Multi - photon interferometer simulation method and device, electronic device and medium

Abstract

The present disclosure provides a multi - photon interferometer simulation method, apparatus, electronic device, computer - readable storage medium, and computer program product, which relate to the field of quantum computers, and particularly to the field of quantum entanglement technology. The implementation solution is as follows: determining a first quantum state vector of a target entangled state; obtaining first characteristic parameters of an optical transmission element corresponding to a target entanglement source to determine a first transformation matrix of the optical transmission element with respect to the parametric light of the target entanglement source; determining a second quantum state vector after the action of the optical transmission element based on the first transformation matrix and the first quantum state vector; determining a second transformation matrix of a polarization beam splitter with respect to the parametric light of the target entanglement source; determining a second coincidence probability of each second coincidence item caused by the target entanglement source in the process of spontaneous parametric down - conversion after measurement based on the second transformation matrix and the second quantum state vector; and determining a first coincidence count of the target entanglement source under each second coincidence item based on the second coincidence probability.

Description

Technical Field

[0001] The present disclosure relates to the field of quantum computers, in particular to the field of quantum entanglement technology, and specifically relates to a multi-photon interferometer simulation method, apparatus, electronic device, computer-readable storage medium, and computer program product. Background Art

[0002] Quantum entanglement is the core resource of quantum science and technologies such as quantum computing, quantum communication, and quantum sensing. Quantum entanglement states can be prepared through entanglement sources. With the help of a multi-photon interferometer based on linear optics, multiple independent entanglement sources can be "bonded" to prepare quantum states on a larger scale.

[0003] It is relatively easy to obtain and operate to prepare an entanglement source by using the spontaneous parametric down-conversion process of a barium metaborate (BBO) crystal. When actually building an entanglement source, due to factors such as complex real physical processes and environmental noise, before the actual construction is completed, it cannot be ensured that the overall quality of the entanglement source meets the expectations of actual applications or experiments. In terms of yield, this will affect the construction and R & D efficiency of optical quantum devices. Therefore, the simulation of entanglement sources is very important.

[0004] Currently, the simulation method of entanglement sources usually only considers the first-order term of the spontaneous parametric down-conversion of the BBO crystal. Summary of the Invention

[0005] The present disclosure provides a multi-photon interferometer simulation method, apparatus, electronic device, computer-readable storage medium, and computer program product.

[0006] According to one aspect of the present disclosure, there is provided a method for simulating a multi - photon interferometer, including: determining a first quantum state vector of a target entangled state prepared by one or more target entanglement sources, wherein each target entanglement source includes a barium metaborate (BBO) crystal for converting pump light into two parametric lights with a spatial distribution of either an intersecting type or a laser type in the spontaneous parametric down - conversion process, wherein the first quantum state vector is determined based on the first coincidence probabilities of respective first coincidence terms triggered in the spontaneous parametric down - conversion process by the plurality of target entanglement sources, wherein the first coincidence terms are used to characterize the polarization states of photons in the two parametric lights, and the spontaneous parametric down - conversion process includes a first - order process and a second - order process; obtaining first characteristic parameters of optical transmission elements corresponding to the one or more target entanglement sources to determine a first transformation matrix of the optical transmission elements with respect to the parametric lights of the one or more target entanglement sources; determining a second quantum state vector after the action of the optical transmission elements based on the first transformation matrix and the first quantum state vector; determining a second transformation matrix of one or more polarization beam splitters with respect to the parametric lights of the one or more target entanglement sources, wherein each polarization beam splitter is used for performing two - photon interference on two preset parametric lights of the one or more target entanglement sources; determining the second coincidence probabilities of respective second coincidence terms triggered in the spontaneous parametric down - conversion process by the one or more target entanglement sources after measurement based on the second transformation matrix and the second quantum state vector, wherein the second coincidence terms are used to characterize the polarization states of photons in the two parametric lights, and the second coincidence terms are triggered by performing measurements on the one or more target entanglement sources under a first measurement basis; and determining a first coincidence count of the one or more target entanglement sources under each second coincidence term based on the second coincidence probabilities, wherein the first coincidence count is used to determine the quality factor of the target entangled state.

[0007] According to another aspect of the present disclosure, there is provided a multi - photon interferometer simulation device, including: a first determination unit configured to determine a first quantum state vector of a target entangled state prepared by one or more target entanglement sources, wherein each target entanglement source includes a barium metaborate (BBO) crystal for converting pump light into two parametric lights with a spatial distribution of either an intersecting type or a laser type in the spontaneous parametric down - conversion process, wherein the first quantum state vector is determined based on first coincidence probabilities of respective first coincidence terms triggered in the spontaneous parametric down - conversion process by the multiple target entanglement sources, wherein the first coincidence terms are used to characterize the polarization states of photons in the two parametric lights, and wherein the spontaneous parametric down - conversion process includes a first - order process and a second - order process; a first acquisition unit configured to acquire first characteristic parameters of an optical transmission element corresponding to the one or more target entanglement sources to determine a first transformation matrix of the optical transmission element with respect to the parametric lights of the one or more target entanglement sources; a second determination unit configured to determine a second quantum state vector after the action of the optical transmission element based on the first transformation matrix and the first quantum state vector; a third determination unit configured to determine a second transformation matrix of one or more polarization beam splitters with respect to the parametric lights of the one or more target entanglement sources, wherein each polarization beam splitter is used for performing two - photon interference on two preset parametric lights of the one or more target entanglement sources; a fourth determination unit configured to determine second coincidence probabilities of respective second coincidence terms triggered in the spontaneous parametric down - conversion process by the one or more target entanglement sources after measurement based on the second transformation matrix and the second quantum state vector, wherein the second coincidence terms are used to characterize the polarization states of photons in the two parametric lights, and the second coincidence terms are triggered by performing measurement under a first measurement basis on the one or more target entanglement sources; and a simulation unit configured to determine first coincidence counts of the one or more target entanglement sources under respective second coincidence terms based on the second coincidence probabilities, and the first coincidence counts are used to determine a quality factor of the target entangled state.

[0008] According to another aspect of the present disclosure, there is provided an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute the method described in the present disclosure.

[0009] According to another aspect of the present disclosure, there is provided a non - transitory computer - readable storage medium storing computer instructions for causing a computer to execute the method described in the present disclosure.

[0010] According to another aspect of the present disclosure, there is provided a computer program product including a computer program which, when executed by a processor, implements the method described in the present disclosure.

[0011] According to one or more embodiments of the present disclosure, considering the second-order term of spontaneous parametric down-conversion and modeling optical transmission elements and polarization beam splitters, efficient simulation of a large-scale multi-photon interferometer can be achieved, which is of great guiding significance for the design, construction, and optimization of multi-photon interferometers.

[0012] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it used to limit the scope of the present disclosure. Other features of the present disclosure will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The drawings exemplarily illustrate embodiments and form a part of the specification, and are used together with the written description of the specification to explain the exemplary embodiments. The illustrated embodiments are for illustrative purposes only and do not limit the scope of the claims. In all the drawings, the same reference numerals refer to similar but not necessarily identical elements.

[0014] Figure 1 Schematic diagrams showing three typical parametric optical spatial distributions according to embodiments of the present disclosure are presented;

[0015] Figure 2a and 2b Schematic diagrams of parametric light of an intersecting type and a Beam-Like type BBO entanglement source according to embodiments of the present disclosure are respectively presented;

[0016] Figure 3 Schematic diagram of a two-photon interferometer of PBS under polarization degree of freedom encoding according to embodiments of the present disclosure is presented;

[0017] Figure 4 Flowchart of a multi-photon interferometer simulation method according to embodiments of the present disclosure is presented;

[0018] Figure 5 Flowchart of simulating two-photon interference according to embodiments of the present disclosure is presented;

[0019] Figure 6 Flowchart of determining eigenstates according to embodiments of the present disclosure is presented;

[0020] Figure 7a and 7b Schematic diagrams of simulated sampling coincidence counting of two Beam-Like type BBO entanglement sources according to embodiments of the present disclosure are respectively presented;

[0021] Figure 8a and 8b respectively show the GHZ state in basis and Schematic diagram of sampling results below the base;

[0022] Figure 9 A structural block diagram of a multi - photon interferometer simulation device according to an embodiment of the present disclosure is shown; and

[0023] Figure 10 A structural block diagram of an exemplary electronic device capable of implementing the embodiments of the present disclosure is shown. Detailed implementation manners

[0024] The following describes exemplary embodiments of the present disclosure with reference to the accompanying drawings. Various details of the embodiments of the present disclosure are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope of the present disclosure. Similarly, for clarity and conciseness, descriptions of well - known functions and structures are omitted below.

[0025] In the present disclosure, unless otherwise specified, the terms "first", "second", etc. are used to describe various elements and are not intended to limit the positional relationship, timing relationship, or importance relationship of these elements. Such terms are only used to distinguish one element from another. In some examples, the first element and the second element may refer to the same instance of the element, and in certain cases, based on the context description, they may also refer to different instances.

[0026] In the description of various examples in the present disclosure, the terms used are only for the purpose of describing specific examples and are not intended to be restrictive. Unless the context clearly indicates otherwise, if the number of elements is not specifically limited, the element may be one or more. In addition, the term "and / or" used in the present disclosure covers any one of the listed items and all possible combinations.

[0027] The embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0028] With the help of a quantum network, people can achieve non - classical connections between two or more locations to complete tasks that cannot be accomplished by classical technologies, such as quantum communication protocols, distributed quantum computing, blind quantum computing, etc. In a classical network, light is used as the carrier for information transmission, and the same is true for information transmission in a quantum network. Photons have a series of natural advantages, such as being less prone to decoherence, easy to manipulate and prepare, etc. With the help of a multi - photon interferometer based on linear optics, multiple independent entanglement sources can be "bonded" to prepare quantum states on a larger scale.

[0029] However, as the hardware structure for preparing optical quantum states gradually expands and becomes more complex, the hardware development and testing costs of multi-photon interferometers also increase accordingly. Therefore, an effective simulation algorithm for multi-photon interferometers is particularly important, which can help researchers save testing and development costs.

[0030] The method of preparing entangled states using the spontaneous parametric down-conversion process has been widely used in fields such as optical quantum computing, optical quantum communication, optical quantum sensing, and non-locality verification. Especially in recent years, with the development of entangled source technology and the maturity of optical chip technology, people have achieved verification of the computational superiority of optical quantum computing in directions such as boson sampling and quantum randomness performance. Thanks to the relatively simple construction method and high stability of the barium metaborate (BBO) entangled source, the BBO entangled source is widely used as the preferred choice for preparing quantum states in optical quantum computers and optical quantum communication.

[0031] According to the different spatial distributions of the parametric light generated by the down-conversion process, the entangled source based on the BBO crystal can be divided into the intersecting type, the collinear type, and the Beam-Like type. In addition, according to the different paths of the parametric light, it can be further divided into single-path entangled sources and double-path entangled sources. Single-path entangled sources such as collinear BBO entangled light sources, and double-path entangled sources such as intersecting type and Beam-Like type BBO entangled sources. In particular, intersecting type and Beam-Like type BBO entangled sources are usually used as the light sources of optical quantum computers or for preparing quantum states such as GHZ.

[0032] However, the quantum states generated by the spontaneous parametric down-conversion process are not perfect because, in addition to the first-order down-conversion process, there are also higher-order down-conversion processes. Theory and experiments have shown that the existence of higher-order terms will lead to an inverse relationship between the coincidence counting rate and the contrast of the entangled source. Therefore, during the preliminary design, actual construction, experiment, or actual operation, it is necessary to repeatedly adjust the laser power to change the down-conversion probability in order to find the optimal comprehensive performance. In addition, for a multi-photon interferometer composed of multiple entangled sources, the propagation of photons in multiple paths is very complex. For the existing simulation algorithms of double-path BBO entangled sources, when considering the second-order terms of spontaneous parametric down-conversion, it is impossible to obtain simulation results with an effective calculation method.

[0033] The core process of the entangled source based on the BBO crystal is as follows: when the pump light wave vector forms certain special angles with the BBO optical axis, the spontaneous parametric down-conversion process (SPDC) will occur. Through this process, a pump light beam can split into two beams of light with a certain probability, which are respectively called ordinary light and extraordinary light, and these two beams of light are usually referred to as parametric light.

[0034] As the angle between the pump light wave vector and the BBO optical axis changes, the spatial distribution of the parametric light will also change accordingly. Figure 1 Three typical spatial distributions of the parametric light are shown, namely: intersecting type, collinear type, and Beam-Like type. These three typical spatial distributions are all common methods for building an entanglement source device. From the perspective of the propagation path of the parametric light, it can be divided into a two-path entanglement light source and a single-path entanglement light source. The two-path entanglement light source includes the intersecting type and the Beam-Like type, and the single-path entanglement light source includes the collinear type. The collinear BBO light source is usually used to prepare W states, Cluster states, etc.; the two-path BBO entanglement source is usually used for the preparation of the initial state of an optical quantum computer or for the preparation of quantum states such as GHZ.

[0035] The parametric light of the intersecting type BBO entanglement source is as Figure 2a shown. Among them, the parametric light of the intersecting type BBO entanglement source presents the shape of two light cones, and the cross-section is the shape of two intersecting rings, which is also the origin of the so-called "intersecting type" name. Theory and experiments have proved that the polarization directions of the photons from the two light cones are completely orthogonal. That is, if the photons of one light cone are horizontally polarized |H>, then the photons of the other light cone are vertically polarized |V>. In an actual hardware device, the photons at the two intersection points of the ring propagate along their respective optical links and finally collect the photons of the optical links through two beam couplers. It should be noted that only when photons from both light cones are collected simultaneously will a two-photon coincidence count be generated. If the two detected photons come from the same light cone, no coincidence count will be generated.

[0036] The parametric light of the Beam-Like type entanglement source is as Figure 2b shown. Among them, the Beam-Like type entanglement source does not have only one BBO crystal. It is composed of two BBO crystals bonded together with ultraviolet glue, and the second crystal is flipped 180° relative to the first crystal. Only when the photons of the two paths come from the down-conversion process of the same BBO crystal will a two-photon coincidence count be generated.

[0037] It can be seen that whether it is the intersecting type BBO entanglement source or the Beam-Like type BBO entanglement source, their parametric lights are clearly two optical links (or optical paths, which can be expressed as qumode). In addition, for any type of entanglement source, the spontaneous parametric down-conversion process is a high-order process. Specifically, the first-order process corresponds to: within one pump pulse, there is exactly one photon in each of the two optical paths; the second-order process corresponds to: there are exactly two photons in each of the two optical paths, and so on. Within each pump pulse, there is a probability of a certain order of spontaneous parametric down-conversion process occurring, and the occurrence probabilities corresponding to different orders are different.

[0038] Taking only the first-order term process as an example, such as Figure 2a As shown, when photons from the upper light cone are detected on the path of the left intersection propagation, photons from the lower light cone need to be detected on the path of the right intersection propagation to generate a coincidence count. At this time, the polarization state is |HV> (assuming the upper light cone is horizontally polarized and the lower light cone is vertically polarized); when photons from the lower light cone are detected on the path of the left intersection propagation, photons from the upper light cone need to be detected on the path of the right intersection propagation to generate a coincidence count. At this time, the polarization state is |VH>. Considering only the first-order term, the quantum state form at this time is the Bell state,

[0039]

[0040] In formula (1), |H> represents the horizontal polarization of a photon, and |V> represents the vertical polarization of a photon. In the upper light cone, photons in the horizontal polarization state can be detected by one detector (such as D1), and photons in the vertical polarization state can be detected by another detector (such as D2). In the lower light cone, photons in the horizontal polarization state can be detected by one detector (such as D3), and photons in the vertical polarization state can be detected by a detector (such as D4). |HV> represents that in the case of splitting into two beams of parametric light (i.e., two light cones, ordinary light and extraordinary light respectively), the upper light cone is horizontally polarized and the lower light cone is vertically polarized. |VH> represents that in the case of splitting into two beams of parametric light (i.e., two light cones, ordinary light and extraordinary light respectively), the upper light cone is vertically polarized and the lower light cone is horizontally polarized.

[0041] Generally, when simulating an entanglement source, only the probability of the first-order term is used to obtain coincidence counts or simulate the sampling process. Assuming that the repetition frequency of the laser for outputting pump light is M and the cumulative measurement time is t (unit: second), it means that within the time t, there are a total of tM pump light pulses. Assuming that for an intersecting BBO entanglement source, the probability of first-order spontaneous parametric down-conversion is p (how much probability there is for a first-order process in one pulse), then there is the following relationship:

[0042] B HV = B VH = ptM Formula (2)

[0043] where, B HV and B VH respectively represent that the eigenstates |HV> and |VH> are the coincidence counts obtained within the time t.

[0044] Similarly, currently, the simulation method of the Beam-Like type BBO entanglement source usually only considers the first-order term of spontaneous parametric down-conversion. Still assuming that the repetition frequency of the pump light is M and the cumulative measurement time is t (unit: second); Figure 2b the BBO shown in 1 has a down-conversion probability of p1 , BBO 2 has a down-conversion probability of p 2 , and the coincidence counts of the two coincidence terms |HV> and |VH> within 1 second are B HV and B VH , then the simulation can be carried out according to the following relationship. Usually, the simulation result refers to the coincidence count of the entanglement source. Finally, two non-zero coincidence counts B HV and B VH can be obtained and expressed by formulas (3) and (4):

[0045] B HV = p 1 Mη 2 Formula (3)

[0046] B VH = p 2 Mη 2 Formula (4)

[0047] As described above, the results of existing simulation methods are obtained only under the first-order term of spontaneous parametric down-conversion, while the actual spontaneous parametric down-conversion process is a process that includes high-order terms and follows a thermal distribution. Specifically, the first-order process corresponds to: within a pump pulse, each of the ordinary light and extraordinary light links contains one photon; the second-order process corresponds to: each of the ordinary light and extraordinary light links down-converts two photons within a pulse, and so on. Strictly speaking, the high-order term process including the second-order term will affect the final result. Therefore, the existing simulation scheme will cause a deviation in the simulation accuracy.

[0048] In addition, for the simulation method of the Beam-Like type BBO entanglement source, it can include: (1) calculating the probability of each eigenstate in the first-order and second-order terms according to the input down-conversion probability; (2) using the detector efficiency to convert the second-order term quantum state into the first-order term. For example, assuming the detector efficiency is η, and the occurrence probability of |2H; 2V> in the second-order term is then there is:

[0049]

[0050] Correspondingly, the coincidence count resulting from the second-order term process can be calculated as:

[0051]

[0052] From the perspective of the simulation logic of the optical quantum structure, generally speaking, it can be divided into quantum state initialization, quantum gate operation, and measurement function. In the above simulation algorithm considering the second-order term, the calculation process is very complicated and not scalable. Specifically, the algorithm does not clearly divide the calculation of each part of the entanglement source, and the simulation of the quantum state initialization and measurement processes is merged together, and then the simulation of the quantum gate operation is carried out; if the second-order term is converted into a quantum state represented by the first-order term in the entanglement source simulation step, the multi-photon interference results that will occur later cannot be analyzed.

[0053] The multi-photon interferometer is the most commonly used hardware structure for quantum communication, optical quantum computing, and optical quantum sensing. In the photon polarization degree of freedom, the optical link of a multi-photon interferometer often involves a half waveplate (HWP), a quarter wave plate (QWP), and a polarization beamsplitter (PBS). Although physical models of these optical elements already exist in engineering optics, however, the light source in the multi-photon interferometer often uses an entanglement source of spontaneous parametric down-conversion, which has a photon number distribution with higher-order terms and is not a perfect single-photon source. Therefore, the changes and propagation of photons in the link also need to specifically consider the higher-order modeling of optical transmission elements, that is, the output light can no longer be simulated with the existing modeling matrix.

[0054] The PBS is an optical element that can split the incident light into two paths with orthogonally polarized directions. Figure 3 Shows a schematic diagram of a two-photon interferometer of the PBS under polarization degree of freedom encoding according to an embodiment of the present disclosure. As Figure 3 shown, the thinner arrow represents horizontally polarized light, the thicker arrow represents vertically polarized light, and the gray part represents the entanglement source. It can be seen that the PBS can allow all horizontally polarized photons to pass through and all vertically polarized photons to be reflected. Experimentally, to prepare a larger-scale entangled state, it is necessary to "bond" multiple independent entanglement sources through the PBS, that is, two incident beams of light undergo two-photon interference on the PBS. For example, if it is assumed that the two Bell states for interference are:

[0055]

[0056] Then the process of "bonding" the two Bell states using the PBS can be described as shown in formula (7):

[0057]

[0058] In the last step, the entanglement effect can be achieved by performing a post-selection process, that is, determined by the measurement mechanism of the measurement system. For example, when photons are detected at both output ends of the PBS, a coincidence count is recorded. At this time,Figure 3 The following two cases are "discarded" through the post-selection mechanism. It is easy to obtain that when the truncation number is 1, its transformation matrix is:

[0059]

[0060] However, the existing simulation models of half-wave plates, quarter-wave plates, and PBSs can only calculate the case of single photons. However, as described above, the quantum state corresponding to the parametric light generated by spontaneous parametric down-conversion is a process that includes a high-order photon number distribution. That is, on the time scale of a single pump light pulse, a single optical link may contain multiple photons. At this time, the above existing transformation matrices cannot effectively perform matrix multiplication calculations. The transformation matrix of PBS can only act on two adjacent optical links. However, for a multi-photon interferometer composed of multiple optical links, it is possible to perform interference between any two links.

[0061] Therefore, according to an embodiment of the present disclosure, a method for simulating a multi-photon interferometer is provided. Figure 4 The flowchart of the method for simulating a multi-photon interferometer according to an embodiment of the present disclosure is shown. As Figure 4 shown, method 400 includes: determining a first quantum state vector of a target entangled state prepared by one or more target entanglement sources, where each target entanglement source includes a barium metaborate (BBO) crystal for converting pump light into two beams of parametric light with any one of an intersecting type and a laser type in spatial distribution during the spontaneous parametric down-conversion process (step 410); obtaining first characteristic parameters of optical transmission elements corresponding to the one or more target entanglement sources to determine a first transformation matrix of the optical transmission elements with respect to the parametric light of the one or more target entanglement sources (step 420); determining a second quantum state vector after the action of the optical transmission elements based on the first transformation matrix and the first quantum state vector (step 430); determining a second transformation matrix of one or more polarization beam splitters with respect to the parametric light of the one or more target entanglement sources, where each polarization beam splitter is used for performing two-photon interference on two preset beams of parametric light of the one or more target entanglement sources (step 440); determining a second coincidence probability of each second coincidence term caused by the one or more target entanglement sources during the spontaneous parametric down-conversion process based on the second transformation matrix and the second quantum state vector, where the second coincidence term is used to characterize the polarization state of photons in the two beams of parametric light, and the second coincidence term is caused by performing a measurement in a first measurement basis on the one or more target entanglement sources (step 450); and determining a first coincidence count of the one or more target entanglement sources under each second coincidence term based on the second coincidence probability, where the first coincidence count is used to determine the figure of merit of the target entangled state (step 460).

[0062] Wherein, the first quantum state vector is determined based on the first coincidence probabilities of respective first coincidence terms triggered by the multiple target entanglement sources in the spontaneous parametric down-conversion process, wherein the first coincidence terms are used to characterize the polarization states of photons in the two beams of parametric light, and the spontaneous parametric down-conversion process includes a first-order process and a second-order process.

[0063] According to an embodiment of the present disclosure, by considering the second-order term of the spontaneous parametric down-conversion and modeling the optical transmission element and the polarization beam splitter, an efficient simulation of a large-scale multi-photon interferometer can be achieved, which has important guiding significance for the design, construction, and optimization of the multi-photon interferometer.

[0064] According to some embodiments, determining the first quantum state vector of the target entangled state prepared by one or more target entanglement sources includes: determining the expression of the first quantum state vector corresponding to the target entangled state; and determining the first quantum state vector based on the characteristic parameters corresponding to each of the one or more target entanglement sources and the expression of the first quantum state vector, wherein the characteristic parameters include the down-conversion probability of the BBO crystal in the spontaneous parametric down-conversion process.

[0065] According to some embodiments, each target entanglement source includes two optical paths respectively used for measuring the two beams of parametric light, and wherein determining the expression of the first quantum state vector of the target entangled state includes: determining the expressions of the second quantum state vector and the third quantum state vector corresponding to each optical path in the one or more target entanglement sources, wherein the elements in the expression of the second quantum state vector are determined based on the third coincidence probabilities of respective third coincidence terms triggered by the first-order process in the current optical path, and the elements in the expression of the third quantum state vector are expressions of the fourth coincidence probabilities of respective fourth coincidence terms triggered by the second-order process in the current optical path; determining the expression of the fourth quantum state vector corresponding to each optical path based on the corresponding expressions of the second quantum state vector and the third quantum state vector, wherein the elements in the expression of the fourth quantum state vector are determined based on the fifth coincidence probabilities of respective fifth coincidence terms triggered by the first-order process and the second-order process in the current optical path; and determining the expression of the first quantum state vector of the target entangled state based on the expressions of the fourth quantum state vectors corresponding to all the optical paths in the one or more target entanglement sources.

[0066] That is to say, the expression of the quantum state vector of each optical path in the first-order process can be determined first, and then the expression of the quantum state vector of this optical path in the second-order process can be determined. Furthermore, it is extended from one optical path to multiple optical paths to obtain the expression of the quantum state vector corresponding to the simulation of the multi-photon interferometer formed by the one or more target entanglement sources.

[0067] According to some embodiments, determining the fourth quantum state vector representation corresponding to each of the two optical paths includes: determining the fourth quantum state vector representation based on the direct sum representation between the corresponding second quantum state vector representation and third quantum state vector representation; and determining the first quantum state vector representation of the target entangled state based on the fourth quantum state vector representation corresponding to each of the two optical paths of each target entanglement source includes: determining the first quantum state vector representation of the target entangled state based on the direct product representation between the fourth quantum state vector representations corresponding to each of the two optical paths of each target entanglement source.

[0068] Exemplarily, in a quantum circuit based on qubits (quantum bits), a single qubit can be represented by a 2-dimensional vector, and a quantum state composed of multiple qubits can be represented by taking the direct product of the vectors corresponding to the single qubits. In a quantum circuit based on Fock states, the number of photons in a single optical path (i.e., an optical link, which can be simply referred to as an optical path) can be represented by only one element (i.e., 1-dimensional), and a quantum state composed of multiple optical paths can be represented by taking the direct sum of the vectors corresponding to the single optical paths.

[0069] Different from the conventional representation methods described above, even when only considering a single entangled light source, the situation is very complex, including different order terms of a single optical path and calculation methods between different optical paths. Therefore, it is far from enough to use only direct sum or direct product. Therefore, in the above embodiments, a direct sum is used to represent between different down-conversion orders of the same optical path (also called a spatial mode, or mode), and a direct product is used between multiple optical paths.

[0070] By combining direct product and direct sum, the quantum state vector representation of a two-path target entanglement source can be regularly represented, further making it easier to extend the simulation method of a single entanglement source to the simulation of a multi-photon interferometer composed of multiple entanglement sources.

[0071] In some embodiments, specifically, since only the second-order term of spontaneous parametric down-conversion is considered at most, for a single optical path, its quantum state is represented as:

[0072]

[0073] where P represents probability, H represents the horizontal polarization of a photon, V represents the vertical polarization of a photon, that is, P 1H represents the probability of 1 photon with horizontal polarization, P 1H1V represents the probability of 1 photon with horizontal polarization and 1 photon with vertical polarization, P 2H represents the probability of 2 photons with horizontal polarization, P 2V The superscript represents the probability of 2 photons with vertical polarization, and T represents matrix transpose.

[0074] It should be noted that a multi - photon interferometer includes multiple optical paths, and its quantum state representation can be written in the form of the direct product above, that is:

[0075]

[0076] where \(|\psi\rangle\) i represents the quantum state vector representation corresponding to a single optical path.

[0077] According to some embodiments, the optical transmission element includes at least one of a half - wave plate and a quarter - wave plate, and wherein, the first characteristic parameter includes the angle between the optical axis of the half - wave plate and the horizontal direction, and the angle between the optical axis of the quarter - wave plate and the horizontal direction.

[0078] In some examples, setting \(\theta\) as the angle between the optical axis of the half - wave plate and the horizontal direction, when considering the truncation number is 1, the Jones matrix of the half - wave plate is:

[0079]

[0080] It should be noted that formula (10) is a common representation in engineering optics and is applicable when considering that there is exactly one photon in the optical path (qumode), that is,

[0081]

[0082] Similarly, it can also be extended to higher orders according to the above changes. Here, when considering the second - order term, there are the following transformation relations:

[0083]

[0084] Since the time mode and space mode of two photons in the same optical path are identical, they satisfy commutativity, and the above transformation process can be written as

[0085]

[0086] Based on a similar analysis process, it can be obtained that

[0087]

[0088] According to the above conclusion, the second - order Jones matrix of the half - wave plate is written as:

[0089]

[0090] The overall Jones matrix can be obtained by direct sum:

[0091]

[0092] In some examples, the modeling method of the quarter-wave plate is similar to that of the half-wave plate. Let θ be the angle between the optical axis of the quarter-wave plate and the horizontal direction. When considering the truncation number is 1, the Jones matrix of the quarter-wave plate is:

[0093]

[0094] When considering the second-order terms, there are three kinds of transformations. For the sake of simplicity, the elements in are represented by j, and they will not be expanded here. We get:

[0095]

[0096] Then for a single optical path, the overall Jones matrix can be obtained through the direct sum,

[0097]

[0098] It can be understood that the user can select the corresponding half-wave plate and / or quarter-wave plate according to needs and set them on the corresponding optical paths of the one or more target entanglement sources. After obtaining the overall Jones matrix of the corresponding half-wave plate and / or quarter-wave plate, it can be conveniently tensored to the total number M of optical paths of the one or more target entanglement sources, which will not be elaborated here.

[0099] According to some embodiments, when there are multiple target entanglement sources and multiple polarization beam splitters, where the number of the polarization beam splitters is less than or equal to the number of the target entanglement sources. Determining the second transformation matrix of the polarization beam splitter with respect to the idler lights of the multiple target entanglement sources includes: determining the initial transformation matrix of a polarization beam splitter with respect to two adjacent idler lights; in response to determining that the preset two idler lights are two adjacent idler lights, determining the second transformation matrix T based on the following formula:

[0100]

[0101] where the total number of the idler lights of the multiple target entanglement sources is M, the preset two idler lights are the k-th and l-th idler lights among the M idler lights respectively, and l - k = 1, M PBS is the initial transformation matrix, I is the identity matrix; and, in response to determining that the preset two idler lights are not two adjacent idler lights, determining the second transformation matrix T based on the following formula:

[0102]

[0103] where the total number of the idler lights of the multiple target entanglement sources is M, the preset two idler lights are the k-th and l-th idler lights among the M idler lights respectively, and l - k > 1, M PBSis the initial transformation matrix, and I is the identity matrix.

[0104] The simulation principle of two-photon interference is relatively complicated. The core component in the physical hardware is the PBS, whose function is that all horizontally polarized light exits from the transmission end of the polarization beam splitter, and all vertically polarized light exits from the reflection end of the polarization beam splitter. All the transformations corresponding to the PBS are shown in Table 1:

[0105]

[0106] Table 1

[0107] In some examples, it is first necessary to construct a model of the PBS when the truncation number is 2 (that is, considering the second-order term). Before constructing the model, a constraint condition can be introduced to achieve the entanglement effect. For example, if the number of photons at either output end is greater than or equal to 3 after the photons incident on the PBS are transmitted or reflected, then this term is "discarded".

[0108] M PBS is the transformation matrix for the quantum state corresponding to the two optical paths, but this matrix can only achieve the interference of adjacent two optical paths and is a 25×25 matrix. Denote the matrix element by M PBS (x,y), where x, y = 1, 2, …, 5. Then its matrix elements satisfy:

[0109] M PBS (1,1) = M PBS (3,3) = M PBS (7,7) = M PBS (9,9) = M PBS (11,11) = 1

[0110] M PBS (13,13) = M PBS (17,17) = M PBS (19,19) = M PBS (25,25) = 1

[0111] M PBS (16,4) = M PBS (22,10) = M PBS (4,16) = M PBS (10,22) = -1

[0112] In general, a multi - photon interferometer as a whole includes more than two optical paths. Therefore, in some embodiments, a Swap operation can be introduced. It should be noted that this Swap operation does not correspond to any hardware structure in the actual multi - photon interferometer, but is only for calculating the results of two - photon interference for any optical path. Thus, the two optical paths that need to perform two - photon interference on the PBS can be successively swapped to the first two modes in the quantum state representation through the Swap operation. The Swap operation is still a 25×25 matrix. Generally, for any quantum state, it can be realized that,

[0113]

[0114] According to the above formula, a Swap matrix S can be constructed as follows:

[0115] S(1,1) = S(2,6) = S(3,11) = S(4,16) = S(5,21) = S(6,2) = S(7,7) = 1

[0116] S(8,12) = S(9,17) = S(10,22) = S(11,3) = S(12,8) = S(13,13) = 1

[0117] S(14,18) = S(15,23) = S(16,4) = S(17,9) = S(18,14) = S(19,19) = 1

[0118] S(20,24) = S(21,5) = S(22,10) = S(23,15) = S(24,20) = S(25,25) = 1

[0119] Suppose the interferometer as a whole has M optical paths, that is, M optical links; in addition, suppose the k - th and l - th optical paths perform PBS two - photon interference, and it is agreed that l must be greater than k, and both are positive integers. Figure 5 The flowchart of simulating two - photon interference according to an embodiment of the present disclosure is shown. As Figure 5 shown, first, the optical paths k and l to be interfered are obtained (i.e., step 501), and it is judged whether l is greater than k (i.e., step 502). At this time, there are the following situations:

[0120] (1) If l - k = 1 (i.e., step 504, "yes"), then the two optical paths for interference are adjacent, and at this time, the Swap is not executed. It is easy to obtain that there are k - 1 optical paths in front of the k - th optical path, and there are M - 1 optical paths behind the l - th optical path. Then the overall transformation matrix of the M optical paths under PBS interference is (i.e., step 510 is executed):

[0121]

[0122] Wherein, I represents the identity matrix.

[0123] Then, perform matrix multiplication on matrix T and the quantum state matrix obtained previously to obtain the corresponding quantum state vector (i.e., steps 511 - 512).

[0124] (2) If l - k > 1 (i.e., step 504, "No"), then the two optical paths for interference are not adjacent. At this time, perform the following steps in sequence: Move the k-th optical path to the first position and the l-th optical path to the second position through Swap (step 505); at this time, there are M - l optical paths after the l-th optical path, calculate the overall transformation matrix of the M optical paths under the PBS interference (i.e., perform step 506):

[0125]

[0126] Then, perform matrix multiplication calculation to obtain the corresponding quantum state vector (step 507); move the first and second optical paths back to their original positions through Swap (step 508) to obtain the output quantum state (step 509).

[0127] It should be noted that the above process is only for computational consideration, and this Swap operation does not correspond to any hardware structure in the actual multi - photon interferometer. Therefore, after obtaining the corresponding transformation matrix and the quantum state after the action of the optical transmission element, the matrix multiplication can be performed on the obtained quantum state after the action and the transformation matrix to obtain the quantum state to be measured.

[0128] It can be understood that through the above process, it can be easily extended to the case of multiple PBSs, which will not be elaborated here.

[0129] According to some embodiments, each of the target entanglement sources includes two optical paths for measuring the two beams of parametric light, and each optical path includes two detectors, and each detector is used to detect the photons in the parametric light measured by the optical path that match the polarization state of the detector.

[0130] Wherein, determining the second coincidence probability of each of the second coincidence terms triggered by one or more target entanglement sources obtained after measurement during the spontaneous parametric down - conversion process includes: determining a first transformation matrix based on the detection efficiency of the detector, where the first transformation matrix is used to represent the measurement process of performing the first measurement basis on the target entangled state; and determining the second coincidence probability of each of the second coincidence terms triggered by the one or more target entanglement sources obtained after measurement during the spontaneous parametric down - conversion process based on the first transformation matrix and the second quantum state vector.

[0131] According to some embodiments, determining the first transformation matrix based on the detection efficiency of the detector includes: for each optical path in the one or more target entanglement sources, determining a second transformation matrix corresponding to the optical path based on the detection efficiency of the detector, where the second transformation matrix is used to represent the measurement process of performing the first measurement basis on the single-bit quantum state prepared on the optical path; and determining the first transformation matrix based on the second transformation matrices corresponding to all the optical paths in the one or more target entanglement sources.

[0132] In this embodiment, since joint measurements are not performed on all optical paths, the measurement of a single optical path can be analyzed first and then extended to multiple optical paths. For a single optical path with a truncation number of 2, as described above, its quantum state vector can be represented as a 5-dimensional column vector; for a single bit encoded by polarization, its quantum state vector can be represented as a 2-dimensional column vector. Therefore, in principle, for the conversion from a single path to a single bit, it is achieved through a 2×5 matrix.

[0133] Specifically, assume that the detection efficiencies of two detectors placed on a certain optical path are E H and E V , then the matrix is:

[0134]

[0135] where E H represents the detection efficiency of the detector for detecting photons polarized in the horizontal direction, and E V represents the detection efficiency of the detector for detecting photons polarized in the vertical direction, then there is a relationship,

[0136] P singlequbit = EP single mode Formula (19)

[0137] where P singlequbit and P single mode respectively represent the probability vectors obtained by squaring the elements in the quantum state vectors of the single bit and the single path. For an entanglement source containing 2 optical paths, the conversion matrix at its measurement end can be written as,

[0138]

[0139] where E H,1 represents the detection efficiency of the detector for detecting photons polarized in the horizontal direction on one optical path (i.e., path "1"), and E H,2 represents the detection efficiency of the detector for detecting photons polarized in the horizontal direction on another optical path (i.e., path "2").

[0140] For an interferometer with M optical links, if two detectors are placed on each link, the efficiencies of the 2M detectors form a 2 M ×5 M transformation matrix:

[0141]

[0142] where E H / V,i represents the detector corresponding to the H / V polarized light in the i-th optical path. Therefore, the quantum state P final finally considering the actual probability is a 2 M dimensional vector. It can be calculated as,

[0143] P final = EP multi-qumode Formula (22)

[0144] where P multi-qumode represents the probability vector formed by calculating the squares of the elements after the transformation of |ψ> multi-qumode by optical elements.

[0145] According to P final , the sampling process of the target entanglement source in each coincidence term (i.e., the second coincidence term) can be simulated. However, to obtain the final simulation result, i.e., the coincidence count vector B, two functions need to be implemented: (1) Simulate the random sampling process of coincidence counts; (2) Mark and list the eigenstate forms corresponding to each position of the vector B.

[0146] For example, the repetition frequency of the laser used to output the pump light can be set to R; in addition, within the cumulative time t (in seconds), the cumulative coincidence count obtained by sampling is the vector B. When M = 2, its form can be conveniently obtained as:

[0147] B = [B H；H B H；V B V；H B V；V T

[0148] For example, for a quantum state with 4 optical paths, B is a 16-dimensional vector. If |0> encodes the horizontal polarized light |H>; |1> encodes the vertical polarized light |V>. Then the first element of B is the coincidence count after random sampling, and the eigenstate form it represents is |0000>, the eigenstate corresponding to the second element is |0001>, the eigenstate corresponding to the third element is |0010>, and so on.

[0149] ​For the random sampling process of analog coincidence counting, in some embodiments, the built-in function "numpy.random.choice" in Python can be used. Optionally, this process can also be implemented in other languages. It should be noted that regardless of the language used to implement this process, it is necessary to: (1) calculate the square of each element in P final The vector formed by the squares of each element in is the probability distribution; (2) calculate the number of samplings. At this time, the laser repetition frequency R and the measurement time t (in seconds) need to be input, and the number of samplings is Rt.

[0150] In some examples, the eigenstate form corresponding to each position of the vector B can be marked and listed by using the backtracking method. First, initialize an empty vector named "state_path", and then initialize a two-dimensional array "encode_array" = [0 1]. Name the backtracking function "FindStateList", which is a function of "state_path", "encode_array" and the number of optical paths M. For ease of understanding, the steps are described through a Figure 6 flowchart as shown:

[0151] a), Input "state_path", "encode_array" and M (step 601), and execute the function "FindStateList" (step 602);

[0152] b), Determine whether the dimension of "state_path" is equal to M (step 603);

[0153] c), If not (step 603, "no"), loop through the elements in "encode_array" and fill them into "state_path" (step 604);

[0154] d), Execute the function "FindStateList" and enter the next layer of this function (step 602);

[0155] e), If equal (step 603, "yes"), then store "state_path" (step 605);

[0156] c), Pop the element filled in before executing the last layer of the FindStateList function and return to the previous layer function (step 606). In the same layer function, the values in encode_array are taken in sequence through a for loop, that is, the value is first taken as 0 and then as 1 in each layer function before.

[0157] Until the eigenstate set is output (step 607).

[0158] In an exemplary embodiment according to the present disclosure, for ease of understanding, the following steps are used for description:

[0159] First step: Initialize the actual probability vector of the target entanglement source. 1. Input the down-conversion probability of the target entanglement source; 2. Initialize the quantum state form of the entanglement source when the truncation number is 2, and calculate the actual probability vector of the 5 M -dimensional overall quantum state through the direct product of multiple entanglement sources.

[0160] Second step: Perform optical link transformation. 1. Input the rotation angles of each half-wave plate and quarter-wave plate, and model the half-wave plate and quarter-wave plate; 2. Calculate the two-photon interference through the Figure 5 calculation process shown; 3. Calculate the actual probability vector of the quantum state after the optical link transformation according to the result of the first step.

[0161] Third step: Perform measurement function simulation. 1. Input the quantum efficiency of 2M single-photon detectors; 2. Construct the transformation matrix of the measurement end 2 M ×5 M and calculate the actual probability vector of the quantum state after the action according to the result of the second step.

[0162] Fourth step: Simulate the sampling process. 1. Input the repetition frequency R of the laser and the cumulative measurement time t, and calculate the sampling times Rt; 2. Square each element of the result of the third step to calculate the actual occurrence probability; 3. According to the results of the fourth step 1 and 2, obtain the coincidence counts of each eigenstate through simulating the random sampling process and output; 4. According to the backtracking algorithm, obtain the eigenstate vector set and output.

[0163] To verify the effect of the embodiment according to the present disclosure, the method described in the embodiment of the present disclosure is used to simulate the preparation of the Bell state |Ψ + > using 2 Beam-Like type BBO entanglement sources, convert it to the Bell state |Φ + > using a half-wave plate, and finally perform two-photon interference to prepare the 4-photon GHZ state, and the simulation results of the 4-photon GHZ state in and bases are shown. The simulation parameter settings are as follows: the down-conversion probability of the first entanglement source is set to {0.015, 0.014}, the down-conversion probability of the first entanglement source is set to {0.014, 0.013}, the angle of the half-wave plate for converting the Bell state is set to 45°, the angle of the half-wave plate for performing measurement is set to 22.5°, the detector efficiency is set to 0.6, the coincidence count cumulative acquisition time is 20 seconds, and the pump laser repetition frequency is 8×10 7 Hz. Figure 7a and 7bSchematic diagrams of simulated sampling coincidence counts of two Beam-Like type BBO entanglement sources according to embodiments of the present disclosure are respectively shown.

[0164] Next, two-photon interference is performed using a PBS, and the sampling results of the GHZ state in and bases are respectively as shown in Figure 8a and 8b . When measuring the quantum state in the basis, in the ideal case or when only considering first-order parametric down-conversion, the 4-photon GHZ state only includes two non-zero terms |HHHH> and |VVVV>; when measuring the quantum state in the basis, in the ideal case or when only considering first-order parametric down-conversion, the 4-photon GHZ state includes eight non-zero terms. Since both the calculation of the entanglement source and the modeling of the link in our work consider the existence of second-order terms, that is, the truncation number is 2, Figure 8a and 8b the sampling results shown in each item are all non-zero, truly reflecting the actual preparation process.

[0165] In an embodiment according to the present disclosure, the second-order term of spontaneous parametric down-conversion is considered. By modeling the optical elements commonly used in a multi-photon interferometer and designing a measurement system simulation method for a multi-optical-link interferometer, a simulation scheme of a multi-photon interferometer based on the polarization degree of freedom is constructed. With the representation method of the entanglement source under the second-order term, it is possible to efficiently simulate large-scale multi-photon interferometers, which has important guiding significance for the design, construction, and optimization of multi-photon interferometers; before actually constructing, designing, and optimizing large-scale multi-photon interferometers, the sampling process of multi-photon interferometers can be simulated. The simulation process only needs to be carried out on a computer, with low simulation overhead, and can efficiently accelerate the iteration and R & D process of multi-photon interferometers; motivated by the second-order term of the spontaneous parametric down-conversion process, high-order modeling of the half-wave plate, quarter-wave plate, polarization beam splitter, and multi-link measurement system commonly used in the optical link can calculate the final result through typical matrix multiplication;

[0166] In the actual hardware of a multi-photon interferometer, measurements in different bases are achieved by rotating the wave plate at different angles. The modeling of the optical elements according to the scheme of the embodiment of the present disclosure can flexibly transform the quantum state, calculate the probability vector in different measurement bases, and further obtain the sampling result.

[0167] According to an embodiment of the present disclosure, as shown in Figure 9As shown, a multi - photon interferometer simulation device 900 is also provided, including: a first determination unit 910 configured to determine a first quantum state vector of a target entangled state prepared by one or more target entanglement sources. Each target entanglement source includes a barium metaborate (BBO) crystal, which is used to convert pump light into two parametric lights with a spatial distribution of either an intersecting type or a laser type during the spontaneous parametric down - conversion process. The first quantum state vector is determined based on the first coincidence probabilities of each first coincidence item triggered during the spontaneous parametric down - conversion process by the multiple target entanglement sources. The first coincidence item is used to characterize the polarization state of photons in the two parametric lights, and the spontaneous parametric down - conversion process includes a first - order process and a second - order process; a first acquisition unit 920 configured to acquire a first characteristic parameter of an optical transmission element corresponding to the one or more target entanglement sources to determine a first transformation matrix of the optical transmission element with respect to the parametric lights of the one or more target entanglement sources; a second determination unit 930 configured to determine a second quantum state vector after the action of the optical transmission element based on the first transformation matrix and the first quantum state vector; a third determination unit 940 configured to determine a second transformation matrix of one or more polarization beam splitters with respect to the parametric lights of the one or more target entanglement sources. Each polarization beam splitter is used to perform two - photon interference on two preset parametric lights of the one or more target entanglement sources; a fourth determination unit 950 configured to determine the second coincidence probabilities of each second coincidence item triggered during the spontaneous parametric down - conversion process by the one or more target entanglement sources obtained after measurement based on the second transformation matrix and the second quantum state vector. The second coincidence item is used to characterize the polarization state of photons in the two parametric lights, and the second coincidence item is triggered by performing a measurement under a first measurement basis on the one or more target entanglement sources; and a simulation unit 960 configured to determine a first coincidence count of the one or more target entanglement sources under each second coincidence item based on the second coincidence probabilities. The first coincidence count is used to determine the quality factor of the target entangled state.

[0168] Here, the operations of the above - mentioned units 910 - 960 of the multi - photon interferometer simulation device 900 are respectively similar to the operations of steps 410 - 460 described above, and will not be elaborated here.

[0169] According to an embodiment of the present disclosure, an electronic device, a readable storage medium, and a computer program product are also provided.

[0170] Reference Figure 10, a block diagram of an electronic device 1000 that can be a server or a client of the present disclosure will now be described. It is an example of a hardware device that can be applied to various aspects of the present disclosure. The electronic device is intended to represent various forms of digital electronic computer devices, such as, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as, personal digital processors, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0171] As Figure 10 shown, the electronic device 1000 includes a computing unit 1001, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 1002 or a computer program loaded from a storage unit 1008 into a random access memory (RAM) 1003. In the RAM 1003, various programs and data required for the operation of the electronic device 1000 can also be stored. The computing unit 1001, the ROM 1002, and the RAM 1003 are connected to each other via a bus 1004. An input / output (I / O) interface 1005 is also connected to the bus 1004.

[0172] Multiple components in the electronic device 1000 are connected to the I / O interface 1005, including: an input unit 1006, an output unit 1007, a storage unit 1008, and a communication unit 1009. The input unit 1006 can be any type of device that can input information into the electronic device 1000. The input unit 1006 can receive input digital or character information, and generate key signal inputs related to the user settings and / or function controls of the electronic device, and can include, but is not limited to, a mouse, a keyboard, a touch screen, a trackpad, a trackball, a joystick, a microphone, and / or a remote control. The output unit 1007 can be any type of device that can present information, and can include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. The storage unit 1008 can include, but is not limited to, magnetic disks, optical disks. The communication unit 1009 allows the electronic device 1000 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks, and can include, but is not limited to, a modem, a network card, an infrared communication device, a wireless communication transceiver, and / or a chipset, such as a Bluetooth device, an 802.11 device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0173] The computing unit 1001 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 1001 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 1001 executes the various methods and processes described above, such as method 400. For example, in some embodiments, method 400 can be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 1008. In some embodiments, part or all of the computer program can be loaded and / or installed onto the electronic device 1000 via the ROM 1002 and / or the communication unit 1009. When the computer program is loaded into the RAM 1003 and executed by the computing unit 1001, one or more steps of method 400 described above can be executed. Alternatively, in other embodiments, the computing unit 1001 can be configured to execute method 400 in any other suitable manner (e.g., by means of firmware).

[0174] Various embodiments of the systems and techniques described above in this document can be implemented in digital electronic circuitry, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on a chip (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special-purpose or general-purpose programmable processor that receives data and instructions from a storage system, at least one input device, and at least one output device, and transmits the data and instructions to the storage system, the at least one input device, and the at least one output device.

[0175] The program code for implementing the methods of the present disclosure can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when the program code is executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0176] In the context of this disclosure, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. The machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of the machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0177] In order to provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer. Other kinds of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, speech input, or tactile input).

[0178] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer having a graphical user interface or a web browser through which the user can interact with an implementation of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), the Internet, and a blockchain network.

[0179] A computer system may include a client and a server. The client and the server are generally far from each other and usually interact via a communication network. The relationship between the client and the server is generated by computer programs running on respective computers and having a client-server relationship with each other. The server may be a cloud server, a server of a distributed system, or a server incorporating a blockchain.

[0180] It should be understood that various forms of the processes shown above can be used, steps can be reordered, added or deleted. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and no limitation is imposed herein.

[0181] Although embodiments or examples of the present disclosure have been described with reference to the accompanying drawings, it should be understood that the above methods, systems, and devices are merely exemplary embodiments or examples, and the scope of the present invention is not limited by these embodiments or examples, but is only defined by the authorized claims and their equivalent scope. Various elements in the embodiments or examples can be omitted or replaced by their equivalent elements. In addition, the steps can be executed in an order different from that described in this disclosure. Further, various elements in the embodiments or examples can be combined in various ways. Importantly, with the evolution of technology, many of the elements described herein can be replaced by equivalent elements that emerge after this disclosure.

Claims

1. A multi - photon interferometer simulation method, including: Determining a first quantum state vector of a target entangled state prepared by one or more target entanglement sources, where each target entanglement source includes a barium metaborate (BBO) crystal for converting pump light into two parametric lights with a spatial distribution of either an intersecting type or a laser type during the spontaneous parametric down - conversion process, where the first quantum state vector is determined based on the first coincidence probabilities of each first coincidence term triggered during the spontaneous parametric down - conversion process by the multiple target entanglement sources, where the first coincidence term is used to characterize the polarization states of photons in the two parametric lights, and where the spontaneous parametric down - conversion process includes a first - order process and a second - order process; Obtaining first characteristic parameters of an optical transmission element corresponding to the one or more target entanglement sources to determine a first transformation matrix of the optical transmission element with respect to the parametric lights of the one or more target entanglement sources; Determining a second quantum state vector after the action of the optical transmission element based on the first transformation matrix and the first quantum state vector; Determining a second transformation matrix of one or more polarization beam splitters with respect to the parametric lights of the one or more target entanglement sources, where each polarization beam splitter is used for two - photon interference of two preset parametric lights of the one or more target entanglement sources; Determining the second coincidence probabilities of each second coincidence term triggered during the spontaneous parametric down - conversion process by the one or more target entanglement sources obtained after measurement based on the second transformation matrix and the second quantum state vector, where the second coincidence term is used to characterize the polarization states of photons in the two parametric lights, and the second coincidence term is triggered by performing measurements in a first measurement basis on the one or more target entanglement sources; and Determining a first coincidence count of the one or more target entanglement sources under each second coincidence term based on the second coincidence probabilities, where the first coincidence count is used to determine the quality factor of the target entangled state.

2. The method according to claim 1, wherein, The optical transmission element includes at least one of a half - wave plate and a quarter - wave plate, and wherein the first characteristic parameters include the angle between the optical axis of the half - wave plate and the horizontal direction, and the angle between the optical axis of the quarter - wave plate and the horizontal direction.

3. The method according to claim 1, wherein, When there are multiple target entanglement sources and also multiple polarization beam splitters, where the number of polarization beam splitters is less than or equal to the number of target entanglement sources, determining a second transformation matrix of one or more polarization beam splitters with respect to the parametric lights of the one or more target entanglement sources includes: Determining an initial transformation matrix of a polarization beam splitter with respect to two adjacent parametric lights; In response to determining that the two preset parametric lights are two adjacent parametric lights, determining the second transformation matrix T based on the following formula: Among them, the total number of parametric lights of the multiple target entanglement sources is M, the two preset parametric lights are the k-th and l-th parametric lights among the M parametric lights respectively, and l - k = 1, M PBS is the initial transformation matrix, and I is the identity matrix; In response to determining that the two preset parametric lights are not two adjacent parametric lights, determining the second transformation matrix T based on the following formula: Among them, the total number of parametric lights of the multiple target entanglement sources is M. The two preset parametric lights are the k-th and l-th parametric lights among the M parametric lights respectively, and l - k > 1, M PBS is the initial transformation matrix, and I is the identity matrix.

4. The method according to claim 1, wherein, Determining a first quantum state vector of a target entangled state prepared by one or more target entanglement sources includes: Determine the first quantum state vector representation corresponding to the target entangled state; and Based on the characteristic parameters corresponding to each of the one or more target entanglement sources and the first quantum state vector representation, determine the first quantum state vector, where the characteristic parameters include the down-conversion probability of the BBO crystal in the spontaneous parametric down-conversion process.

5. The method according to claim 4, wherein each target entanglement source includes two optical paths respectively for measuring the two beams of parametric light, and wherein determining the first quantum state vector representation of the target entangled state includes: Determine the second quantum state vector representation and the third quantum state vector representation corresponding to each optical path in the one or more target entanglement sources, where the elements in the second quantum state vector representation are determined based on the third coincidence probabilities of the respective third coincidence terms caused by the first-order process in the current optical path, and the elements in the third quantum state vector representation are the expressions of the fourth coincidence probabilities of the respective fourth coincidence terms caused by the second-order process in the current optical path; Based on the corresponding second quantum state vector representation and third quantum state vector representation, determine the fourth quantum state vector representation corresponding to each optical path, where the elements in the fourth quantum state vector representation are determined based on the fifth coincidence probabilities of the respective fifth coincidence terms caused by the first-order process and the second-order process in the current optical path; and Based on the fourth quantum state vector representations corresponding to all the optical paths in the one or more target entanglement sources, determine the first quantum state vector representation of the target entangled state.

6. The method according to claim 5, wherein determining the fourth quantum state vector representations corresponding to the two optical paths respectively includes: determining the fourth quantum state vector representation based on the direct sum representation between the corresponding second quantum state vector representation and third quantum state vector representation; and determining the first quantum state vector representation of the target entangled state based on the fourth quantum state vector representations corresponding to the two optical paths of each target entanglement source includes: determining the first quantum state vector representation of the target entangled state based on the direct product representation between the fourth quantum state vector representations corresponding to the two optical paths of each target entanglement source.

7. The method according to claim 1, wherein each target entanglement source includes two optical paths for measuring the two beams of parametric light, each optical path includes two detectors, and each detector is used to detect photons in the parametric light measured by the optical path that match the polarization state of the detector, where determining the second coincidence probabilities of the respective second coincidence terms caused by the one or more target entanglement sources obtained after measurement in the spontaneous parametric down-conversion process includes: Based on the detection efficiency of the detector, determine the first transformation matrix, where the first transformation matrix is used to represent the measurement process of performing the first measurement basis on the target entangled state; and Based on the first transformation matrix and the second quantum state vector, determine the second coincidence probabilities of the respective second coincidence terms caused by the one or more target entanglement sources obtained after measurement in the spontaneous parametric down-conversion process.

8. The method according to claim 7, wherein, determining the first transformation matrix based on the detection efficiency of the detector includes: for each optical path in the one or more target entanglement sources, determining a second transformation matrix corresponding to the optical path based on the detection efficiency of the detector, where the second transformation matrix is used to represent the measurement process of performing the measurement in the first measurement basis on the single-bit quantum state prepared for the optical path; and determining the first transformation matrix based on the second transformation matrices corresponding to all the optical paths in the one or more target entanglement sources.

9. A multi-photon interferometer simulation device, comprising: a first determination unit configured to determine a first quantum state vector of a target entangled state prepared by one or more target entanglement sources, where each target entanglement source includes a barium metaborate (BBO) crystal for converting pump light into two parametric lights with any one of an intersecting type and a laser type in spatial distribution during the spontaneous parametric down-conversion process, where the first quantum state vector is determined based on the first coincidence probabilities of each first coincidence item generated during the spontaneous parametric down-conversion process by the multiple target entanglement sources, where the first coincidence item is used to characterize the polarization state of photons in the two parametric lights, and the spontaneous parametric down-conversion process includes a first-order process and a second-order process; a first acquisition unit configured to acquire first characteristic parameters of an optical transmission element corresponding to the one or more target entanglement sources to determine a first transformation matrix of the optical transmission element with respect to the parametric lights of the one or more target entanglement sources; a second determination unit configured to determine a second quantum state vector after the action of the optical transmission element based on the first transformation matrix and the first quantum state vector; a third determination unit configured to determine a second transformation matrix of one or more polarization beam splitters with respect to the parametric lights of the one or more target entanglement sources, where each polarization beam splitter is used to perform two-photon interference on two preset parametric lights of the one or more target entanglement sources; a fourth determination unit configured to determine the second coincidence probabilities of each second coincidence item generated during the spontaneous parametric down-conversion process of the one or more target entanglement sources obtained after measurement based on the second transformation matrix and the second quantum state vector, where the second coincidence item is used to characterize the polarization state of photons in the two parametric lights, and the second coincidence item is caused by performing a measurement in the first measurement basis on the one or more target entanglement sources; and a simulation unit configured to determine a first coincidence count of the one or more target entanglement sources under each second coincidence item based on the second coincidence probability, where the first coincidence count is used to determine the figure of merit of the target entangled state.

10. The device according to claim 9, wherein, the optical transmission element includes at least one of a half-wave plate and a quarter-wave plate, and wherein the first characteristic parameters include the angle between the optical axis of the half-wave plate and the horizontal direction, and the angle between the optical axis of the quarter-wave plate and the horizontal direction.

11. The device according to claim 9, wherein, When there are multiple target entanglement sources and multiple polarization beam splitters, where the number of polarization beam splitters is less than or equal to the number of target entanglement sources, the third determination unit includes: A first determination subunit, configured to determine an initial transformation matrix of a polarization beam splitter with respect to two adjacent parametric light beams; A first response subunit, configured to, in response to determining that the two preset parametric light beams are two adjacent parametric light beams, determine the second transformation matrix T based on the following formula: Among them, the total number of parametric lights of the multiple target entanglement sources is M. The two preset parametric lights are the k-th and l-th parametric lights among the M parametric lights respectively, and l - k = 1, M PBS is the initial transformation matrix, and I is the identity matrix; A second response subunit, configured to, in response to determining that the two preset parametric light beams are not two adjacent parametric light beams, determine the second transformation matrix T based on the following formula: Among them, the total number of parametric lights of the multiple target entanglement sources is M, the two preset parametric lights are the k-th and the l-th parametric lights among the M parametric lights respectively, and l - k > 1, M PBS is the initial transformation matrix, and I is the identity matrix.

12. The apparatus according to claim 9, wherein, the first determination unit includes: A second determination subunit, configured to determine a first quantum state vector representation corresponding to the target entangled state; and A third determination subunit, configured to determine the first quantum state vector based on the characteristic parameters corresponding to each of the one or more target entanglement sources and the first quantum state vector representation, wherein the characteristic parameters include the down-conversion probability of the BBO crystal in the spontaneous parametric down-conversion process.

13. The apparatus according to claim 12, wherein, each target entanglement source includes two optical paths respectively for measuring the two parametric light beams, and wherein the second determination subunit includes: A fourth determination subunit, configured to determine a second quantum state vector representation and a third quantum state vector representation corresponding to each optical path in the one or more target entanglement sources, wherein the elements in the second quantum state vector representation are determined based on the third coincidence probabilities of the respective third coincidence terms caused by the first-order process in the current optical path, and the elements in the third quantum state vector representation are expressions of the fourth coincidence probabilities of the respective fourth coincidence terms caused by the second-order process in the current optical path; A fifth determination subunit, configured to determine a fourth quantum state vector representation corresponding to each optical path based on the corresponding second quantum state vector representation and third quantum state vector representation, wherein the elements in the fourth quantum state vector representation are determined based on the fifth coincidence probabilities of the respective fifth coincidence terms caused by the first-order process and the second-order process in the current optical path; and A sixth determination subunit, configured to determine the first quantum state vector representation of the target entangled state based on the fourth quantum state vector representations corresponding to all the optical paths in the one or more target entanglement sources.

14. The apparatus according to claim 13, wherein, the fifth determination subunit is configured to: determine the fourth quantum state vector representation based on the direct sum representation between the corresponding second quantum state vector representation and third quantum state vector representation; and the sixth determination subunit is configured to: determine the first quantum state vector representation of the target entangled state based on the direct product representation between the fourth quantum state vector representations corresponding to the two optical paths of each target entanglement source.

15. The apparatus according to claim 9, wherein, Each of the target entanglement sources includes two optical paths for measuring the two beams of parametric light. Each optical path includes two detectors, and each detector is used to detect photons in the parametric light measured by the optical path in a polarization state matching the detector. Among them, The fourth determination unit includes: A seventh determination subunit, configured to determine a first transformation matrix based on the detection efficiency of the detector, where the first transformation matrix is used to represent the measurement process of performing the measurement in the first measurement basis on the target entangled state; and An eighth determination subunit, configured to determine the second coincidence probability of each of the second coincidence terms caused by the one or more target entanglement sources during the spontaneous parametric down-conversion process based on the first transformation matrix and the second quantum state vector.

16. The apparatus according to claim 15, wherein, The seventh determination subunit includes: A unit for determining, for each optical path of the one or more target entanglement sources, a second transformation matrix corresponding to the optical path based on the detection efficiency of the detector, where the second transformation matrix is used to represent the measurement process of performing the measurement in the first measurement basis on the single-bit quantum state prepared by the optical path; and A unit for determining the first transformation matrix based on the second transformation matrices corresponding to all the optical paths of the one or more target entanglement sources.

17. An electronic device, including: At least one processor; and A memory communicatively connected to the at least one processor; wherein The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method according to any one of claims 1-8.

18. A non-transitory computer-readable storage medium storing computer instructions, wherein, The computer instructions are used to cause the computer to execute the method according to any one of claims 1-8.

19. A computer program product, including a computer program, wherein, The computer program, when executed by a processor, implements the method according to any one of claims 1-8.

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