Searching method based on graph structure data

Abstract

The invention discloses a search method based on graph structure data, which relates to the graph search and quantum computing technology, and comprises the following steps: trapping neutral atoms in an optical lattice; an interconnected graph structure and graph data codes are constructed according to the neutral atoms, each neutral atom describes a node of the graph structure, interaction among the neutral atoms describes an edge of the graph structure, and data are coded by utilizing an intrinsic spin state of a neutral atom system; marking search nodes based on the constructed graph structure and graph data codes; preparing an atomic initial state; and measuring the state of the atomic system by adopting a ramsey interference method, and taking the measured state of the atomic system as a search result of the search system. The invention provides a method for avoiding the influence of quantum noise by regulating and controlling non-Markov heat library parameters, so that a rapid Grover search algorithm based on graph structure data, which is close to a noise-free ideal condition, can be obtained in an actual noise environment.

Description

Technical Field

[0001] This application relates to the fields of graph search and quantum computing technology, and particularly relates to a search method based on graph-structured data. Background Art

[0002] Graph-structured data search has extremely wide application scenarios, covering multiple fields such as computer science, artificial intelligence, geographic information systems, network optimization, data mining, game development, and biology and chemistry. For traditional search methods for graph-structured data containing N nodes, the time consumption mainly depends on the specific implementation of the search algorithm and the complexity of the graph structure. In classical algorithms, if one wants to perform a traversal search on a graph-structured data of N nodes, then in the worst case, it may be necessary to check nearly N nodes, and the time complexity is usually close to or higher (for example, when the graph is not a sparse graph). This is because classical algorithms usually need to check each node one by one until the target node is found or all nodes are traversed.

[0003] The emergence of quantum search algorithms has brought revolutionary changes to graph-structured data search. Quantum search algorithms, such as Grover's algorithm, can achieve exponential or at least square-root level acceleration. When combined with graph-structured data, quantum search algorithms can be applied to a variety of scenarios, including but not limited to the quantum walk algorithm that can significantly improve search efficiency when dealing with large and complex networks, the quantum graph coloring algorithm, and the quantum shortest path algorithm applied in fields such as path planning and network optimization.

[0004] Although quantum search algorithms have great potential, they are still in the research and experimental stage. Implementing these algorithms requires advanced quantum computing hardware and complex algorithm design. In addition, quantum algorithms also face many challenges in practical applications, such as the stability of qubits, the maintenance of quantum entanglement, and the accuracy of quantum measurement. Therefore, before applying quantum search algorithms to graph-structured data search, a large amount of research and experimental work still needs to be carried out.

[0005] At present, the systems for implementing quantum computing include neutral atom systems, superconducting qubit systems, ion trap systems, etc. These quantum systems are extremely sensitive to the influence of environmental noise, and the influence of weak noise is very likely to quickly destroy the experimental implementation of the entire quantum system algorithm. Therefore, how to implement a stable quantum search algorithm considering the influence of the actual environmental noise is an important research issue. In many studies, for the convenience of analyzing problems, it is generally defaulted that the heat bath coupled to the experimental system is a Markov heat bath. Non-Markovian heat baths can also be actually constructed, for example, through the coupling design of atoms and optical cavities, or the bandgap structure design of photonic crystals can form various non-Markovian heat baths. Existing research has shown that under the action of a non-Markovian heat bath, there is a backflow effect of the heat bath towards the quantum system, and its dynamic evolution is completely different from that under the action of a Markov heat bath. Summary of the Invention

[0006] An embodiment of the present application provides a search method based on graph-structured data, which uses a neutral atom system to construct a model for implementing a fast Grover search algorithm based on graph-structured data, and proposes a method for regulating the parameters of a non-Markovian heat bath to avoid the influence of quantum noise, so as to realize a fast Grover search algorithm based on graph-structured data that can approach the noise-free ideal situation in an actually noisy environment.

[0007] An embodiment of the present application provides a search method based on graph-structured data, including the following steps:

[0008] Trapping neutral atoms in an optical lattice;

[0009] Constructing an interconnected graph structure and graph data encoding according to neutral atoms, where each neutral atom describes a node of the graph structure, and the interaction between neutral atoms describes an edge of the graph structure, and using the intrinsic spin state of the neutral atom system to encode data;

[0010] Based on the constructed graph structure and graph data encoding, marking the search nodes;

[0011] Preparing the initial atomic state;

[0012] Adopting the ramsey interference method to measure the state of the atomic system, and taking the measured state of the atomic system as the search result of the search system.

[0013] An embodiment of the present application uses a neutral atom system to construct a model for implementing a fast Grover search algorithm based on graph-structured data, and proposes a method for regulating the parameters of a non-Markovian heat bath to avoid the influence of quantum noise, so as to realize a fast Grover search algorithm based on graph-structured data that can approach the noise-free ideal situation in an actually noisy environment.

[0014] The above description is only an overview of the technical solution of the present application. In order to understand the technical means of the present application more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features and advantages of the present application more obvious and understandable, the following specifically illustrates the specific implementation manners of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of illustrating the preferred embodiments and are not considered to be a limitation of the present application. And throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0016] Figure 1 It is a schematic diagram of the basic process of the search method based on graph-structured data in an embodiment of the present application;

[0017] Figure 2 It is an example of the search system architecture of the search method based on graph-structured data in an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0019] An embodiment of the present application provides a search method based on graph-structured data, including the following steps:

[0020] In step S101, neutral atoms are trapped in an optical lattice. In some embodiments, trapping neutral atoms in the optical lattice further includes adjusting the intensity of the trapping laser beam to maintain the trapping intensity and temperature. A bilateral optical cavity is arranged outside the neutral atom system for filtering and adjusting the color noise spectrum in subsequent steps.

[0021] In step S102, an interconnected graph structure and graph data encoding are constructed according to the neutral atoms, where each neutral atom describes a node of the graph structure, and the interaction between neutral atoms describes an edge of the graph structure, and the intrinsic spin state of the neutral atom system is used to encode data.

[0022] In step S103, based on the constructed graph structure and graph data encoding, search nodes are marked. In a specific example, marking search nodes based on the constructed graph structure and graph data encoding includes:

[0023] Any atom serving as a search node applies a uniform magnetic field in a specified direction to the remaining atoms;

[0024] Adjust the intensity of the trapped laser beam so that the atoms serving as search nodes acquire a specific phase relative to other atoms. At this time, the Hamiltonian of the atomic system is:

[0025]

[0026]

[0027] In step S104, prepare the initial atomic state. In some embodiments, preparing the initial atomic state includes:

[0028] Prepare the initial atomic state as an equally probable amplitude superposition state , where represents the j-th atom being in the state, and the remaining atoms are all in the state.

[0029] In step S105, use the Ramsey interference method to measure the state of the atomic system, and use the measured state of the atomic system as the search result of the search system.

[0030] The embodiments of the present application use a neutral atomic system to construct a model for implementing the fast Grover search algorithm based on graph-structured data, and propose a method for regulating non-Markovian reservoir parameters to avoid the influence of quantum noise, so as to achieve a fast Grover search algorithm based on graph-structured data that can obtain a result close to the noiseless ideal situation in an actually noisy environment.

[0031] In some embodiments, constructing an interconnected graph structure and graph data encoding according to neutral atoms includes:

[0032] Trapping 2N neutral atoms in an optical lattice, where N atoms are regarded as a subsystem;

[0033] Adjust the trapped laser so that any two neutral atoms located at the lattice vertices in any subsystem are equidistantly distributed, the two subsystems are symmetrically distributed in space, and the two subsystems are interconnected only through the interaction of two atoms interconnect, and the two subsystems are interconnected through the interaction γ to form an interconnected complete graph structure.

[0034] Based on the two internal states of the atom, spin up and spin down , perform data encoding, where the interaction of the atoms can transfer the excitons between the atoms.

[0035] By applying an external magnetic field, a phase label is applied to specific atoms to mark the nodes to be searched. In a graph structure data computing system constructed of neutral atoms, a quantum exponential acceleration Grover fast search can be realized, that is, with a time complexity of Θ( ), the marked atomic node can be searched with a 50% success probability.

[0036] Prepare the initial atomic state and prepare the initial atomic state as an equally probable amplitude superposition state , at this time, for example, the first atom is the node to be searched. If only the evolution under the Hamiltonian is considered, then the interaction between the system and the environment is not considered at this time, that is, the system is closed and always in a single-excitation state. The general state of the atomic system can be expressed as , and the evolution of the atomic system satisfies the Schrödinger equation . Only considering the action of without environmental noise, the atomic system can search for the marked node with a 50% success probability on the time scale of under . .

[0037] In some embodiments, after preparing the initial atomic state, it further includes:

[0038] Adjust the mirrors of the double-sided optical cavity, and by adjusting the mirror transmittance, make the line width of the optical cavity meet the requirements. For example, the line width is narrow enough to filter the external white noise into narrow-linewidth Lorentz spectral noise and interact with the atomic system in the cavity. Through this step of operation, the loss impact caused by environmental noise can be greatly eliminated.

[0039] In some embodiments, adjusting the mirrors of the double-sided optical cavity to make the line width of the optical cavity meet the requirements specifically includes:

[0040] Quantize the environmental noise into a series of one-dimensional linear harmonic oscillators with continuous frequencies ω, and describe the interaction between the atomic system and the environment as:

[0041]

[0042] where is the atomic state and the transition frequency between, is the annihilation operator of the environment, represents the coupling strength between the atom and the environment;

[0043] The entire system including the atom and the environment evolves under the Hamiltonian , and the overall state is expressed as:

[0044]

[0045] wherein represents the state where the atom has no excitons, which is the vacuum state of the environment;

[0046] At the initial moment, the states of the atom and the environment are , and substituting and into the Schrödinger equation, the evolution of the atomic system and the environment is obtained as:

[0047]

[0048]

[0049] When j = 2, …, N - 1,

[0050]

[0051]

[0052]

[0053] When j = N + 2, …, 2N,

[0054]

[0055] wherein

[0056]

[0057] is the time correlation function of the environmental noise, taking into account the structure and memory effect of the environmental noise. Different environmental noises correspond to different time correlation functions, resulting in different time evolutions, and the search results based on this neutral atom system are also different. Consider a common colored noise spectrum, namely the Lorentz spectrum, which widely exists in atom-optical cavity systems, photonic crystals, etc.

[0058] In some embodiments, adjusting the mirrors of the double-sided optical cavity to meet the requirements of the linewidth of the optical cavity by adjusting the mirror transmittance specifically further includes:

[0059] For a white noise environment, constructing a Lorentz spectrum noise by introducing an optical cavity, and the Lorentz spectrum noise is described as:

[0060]

[0061] wherein and respectively represent the coupling strength and spectral width between the atom and the environment, and the corresponding time correlation function is

[0062]

[0063] In some embodiments, adjusting the cavity mirrors of the bilateral optical cavity to meet the requirements of the linewidth of the optical cavity by adjusting the transmittance of the cavity mirrors specifically further includes:

[0064] Using the pseudo-mode method, the interaction between the atomic system and the Lorentz spectral environment is equivalently described as the coupling between the system and the pseudo-mode, and the pseudo-mode is lossy to an independent Markov environment. Specifically, the frequency and loss rate of the pseudo-mode can be obtained from the poles of the Lorentz spectrum (7) as and , and the coupling strength can be obtained from the residue of the Lorentz spectrum (7) as . The evolution of the atomic system and the environment is:

[0065]

[0066] When j = 2, …, N - 1,

[0067]

[0068]

[0069]

[0070] When j = N + 2, …, 2N,

[0071]

[0072]

[0073] where b(t) represents the probability amplitude of the pseudo-mode, and there is

[0074]

[0075] As the environmental spectral width decreases, the equivalent coupling strength and loss of the pseudo-mode become weaker, regarded as the net effect brought by the environmental backflow. By reducing the spectral width , the atomic system can be approximately decoupled from the pseudo-mode, and a fast search system for graph-structured data based on neutral atoms can be realized.

[0076] Finally, the Ramsey interference method is used to measure the state of the atomic system, that is, the search result of the search system.

[0077] An embodiment of a search method based on graph-structured data is also proposed in the embodiments of the present application. As Figure 2 shown, this example considers a system for realizing fast search of graph-structured data in an actual environment with 8 atoms (N = 4) and 16 atoms (N = 8). The atomic system parameters are respectively and 。

[0078] The results show that when the number of atoms is 8, when the Lorentz spectrum parameter is , the maximum success rate of the search system is 33.11%, and the running time t = 3.184; when the Lorentz spectrum parameter is , the maximum success rate of the search system is 45.15%, and the running time t = 3.183; when the Lorentz spectrum parameter is , the maximum success rate of the search system is 48.23%, and the running time t = 3.19. When the number of atoms is 16, when the Lorentz spectrum parameter is , the maximum success rate of the search system is 16.31%, and the running time t = 2.391; when the Lorentz spectrum parameter is , the maximum success rate of the search system is 44.94%, and the running time t = 4.697; when the Lorentz spectrum parameter is , the maximum success rate of the search system is 49.16%, and the running time t = 4.455. The experimental results show that the smaller the Lorentzian colored noise spectral width, the better the search performance of the system.

[0079] Table 1 Experimental results (search time) under different colored noise spectra

[0080] Number of atoms Atomic system parameters Lorentzian colored noise spectrum parameters Maximum search success rate Search time 8 #timg# #timg# 33.11% 3.184 8 #timg# #timg# 45.15% 3.183 8 #timg# #timg# 48.23% 3.19 16 #timg# #timg# 16.31% 2.391 16 #timg# #timg# 44.94% 4.697 16 #timg# #timg# 49.16% 4.455

[0081] In the above embodiments, the fast search system can be constructed through the Heisenberg XY interaction, and can be implemented on platforms such as cold atoms, quantum dot spins, and cavity QED. The graph structure can be constructed by trapping neutral atoms in an optical lattice, etc., and the search nodes can be marked by applying an external magnetic field, etc. An external optical cavity and adjusting the cavity linewidth can construct Lorentzian spectral colored noise with a certain spectral width.

[0082] This application uses an optical cavity to filter white noise into Lorentzian spectral colored noise, analyzes the search evolution in the presence of colored noise based on the pseudo-mode method, and proposes that the influence of noise on the search system is inversely proportional to the noise spectral width. By further narrowing the optical cavity linewidth, the influence of quantum noise can be avoided, and a 50% success probability can be achieved under the time complexity in the actual environment. The method of this application avoids the influence of noise in the actual search algorithm running environment, and proposes a method to filter out noise from the principle based on the pseudo-mode method, which significantly improves the search running effect.

[0083] ​It should be noted that in the embodiments of the present application, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device including a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or device including such element.

[0084] The serial numbers of the embodiments of the present application above are merely for description and do not represent the superiority or inferiority of the embodiments.

[0085] Through the description of the above embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disc) and includes several instructions for causing a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present application.

[0086] The embodiments of the present application have been described above in conjunction with the accompanying drawings. However, the present application is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present application, those of ordinary skill in the art can also make many forms without departing from the purpose of the present application and the scope protected by the claims. All of these are within the protection scope of the present application.

Claims

1. A search method based on graph structure data, characterized in that: The steps include: Trapping neutral atoms in optical lattices; Constructing interconnected graph structures and graph data encoding based on neutral atoms, where each neutral atom describes a node of the graph structure, and the interactions between neutral atoms describe the edges of the graph structure, and using the intrinsic spin state of the neutral atomic system to encode data; Based on the constructed graph structure and graph data encoding, mark the search nodes; Prepare the initial state of atoms; The Ramsey interferometer method is used to measure the state of the atomic system, and the measured state of the atomic system is used as the search result of the search system.

2. The search method based on graph structure data according to claim 1, characterized in that: Trapping neutral atoms in an optical lattice also includes maintaining the trapping intensity and temperature by adjusting the intensity of a trapping laser beam, and setting a double-sided optical cavity outside the neutral atom system.

3. The search method based on graph structure data according to claim 1, characterized in that: The graph structure and graph data encoding based on the interconnection of neutral atoms include: Trapping 2N neutral atoms in an optical lattice, where N atoms are considered as a subsystem; Adjust the trapped laser so that any two neutral atoms at the lattice vertices in any subsystem are equally spaced, the two subsystems are symmetrically distributed in space, and the two subsystems interact only through the interaction of the two atoms. interconnected; Based on the two internal states of the atom, spin up and spin down , to encode data, where the atomic interactions It can transfer excitons between atoms.

4. The search method based on graph structure data according to claim 3, characterized in that: Based on the constructed graph structure and graph data encoding, the marked search nodes include: Any atom used as a search node applies a uniform magnetic field in a specified direction to the remaining atoms; The intensity of the trapping laser beam is adjusted so that the atom serving as the search node acquires a specific phase relative to other atoms.

5. The search method based on graph structure data according to claim 4, characterized in that: Preparing the initial state of atoms includes: Prepare the initial atomic state into an equal probability amplitude superposition state ,in Indicates that the jth atom is in state, and the rest of the atoms are in state.

6. The search method based on graph structure data according to claim 5, characterized in that: After preparing the initial state of the atom, it also includes: The cavity mirrors of the double-sided optical cavity are adjusted, and the line width of the optical cavity is made to meet the requirements by adjusting the transmittance of the cavity mirrors, so as to filter the external white noise into Lorentz spectral color noise with narrow line width, which interacts with the atomic system in the cavity.

7. The search method based on graph structure data according to claim 6, characterized in that: Adjust the cavity mirror of the double-sided optical cavity and adjust the cavity mirror transmittance to make the line width of the optical cavity meet the requirements. Specifically include: The environmental noise is quantized into a series of one-dimensional linear oscillators with continuous frequency ω, and the interaction between the atomic system and the environment is described as: in Atomic and The transition frequency between is the annihilation operator of the environment, represents the coupling strength between the atom and the environment; The entire system including atoms and environment is described in the Hamiltonian The overall state is expressed as: in represents the state of an atom without excitons, It is the vacuum state of the environment; At the initial moment, the state of the atom and the environment is ,Depend on and Substituting into the Schrödinger equation, the atomic system and the environment evolution are obtained as: When j=2,…,N-1, When j=N+2,…,2N, in 8. The search method based on graph structure data according to claim 7, characterized in that: Adjust the cavity mirror of the double-sided optical cavity, and adjust the cavity mirror transmittance to make the line width of the optical cavity meet the requirements, which specifically includes: For a white noise environment, the Lorentz spectrum noise is constructed by introducing an optical cavity. The Lorentz spectrum noise is described as: in , Represent the intensity and spectral width of the coupling between atoms and the environment respectively, and the corresponding time correlation function is 9. The search method based on graph structure data according to claim 8, characterized in that: Adjust the cavity mirror of the double-sided optical cavity, and adjust the cavity mirror transmittance to make the line width of the optical cavity meet the requirements, which specifically includes: Using the pseudomode method, the interaction between the atomic system and the Lorentz spectral environment is equivalently described as the coupling between the system and the pseudomode, and the pseudomode is lost to an independent Markov environment; With the environmental spectrum The equivalent coupling intensity and loss of the pseudomode are weakened, which is regarded as the net effect of the environmental backflow, so as to reduce the spectral width. , the atomic system can be approximately decoupled from the pseudomode, realizing a fast search system based on graph-structured data of neutral atoms.

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