteration and the ground state result obtained in the next iteration converge, namely, the process of readjusting the value of the predetermined parameter in the evolution model is a parameter optimization process.
Referring to fig. 4, regarding the optimization of the parameters: first, the iteration number Q is assumed to be a positive integer. And when the generalized coordinates and the generalized momentum undergo multiple iterative evolutions, comparing the ground state results obtained by the generalized coordinates and the generalized momentum in any previous iteration with the ground state results obtained by the generalized momentum in the next iteration, and if the ground state results obtained by the previous iteration and the ground state results obtained by the next iteration are different, continuously performing iterative evolutions on the generalized coordinates and the generalized momentum after readjusting the numerical values of the preset parameters until the ground state results are approximately the same.
Referring to fig. 4, regarding the optimization of the parameters: the generalized coordinates and the generalized momentum obtain the evolution result of the evolution model, namely each ground state of the Esino Hamilton in the Q iteration processResult σ1、σ2、…、σi、σjAnd so on.
Referring to fig. 4, regarding the optimization of the parameters: obtaining the evolution result of the evolution model, namely each ground state result sigma of the Isimutant quantity in the Q +1 iteration process by the generalized coordinates and the generalized momentum1、σ2、…、σi、σjAnd so on. According to the rule designed by the application, the ground state result obtained by any previous iteration (such as Q time) of the generalized coordinate and the generalized momentum and the ground state result obtained by the later iteration (such as Q +1 time) of the generalized coordinate and the generalized momentum are required to be compared, if the ground state result obtained by the previous iteration is different from the ground state result obtained by the later iteration, if the ground state result obtained by the Q time iteration is different from the ground state result obtained by the Q +1 time iteration, the preset parameter (such as detuning frequency delta) is required to be readjustediAnd transforming factor n, etc.) and then continuing to carry out iterative evolution on the generalized coordinates and the generalized momentum. Such as re-executing the iteratively evolved flow 12 of fig. 3.
Referring to fig. 4, the scheme of the present application may be implemented by a program written on a conventional computer, and the embodiment of the present application may also be implemented by hardware. For example, the computer stores a computer program for implementing the itacin model, and the flow executed by the computer program when the computer program is executed by a processor equipped in the computer includes: and carrying out iterative evolution on an evolution model which is converted from the Hamiltonian and has generalized coordinates and generalized momentum to obtain a value of a preset parameter in the Hamiltonian based on the Kerr nonlinear optical parametric oscillator, and enabling an evolution result of the evolution model to correspond to a ground state result of the Ocimum based on the Ocimum and according to the value of the preset parameter. The computer may compare the ground state result from the Q-th iteration with the ground state result from the Q + 1-th iteration, the comparison process COMP being performed substantially by the computer in this example. If the traditional computer is replaced by various hardware resources such as a digital signal processor or a microcontroller or a single-chip microcomputer or an advanced reduced instruction set computer, the hardware can also realize the Itanium model. As an example, a digital signal processor is provided, and an iterative evolution module is provided for performing an iterative evolution task on the generalized coordinates and the generalized momentum; and providing a data comparison module for comparing the ground state result obtained by the previous iteration of the generalized coordinate and the generalized momentum with the ground state result obtained by the next iteration of the generalized coordinate and the generalized momentum. The comparison result of the data comparison module can also trigger the iterative evolution module to readjust the value of the preset parameter: if the basic state results obtained by the previous iteration and the next iteration are different, the comparison result of the data comparison module informs the iterative evolution module to readjust the value of the preset parameter and then continue iterative evolution; if the ground state results obtained in the previous iteration and the next iteration are the same, the value of the preset parameter in the Hamilton quantity based on the Kerr nonlinear optical parametric oscillator can be obtained, the ground state result at the moment is considered to be the correct ground state result, and the value of the preset parameter at the moment is defined to be the final value after iterative optimization. The digital signal processor needs to provide more memory cells in the process to store the base state result obtained from each iteration. And the ground state nature obtained by iteration of the iterative evolution module according to the final value after the iterative optimization is a correct ground state result. The iterative evolution module makes the evolution result of the evolution model correspond to the ground state result of the inching hamiltonian based on the inching hamiltonian and according to the value of a predetermined parameter, for example, according to the final value. The measures of the present example are exemplary only and not limiting. For example, the digital signal processor can be replaced by a microcontroller or a single chip microcomputer or hardware such as an advanced reduced instruction set computer.
Referring to fig. 4, regarding the optimization of the parameters: obtaining the evolution result of the evolution model, namely each ground state result sigma of the Isimutant quantity in the Q +2 iteration process by the generalized coordinates and the generalized momentum1、σ2、…、σi、σjAnd so on. According to the rule designed by the application, the ground state result obtained by any previous iteration (Q + 1) of the generalized coordinates and the generalized momentum is compared with the ground state result obtained by the subsequent iteration (such as Q + 2) of the generalized coordinates and the generalized momentum, if the ground state results obtained by the previous iteration and the subsequent iteration are different, such as the ground state result obtained by the Q +1 iteration and the ground state result obtained by the Q +2 iterationThe iteration results in different ground states, requiring readjustment of predetermined parameters (e.g. detuning frequency Δ)iAnd transforming factor n, etc.) and then continuing to carry out iterative evolution on the generalized coordinates and the generalized momentum. Such as re-executing the iteratively evolved flow 12 of fig. 3.
Referring to fig. 5, regarding the optimization of the parameters: it is also assumed that the number of iterations Q is a positive integer. And comparing the ground state result obtained by the generalized coordinates and the generalized momentum in any previous iteration with the ground state result obtained by the generalized coordinates and the generalized momentum in the next iteration while performing multiple iterative evolutions, and if the ground state results obtained by the previous iteration and the next iteration are the same, determining that the ground state result at the moment is the correct ground state result. In addition, the value of the predetermined parameter at this time is defined as the final value after the iterative optimization, and the value of the predetermined parameter does not need to be readjusted in any way.
Referring to fig. 5, regarding the optimization of the parameters: the generalized coordinates and the generalized momentum obtain the evolution result of the evolution model in the Q-th iteration process, namely each ground state result sigma of the Exin Hamiltonian1、σ2、…、σi、σjAnd so on.
Referring to fig. 5, regarding the optimization of the parameters: obtaining the evolution result of the evolution model, namely each ground state result sigma of the Isimutant quantity in the Q +1 iteration process by the generalized coordinates and the generalized momentum1、σ2、…、σi、σjAnd so on. According to the rule designed by the application, the ground state result obtained by any previous iteration (such as Q time) of the generalized coordinate and the generalized momentum and the ground state result obtained by the subsequent iteration (such as Q +1 time) of the generalized coordinate and the generalized momentum are required to be compared, if the ground state result obtained by the previous iteration and the ground state result obtained by the subsequent iteration are the same, if the ground state result obtained by the Q time iteration is the same as the ground state result obtained by the Q +1 time iteration, the preset parameter (such as detuning frequency delta) is not required to be adjusted againiAnd transform factor n, etc.). The value defining the predetermined parameter at this time is the final value after the iterative optimization. The final parameters shown in the figure indicate that the values of the predetermined parameters are the optimized final values if the ground state results obtained from the previous iteration and the next iteration are the same. ToThe method is based on a plurality of iterative evolution processes of the generalized coordinates and the generalized momentum so as to obtain the numerical value of the preset parameter in the Hamiltonian of the Kerr nonlinear optical parametric oscillator. The ground state result at this time is the correct ground state result.
Referring to fig. 5, regarding the optimization of the parameters: obtaining the evolution result of the evolution model, namely each ground state result sigma of the Isimutant quantity in the Q +2 iteration process by the generalized coordinates and the generalized momentum1、σ2、…、σi、σjAnd so on. According to the rule designed by the application, the ground state result obtained by any previous iteration (Q + 1) of the generalized coordinates and the generalized momentum and the ground state result obtained by the later iteration (such as Q + 2) of the generalized coordinates and the generalized momentum are required to be compared, if the ground state result obtained by the previous iteration is the same as that obtained by the later iteration, the ground state result obtained by the Q +1 iteration is the same as that obtained by the Q +2 iteration, and the preset parameter (such as detuning frequency delta) is not required to be adjusted againiAnd transform factor n, etc.). The value defining the predetermined parameter at this time is the final value or the final parameter after the iterative optimization. In the specific scheme, it has an important meaning to compare the ground state result of the generalized coordinate and the generalized momentum obtained in the previous iteration with the ground state result of the generalized coordinate and the generalized momentum obtained in the subsequent iteration, and if the ground state results obtained in the previous iteration and the subsequent iteration are different, readjust the numerical value of the predetermined parameter and then continue to perform iterative evolution on the generalized coordinate and the generalized momentum. For the solution of multiple self-selected system yixin problems, due to the fact that the energy interval between the ground state and the excited state is too close, the generalized coordinate can directly diverge and evolve towards the excited state direction over the ground state when the pumping rate reaches a certain degree, and the wrong solution is obtained. One of the effects of the specific scheme described above is when the generalized coordinates tend to diverge over the ground state directly towards the excited state: the bifurcation evolution direction of the generalized coordinates is changed by readjusting the value of the preset parameter, so that the generalized coordinates are prevented from directly diverging and evolving towards the direction of the excited state over the ground state, and errors in the ground state result evolved by the evolution model are avoided.
Referring to fig. 5, the problem of yixin can be solved or partially solved by using hardware resources such as a traditional computer and various processors to construct the yixin model, and the problem of yixin and other combination problems can be solved based on traditional hardware and software resources. Without any inverter with complex construction and without being limited to severe conditions such as quantum annealing furnaces based on superconducting circuits.
While the above specification teaches the preferred embodiments with a certain degree of particularity, there is shown in the drawings and will herein be described in detail a presently preferred embodiment with the understanding that the present disclosure is to be considered as an exemplification of the principles of the invention and is not intended to limit the invention to the specific embodiment illustrated. Various alterations and modifications will no doubt become apparent to those skilled in the art after having read the above description. Therefore, the appended claims should be construed to cover all such variations and modifications as fall within the true spirit and scope of the invention. Any and all equivalent ranges and contents within the scope of the claims should be considered to be within the intent and scope of the present invention.
Claims (10)
1. A method for implementing an Esin model, comprising:
driving the Kerr nonlinear optical parametric oscillator by using an external pump so as to obtain a Hamilton quantity based on the Kerr nonlinear optical parametric oscillator;
converting the Hamiltonian based on Kerr nonlinear optical parametric oscillator into an evolution model with generalized coordinates and generalized momentum;
iteratively evolving the generalized coordinates and the generalized momentum to obtain values of predetermined parameters in the Hamiltonian based on a Kerr nonlinear optical parametric oscillator according to the iterative evolution of the generalized coordinates and the generalized momentum;
and enabling the evolution result of the evolution model to correspond to the ground state result of the inching Hamiltonian based on the inching Hamiltonian and the value according to the preset parameter.
2. The method of claim 1, wherein:
the Hamiltonian H under Kerr nonlinear optical parametric oscillator conditions is expressed as:
where K is the nonlinear Kerr coefficient and the detuning frequency DeltaiRepresenting the difference between the resonance frequency of the ith resonator of the N resonators and half the pump frequency, epsilon0Is the coupling strength, JijA coupling term corresponding to the quantity of isooctane Hamilton;
and
and aiThe generation operator and annihilation operator of the ith harmonic oscillator are provided, and P is the pumping speed.
3. The method of claim 2, wherein:
the evolution model H (x, p) with generalized coordinates x and generalized momentum p is represented as:
wherein
And aiThe relation between the generalized coordinate x and the generalized momentum p satisfies the following conditions:
4. the method of claim 3, wherein:
the process of iterating the dynamic evolution of the generalized coordinate x and the generalized momentum p includes:
where f represents a white gaussian noise term, t is time, and n represents a transform factor.
5. The method of claim 4, wherein:
and setting the initial values of the generalized coordinates and the generalized momentum to be equal to zero.
6. The method of claim 1, wherein:
and comparing the ground state result obtained by the generalized coordinates and the generalized momentum in the previous iteration with the ground state result obtained by the generalized momentum in the next iteration while the generalized coordinates and the generalized momentum undergo multiple iterative evolutions, and if the ground state results obtained by the previous iteration and the next iteration are the same, determining that the ground state result at the moment is a correct ground state result.
7. The method of claim 1, wherein:
and when the generalized coordinates and the generalized momentum undergo multiple iterative evolution, comparing the ground state result obtained by the generalized coordinates and the generalized momentum in the previous iteration with the ground state result obtained by the generalized momentum in the next iteration, and if the ground state results obtained by the previous iteration and the ground state result obtained by the next iteration are different, readjusting the numerical value of the preset parameter and continuing the iterative evolution until the ground state results are the same.
8. The method of claim 1, wherein:
the isooctane hamilton is expressed as:
whereinσiThe result of the ground state of the pauli corresponding to the ith harmonic oscillator is represented by ± 1 of the spin state of isooctyl.
9. The method of claim 4, wherein:
the predetermined parameter includes at least a detuning frequency ΔiAnd a transform factor n.
10. The method of claim 6, wherein:
and if the ground state results obtained by the previous iteration and the next iteration are the same, defining the value of the preset parameter at the moment as the final value after the iterative optimization.
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| WO2023226310A1 (en) * | 2022-05-23 | 2023-11-30 | 华为云计算技术有限公司 | Molecule optimization method and apparatus |
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| CN114970440A (en) * | 2022-05-07 | 2022-08-30 | 上海图灵智算量子科技有限公司 | Wiring method for VLSI channel |
| CN114970440B (en) * | 2022-05-07 | 2023-07-25 | 上海图灵智算量子科技有限公司 | Wiring method of ultra-large scale integrated circuit channel |
| WO2023226310A1 (en) * | 2022-05-23 | 2023-11-30 | 华为云计算技术有限公司 | Molecule optimization method and apparatus |
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