CN113890627A

CN113890627A - Quantum cooperation multicast method based on hybrid topological structure

Info

Publication number: CN113890627A
Application number: CN202111136166.2A
Authority: CN
Inventors: 陈秀波; 徐刚; 陈思怡
Original assignee: North China University of Technology
Current assignee: North China University of Technology
Priority date: 2021-09-27
Filing date: 2021-09-27
Publication date: 2022-01-04
Anticipated expiration: 2041-09-27
Also published as: CN113890627B

Abstract

The invention relates to a quantum cooperation multicast method based on a mixed topological structure, which comprises the following four steps: step 1: constructing a ring-star mixed topological structure, preparing two particle entangled states (EPR pairs) as quantum resources, and pre-sharing between any adjacent nodes in a central ring network; step 2: the peripheral star network sends an information aggregation request to a central node in a central ring network, and the central ring network determines the central node as a sink node according to the source of the information aggregation request; and step 3: the sink node collects the aggregation information of all nodes of the central ring network; and 4, step 4: the central ring network requires all the nodes of the central ring network to repeat a plurality of rounds of information aggregation processes until the number of the aggregated information reaches the target requirement according to the requirement of the peripheral star network, and multicast-sends the aggregated information to the peripheral star network. The invention designs a high-efficiency and practical quantum cooperative multicast method aiming at a mixed topological structure by combining quantum network communication.

Description

Quantum cooperation multicast method based on hybrid topological structure

Technical Field

The invention relates to a quantum cooperation multicast method based on a hybrid topological structure, and belongs to the technical field of quantum network communication.

Background

Quantum communication is an emerging discipline in quantum information science. At present, point-to-point quantum communication is becoming mature and is becoming more and more practical. With the continuous expansion of communication scale, quantum communication is gradually developing from point-to-point two-way communication to multi-user and networking. How to effectively transmit information among multiple users is the key of large-scale networking of quantum communication, so that realizing multicast communication among multiple users in a quantum network will inevitably become a new development trend in the field of quantum network communication.

The quantum multicast problem, the most major obstacle to its implementation, is the quantum unclonable theorem. Since the theorem prohibits the accurate replication of any unknown quantum state, in the quantum theory, multicast in a true sense cannot be realized, that is, a sender cannot replicate information sent by the sender, thereby achieving the purpose of simultaneously communicating with a plurality of receivers. Early related literature relied on approximate cloning techniques to allow quantum states to be cloned multiple times and then transmitted to multiple recipients. However, the fidelity of the quantum state after the approximate cloning is lost to a certain extent, if the cloned quantum state is used as a sample for carrying out multiple iterations of the approximate cloning, the error of the fidelity between the quantum state finally transmitted to the receiver and the initial quantum state is circularly amplified, and the received information is distorted. On the one hand, since the multicast technology employs that a plurality of senders must send quantum states to a plurality of receivers simultaneously, the requirement of storage capacity of each internal node is too high. On the other hand, the existing multicast network topology, such as the butterfly network, has a bottleneck problem that may restrict the selection of the transmission path, resulting in that the network transmission needs a higher channel transmission capacity to alleviate the bottleneck problem. Therefore, the quantum unclonable theorem is not directly applicable to quantum multicast networks.

The quantum cooperative multicast proposal can better solve the problems. In 2015, Xu et al introduced reasonable definition of quantum cooperative multicast for the first time, and proposed a multi-party quantum cooperative multicast scheme in a butterfly network. According to the scheme, the invisible transmission technology is combined, quantum information is backed up by two source nodes in a cooperative mode, and fidelity distortion caused by adopting approximate cloning is avoided. And the network coding technology is adopted at the intermediate node, original 8-bit classical information is coded into 1-bit classical information, and then the 1-bit classical information is transmitted to two receivers through a bottleneck channel, so that the problem of the transmission capacity of the bottleneck channel is effectively solved.

At present, quantum cooperative multicast research is still in the beginning stage, and most researchers consider the coding problem in the butterfly network. Although the butterfly network can be represented as a topology with bottleneck problems, it does not cover all possible network types. In the face of more complex topologies, it is still unknown whether quantum cooperative multicast is feasible.

On the basis of relevant research, the quantum cooperative multicast method is expanded from the existing butterfly network structure to be applied to a hybrid topology structure. All nodes of the central ring network cooperate together to aggregate information to the sink node, and then the aggregated information is sent to the peripheral star network in a quantum multicast mode, so that quantum cooperative multicast based on the hybrid topological structure is realized.

Disclosure of Invention

The technical problem solved by the invention is as follows: the method breaks through the limitation that the existing quantum cooperative multicast method is only suitable for a butterfly network structure, and designs the quantum cooperative multicast method supporting the mixed topological structure. The technical scheme of the invention is that quantum cooperative communication and quantum multicast technology are combined, and quantum cooperative multicast is realized by adopting quantum basic gate operation and quantum measurement technology based on a ring-star mixed topological structure.

The invention provides a quantum cooperative multicast method based on a hybrid topology structure by taking a quantum system shown in figure 2 as the topology structure. The hybrid topology consists of a central ring network and a peripheral star network. In which there are k sets of peripheral star networks (n)₁₁,n₁₂),(n₂₁,n₂₂),...,(n_k1,n_k2,n_k3) Central node n of each group of peripheral star networks₁,n₂,...,n_kForming a central ring network. The solid lines in fig. 2 represent quantum channels and the dashed lines represent classical channels. Wherein each node n in the central ring network_iI ∈ {1, 2.. k } all have their own information α_i,

Suppose a peripheral star network (n)_s1,n_s2,...,n_st) To a central node n in a central ring network_sAnd sending an information aggregation request for requesting access to the aggregation information of the central ring network. At this time, the intermediate node n_sThe aggregation node is established as a central ring network, and information aggregation is carried out through the central ring network to aggregate all node information to the aggregation node n_s. Last sink node n_sAggregating information in quantum state | ψ>＝cosα|0>+sinα|1>，α＝α₁+α₂+...+α_kIs multicast to a peripheral star network (n)_s1,n_s2,...,n_st). The whole process comprises the following steps:

step 1: constructing a ring-star mixed topological structure, preparing two particle entangled states (EPR pairs) as quantum resources, and pre-sharing quantum states | phi at any adjacent nodes in a central ring network^->. In particular, each node n in the central ring network_iI ∈ {1, 2.. so, k } all with the next node n_i+1Sharing a pair of EPR pairs

Step 2: and the peripheral star network sends an information aggregation request to a central node in the central ring network, and the central ring network determines the central node as a sink node of the central network according to the source of the information aggregation request. The method for specifically determining the sink node comprises the following steps:

step 2.1, peripheral star network (n)_s1,n_s2,...,n_st) To a central node n in a central ring network_sSending an information aggregation request, and then sending the information aggregation request by a central node n_sForwarding aggregated information requests to the entire central ring network (n)₁,n₂,...,n_k)。

Step 2.2, the central ring network aggregates the source n of the request according to the information_sDetermining k sets of peripheral star networks (n)₁₁,n₁₂),(n₂₁,n₂₂),...,(n_k1,n_k2,n_k3) Peripheral star network (n) in which requests are sent_s1,n_s2,...,n_st)。

Step 2.3, the central ring network specifies the peripheral star network (n) to send the request_s1,n_s2,...,n_st) Central node n of_sAs a sink node of the central ring network, and n is added to the central ring network₁As a starting point, according to the counterclockwise n₁→n₂→...→n_kFinds the sink node n_s。

And step 3: sink node n_sCollecting all nodes n of central ring network₁,n₂,...,n_kThe aggregate information of (1). Each node n of the central ring network_iI e {1, 2.. k } is operated by performing a quantum rotation gate

Carrying out information aggregation and carrying out cooperative operation on the information alpha of each node_i,

In a quantum state | ψ>＝cosα|0>+sinα|1>，α＝α₁+α₂+...+α_kIs aggregated to the sink node n_s. Quantum revolving door operation

Belonging to unitary operation, the matrix of which is expressed as

Quantum state | ψ>＝cosα|0>+sinα|1>Is a quantum state in two-dimensional Hilbert space, |0>And |1>Is a set of orthogonal bases whose amplitude information a contains information of all nodes and a ═ a₁+α₂+...+α_k. The specific information aggregation mode is as follows:

step 3.1, each node n of the central ring network_iI e {1, 2.. k } is operated by performing a quantum rotation gate

Information of each node alpha_iEncoding to a pre-shared EPR pair

In (1). Each one of which is

Acting on node n_i-1And node n_iPre-shared EPR vs. | Φ ->_(i-1)′iThe ith qubit of (a);

step 3.2, by sink node n_sAnd s is more than or equal to 1 and less than or equal to k_s+1At the beginning, node n_i(i.e. the initial value of i is s +1) making Bell base { | PhiO on the particle i' i^±>,|Ψ^±>Measuring and transmitting the measurement result to the next node n_i+1. Here, ,

and

respectively, the results after Bell-based measurement. Table 1 gives the next node n_i+1According to the last node n_iThe sent Bell-Based Measurements (BMR) are the unitary transformations that need to be performed to recover the ideal quantum state. As shown in table 1, by node n_iThe next node n_i+1Choosing to perform the corresponding unitary transformation U on particle (i +1)⁽ⁱ⁺¹⁾The quantum state of the collapsed particle s' (i +1) is converted into an ideal quantum state. Unitary transformation U⁽ⁱ⁺¹⁾Is the following unitary operation

One of them. The superscript i +1 indicates that the unitary transformation is performed on particle (i + 1). It should be noted that, in the description of I,

x and Z are both unitary operations, the matrices of which are respectively denoted

And

specifically, the ideal quantum state of the particle s' (i +1) is

If node n_iThe measurement result is | Φ⁺>Then the particle s' (i +1) collapses to a quantum state

Node n_i+1I operation needs to be performed on the particle (I + 1);

if node n_iThe measurement result is | Φ^->Then the particle s' (i +1) collapses to a quantum state

Node n_i+1Needs to execute for particle (i +1)

Operating;

if node n_iThe measurement result is | Ψ⁺>Then the particle s' (i +1) collapses to a quantum state

Node n_i+1Needs to execute for particle (i +1)

Operating;

if node n_iThe measurement result is | Ψ^->Then the particle s' (i +1) collapses to a quantum state

Node n_i+1The XZ operation needs to be performed for particle (i + 1). Then node n_i+1Then (i + 1)' (i +1) is subjected to Bell base { | phi^±>,|Ψ^±>Measure and pass the measurement result to the next node. Slave node n on a central ring network_s+1Starting to sequentially and circularly execute the operations anticlockwise until the sink node n_sReceives the signal from the last node n_s-1And based on the node n_s-1Performs the following unitary operation on the particles s

One of them.

TABLE 1 Ideal Quantum states, Bell Base Measurements (BMR), collapsed states, and unitary transformations U⁽ⁱ⁺¹⁾The relationship between

Wherein,

step 3.3, sink node n_sCarrying out Z-base { |0 on the particles s>,|1>And measuring, and selecting to perform I or XZ unitary operation on the particles s' according to the measurement result. If the measurement result is |0>Sink node n_sPerforming an I operation on the particle s'; if the measurement result is |1>Sink node n_sPerforming XZ operation on the particles s', and finally converging the node n_sObtaining a quantum state | ψ>＝cosα|0>+sinα|1>，α＝α₁+α₂+...+α_kAnd information aggregation is realized.

The specific implementation process of information aggregation is as follows: entangle k pairs of two particles (EPR pairs))

The input quantum states are respectively composed of particles 1k ', particles 1' 2, particles 2 '3, … and particles (k-1)' k, and are adjacent to each other in the central ring network (n)₁,n_k),(n₁,n₂),(n₂,n₃),...,(n_k-1,n_k) Pre-sharing; and performing quantum revolving door operation

All node information alpha_i,

Encoding into an input quantum state; from the sink node n_sNext node n of_s+1Initially, Bell base { | Φ is used in order^±>,|Ψ^±>Measuring, transmitting the measuring information to the next node n through the classical channel_i+1I ∈ {1, 2...., k }, the next node performs a unitary transformation U according to table 1⁽ⁱ⁺¹⁾I belongs to {1, 2.,. k }, and the process is repeated for k-1 times until the aggregation node n_sFinish the unitary transformation U_k ^s _-1Aggregating all node information of the central ring network to the particles ss'; use of Z-base { |0 on particles s>,|1>Measuring and performing a unitary operation Z according to the measurement result_kAnd X_kFinally, the particle s' outputs the polymerization quantum state | psi>＝cosα|0>+sinα|1>，α＝α₁+α₂+...+α_k。

The quantum wires of a round of information aggregation process are shown in fig. 3. A round of information-aggregated quantum wires comprising k rotating gate operations R_αiK-1 Bell base { | φ^±>,|Ψ^±>Measure (MB) 1 times Z-basis 0>,|1>Measurement (MZ), k-1 unitary operations

1 time Z_kAnd X_kThe line depth is k + 2. The double lines in the figure represent classical channels; l Φ^->Is a two-particle entangled state (EP)R pairs);

is operated by a revolving door in the form of a matrix

MB_iIs the ith Bell-based measurement, here

Respectively representing the results after Bell base measurement;

are unitary operations, with the subscript representing the unitary operation performed on the basis of the measurement and the superscript representing the unitary operation performed on the particle. Such as

Indicating that a unitary operation is performed on the particle s +2 according to the 1 st measurement. For a specific unitary operation, refer to table 1 if the measurement result is | Φ⁺>Selecting unitary operation as I; if the measurement result is | Φ^->Unitary operation is selected as

If the measurement result is | Ψ⁺>Unitary operation is selected as

If the measurement result is | Ψ^->Selecting unitary operation as XZ; MZ_kIs the kth Z base { |0>,|1>Measuring; z_kAnd X_kRespectively, if the measurement result is |1 > -based on the k-th measurement result, performing the unitary operation

And

otherwise no operation is performed.

And 4, step 4: central ring shapeThe network requires all the nodes of the central ring network to repeat multi-round information aggregation process according to the requirement of the peripheral star network until the number of information aggregation reaches the target requirement. By a sink node n_sAnd transmitting the collected aggregation information to the peripheral star network in a multicast mode. In particular, according to the sink node n_sOf a peripheral star network sub-node n_s1,n_s2,...,n_stT, the t information aggregation operations are repeatedly cycled to obtain t aggregation information quantum states

Sink node n_sAs a central node of the peripheral star topology, quantum states

Simultaneously sending to a peripheral star network in multicast form (n)_s1,n_s2,...,n_st) And finishing quantum cooperative multicast.

The invention has the beneficial effects that: the multicast transmission of the invention is deterministic, and promotes the further development of quantum multicast. In addition, the invention can realize the information aggregation of the central ring network and transmit the information to the peripheral star network in a multicast mode. The method not only accords with the basic idea of quantum cooperative communication, but also well reflects the quantum multicast characteristic on a ring-star mixed topological structure, and improves the communication efficiency of a large-scale quantum network.

Drawings

FIG. 1 is a flow chart of a hybrid topology-based quantum cooperative multicast method according to the present invention;

FIG. 2 is a diagram of a hybrid topology of the present invention;

FIG. 3 is a diagram of a quantum circuit of a round of information aggregation process in the present invention;

table 1 is the relationship between ideal quantum states, Bell-based measurements BMR, collapsed states, and unitary transformations.

Detailed Description

The invention relates to a quantum cooperative multicast method based on a hybrid topological structure. Aiming at the problem of multiparty quantum communication, the cooperative multicast transmission quantum state is realized based on a quantum ring-star mixed topology structure.

The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.

As shown in fig. 1, the method mainly comprises the following steps:

step 1: constructing a ring-star mixed topological structure, preparing two particle entangled states (EPR pairs) as quantum resources, and pre-sharing between any adjacent nodes in a central ring network;

step 2: the peripheral star network sends an information aggregation request to a central node in a central ring network, and the central ring network determines the central node as a sink node according to the source of the information aggregation request;

and step 3: the sink node collects the aggregation information of all nodes of the central ring network;

and 4, step 4: the central ring network requires all the nodes of the central ring network to repeat a plurality of rounds of information aggregation processes until the number of the aggregated information reaches the target requirement according to the requirement of the peripheral star network, and multicast-sends the aggregated information to the peripheral star network.

The specific embodiment is as follows:

based on the ring-star hybrid topology shown in fig. 2, assume that there are 3 nodes n on the central ring network₁,n₂,n₃They are respectively peripheral star networks (n)₁₁,n₁₂),(n₂₁,n₂₂,n₂₃,n₂₄),(n₃₁,n₃₂,n₃₃) The central node of (2). Node n in a central network₁,n₂,n₃Each having its own information alpha₁,α₂,α₃Here alpha₁,α₂,

Suppose a peripheral star network (n)₂₁,n₂₂,n₂₃,n₂₄) To the center in a central ring networkNode n₂Sending an information aggregation request requesting access to a central network (n)₁,n₂,n₃) The information of (2) is aggregated. At this time, node n₂₁,n₂₂,n₂₃,n₂₄Intermediate node n of star topology₂Will respond to the request and act as an aggregation node with the rest of the nodes n on the central ring network₁,n₃And performing information aggregation through mutual cooperation. Finally, the polymerization information is in quantum state | psi>＝cosα|0>+sinα|1>，α＝α₁+α₂+α₃Is multicast to a peripheral star network (n)₂₁,n₂₂,n₂₃,n₂₄). The following describes specific steps of the present invention.

Step 1: constructing a ring-star mixed topology structure, and each node n in a central ring network_iI ∈ {1,2,3} all with the next node n_i+1Sharing a pair of two-particle entangled states (EPR pair)

In particular, node n₁And node n₂Inter-pre-shared EPR pair | Φ^->_1′2Node n₂And node n₃Inter-pre-shared EPR pair | Φ^->_2′3Node n₃And node n₁Inter-pre-shared EPR pair | Φ^->_3′1. The entire initial quantum system can be written as:

step 2: and the peripheral star network sends a request to the central node to request information aggregation for accessing the central ring network. And the central ring network determines that the central node is the sink node according to the source of the information aggregation request. The method for specifically determining the sink node comprises the following steps:

step 2.1, peripheral star network (n)₂₁,n₂₂,n₂₃,n₂₄) To a central node n in a central ring network₂Sending an information aggregation request, and then sending the information aggregation request by a central node n_sForwarding aggregated information requests to the entire central ringForm network (n)₁,n₂,n₃)。

Step 2.2, the central ring network according to the source n of the aggregation request₂Determining 3 sets of peripheral star networks (n)₁₁,n₁₂),(n₂₁,n₂₂,n₂₃,n₂₄),(n₃₁,n₃₂,n₃₃) Peripheral star network (n) in which requests are sent₂₁,n₂₂,n₂₃,n₂₄)。

Step 2.3, the central ring network specifies the peripheral star network (n) to send the request₂₁,n₂₂,n₂₃,n₂₄) Central node n of₂As a sink node of the central network, and n on the central ring network₁As a starting point, according to the counterclockwise n₁→n₂→n₃Finds the sink node n₂。

And step 3: each node n of the central ring network_iI e {1,2,3} is operated by performing a quantum rotation gate

In a quantum state | ψ>＝cosα|0>+sinα|1>，α＝α₁+α₂+α₃To the sink node. The specific information aggregation mode is as follows:

step 3.1, Central Ring network node n_iI e {1,2,3} operated by quantum rotating gate

Information of each node alpha_i,

Encoding to a pre-shared EPR pair

In (1).Each one of which is

Operation acts on node n_i-1And node n_iPre-shared EPR pair | Φ^->_(i-1)′iOn the particle i of (1).

At this time, the whole quantum system evolves as:

step 3.2, by sink node n₂Next node n of₃Initially, Bell base { | φ is applied to particle 3' 3^±>,|Ψ^±>Measuring, wherein

And transmits the measurement result to the next node n₁. Suppose that the measurement result is | Φ⁺>_3′3At this time, the whole quantum system evolves as:

from table 1, by the next node n₁To particles 1 do

And (5) operating. Then the Bell-based measurement of the particles 1' 1 is carried out^±>,|Ψ^±>}. Suppose that the measurement result is | Φ^->_1′1At this time, the whole quantum system evolves as:

from table 1, by the next node n₂To particles 2

Operation, at this point the entire quantum system evolves to:

step 3.3, sink node n₂Z-base { |0 for particle 2>,|1>And (6) measuring. If the measurement result is |0>Carrying out I operation on the particles 2'; if the measurement result is |1>The particles 2' are subjected to an XZ operation. At a sink node n₂Obtaining a quantum state:

|ψ>＝cos(α₁+α₂+α₃)|0>+sin(α₁+α₂+α₃)|1>

and 4, step 4: according to sink node n₂Of a peripheral star network node n₂₁,n₂₂,n₂₃,n₂₄The number of the aggregation nodes n can be obtained through 4 rounds of information aggregation₂To obtain 4 quantum states

Sink node n₂As a central node of the peripheral star topology, quantum states

Simultaneously sending to peripheral star network nodes n in a multicast mode₂₁,n₂₂,n₂₃,n₂₄And finishing quantum cooperative multicast.

The invention belongs to the field of multiparty quantum communication, and expands the application scene of a quantum multicast network. On the one hand, the information aggregation of the central ring network can be realized deterministically, and on the other hand, the information can be transmitted to the peripheral star network in a multicast mode. Not only accords with the basic idea of quantum cooperative communication, but also well reflects the multicast characteristic on the ring-star mixed topology structure. Therefore, the invention can promote the further development of quantum multicast and improve the communication efficiency of a large-scale quantum network.

Claims

1. A quantum cooperative multicast method based on a hybrid topology structure is characterized by comprising the following steps:

step 1, constructing a ring-star mixed topological structure, preparing two particle entangled states (EPR pairs) as quantum resources, and randomly adjacent nodes (n) in a central ring network_i,n_i+1) In pre-shared quantum states

|Φ^->Is two-particle entangled state (EPR pair), and subscripts i' and i +1 represent the 1 st and 2 nd particles of the EPR pair respectively, and are formed by a central ring network node n_iAnd n_i+1The method comprises the steps that a central ring network has k nodes, namely i belongs to {1, 2.., k };

step 2, the peripheral star network sends an information aggregation request to a central node in the central ring network, and the central ring network determines the central node as a sink node according to the source of the information aggregation request;

step 3. sink node n_sCollecting all nodes n of central ring network₁,n₂,...,n_kThe aggregate information of (1); the method specifically comprises the following steps: each node n of the central ring network_iI e {1, 2.. k } is operated by performing a quantum rotation gate

In a quantum state | ψ>＝cosα|0>+sinα|1>，α＝α₁+α₂+...+α_kIs aggregated to the sink node n_s(ii) a Quantum revolving door operation

Belonging to unitary operation, the matrix of which is expressed as

And 4, the central ring network requires all the nodes of the central ring network to repeat a plurality of rounds of information aggregation processes according to the requirement of the peripheral star network until the number of the aggregated information reaches the target requirement, and the aggregated information is sent to the peripheral star network by the aggregation node in a multicast mode.

2. The method of claim 1, wherein the method for determining sink nodes in step 2 comprises:

step 2.1, peripheral star network (n)_s1,n_s2,...,n_st) To a central node n in a central ring network_sSending an information aggregation request, and then sending the information aggregation request by a central node n_sForwarding the aggregated information request to the entire central ring network;

step 2.2, the central ring network aggregates the source n of the request according to the information_sDetermining k sets of peripheral star networks (n)₁₁,n₁₂),(n₂₁,n₂₂),...,(n_k1,n_k2,n_k3) Peripheral star network (n) in which requests are sent_s1,n_s2,...,n_st)；

3. The method of claim 1, wherein the information aggregation method in step 3 comprises:

step 3.1, each node n of the central ring network_iI e {1, 2.. k } is processed byRow quantum revolving door operation

Information of each node alpha_i,

Encoding to a pre-shared EPR pair

In each case

Acting on node n_i-1And node n_iPre-shared EPR pairs

The ith qubit of (a);

step 3.2, by sink node n_sAnd s is more than or equal to 1 and less than or equal to k_s+1At the beginning, node n_i(i.e. the initial value of i is s +1) making Bell base { | PhiO on the particle i' i^±>,|Ψ^±>Measuring and transmitting the measurement result to the next node n_i+1Here, the

And

respectively representing the results after Bell-based measurements, according to node n_iThe next node n_i+1Choosing to perform a unitary transformation U on particle (i +1)⁽ⁱ⁺¹⁾(ii) a Unitary transformation U⁽ⁱ⁺¹⁾Is the following unitary operation

One of them, wherein, I,

And

if node n_iThe measurement result is | Φ⁺>Node n_i+1I operation needs to be performed on the particle (I + 1); if node n_iThe measurement result is | Φ^->Node n_i+1Needs to execute for particle (i +1)

Operating; if node n_iThe measurement result is | Ψ⁺>Node n_i+1Needs to execute for particle (i +1)

An XZ operation; if node n_iThe measurement result is | Ψ^->Node n_i+1An XZ operation needs to be performed on particle (i + 1); then node n_i+1Then making Bell base { | φ) for the particle (i + 1)' (i +1)^±>,|Ψ^±>Measure and pass the measurement to the next node, from node n on the central ring network_s+1Starting to sequentially and circularly execute the operations anticlockwise until the sink node n_sReceives the signal from the last node n_s-1And based on the node n_s-1Performs the following unitary operation on the particles s

Step 3.3, sink node n_sCarrying out Z-base { |0 on the particles s>,|1>Measuring, and selecting to execute I or XZ unitary operation on the particles s' according to the measurement result; if the measurement result is |0>Sink node n_sPerforming an I operation on the particle s'; if the measurement result is |1>Sink node n_sPerforming XZ operation on the particles s', and finallySink node n_sObtaining a quantum state | ψ>＝cosα|0>+sinα|1>，α＝α₁+α₂+...+α_kAnd information aggregation is realized.