Method for controllably and remotely executing any target quantum operation of single quantum bit

Abstract

The invention relates to the technical field of quantum information, and discloses a method for controllably and remotely executing any target quantum operation of a single quantum bit, and the method comprises the steps: employing a one-dimensional five-quantum-bit cluster state as an entanglement resource, and forming a quantum information transmission channel through the reasonable configuration of quantum bits; quantum bit measurement and classical information transmission are executed by an information control party, and generation of a channel access authorization key and secure transmission of a target quantum state are realized; the operation executor executes a series of quantum operations and Bell state measurement according to the received classic information and transmits a measurement result to the receiving agent; and the receiving agent executes a dynamic conversion operation according to the received classical information and the channel access authorization key, and finally controlled remote execution of the target quantum operation is realized. According to the method and the device, the confidential quantum information is quickly and safely transmitted under the condition that the operation executor does not completely trust the receiving member.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of quantum information technology, and more particularly, to a method for controllable remote execution of single quantum bit arbitrary target quantum operation. BACKGROUND

[0002] In a quantum network key program system, if a quantum state is endowed with core information, it can be encrypted and stored by a certain specific unitary operation. At this time, if the inverse operation is implemented, it is actually the decryption of the core information, thereby successfully activating the key quantum program system. Conversely, if a non-matching random operation is applied, the quantum state endowed with the core information will be damaged, thereby causing the functional failure of the key quantum program system. It is worth noting that in many important fields such as national defense security, commercial secrets and industrial control, the operation permission of such key quantum program system usually needs multi-party remote collaborative authorization.

[0003] Therefore, how to realize such a multi-party collaborative quantum remote control mechanism becomes a technical problem to be solved. SUMMARY

[0004] The present application provides a method for controllable remote execution of single quantum bit arbitrary target quantum operation, which solves the technical problem of how to realize such a multi-party collaborative quantum remote control mechanism in the prior art.

[0005] The present application provides a method for controllable remote execution of single quantum bit arbitrary target quantum operation, comprising:

[0006] The quantum channel construction includes using a one-dimensional five quantum bit cluster state as a quantum channel, wherein quantum bits 3 and 5 are allocated to the target operation execution party, quantum bits 1 and 4 are allocated to the information control party, and quantum bit 2 is allocated to the receiving agent party; such a distributed storage entangled resource enables the secure transmission of quantum information among the three parties, providing optimized quantum channel support for controllable execution of remote quantum operation; the target quantum state is loaded onto the quantum bits of the information control party;

[0007] The quantum information processing includes a first stage, a second stage, a third stage and a fourth stage;

[0008] In the first stage, the target quantum state is transmitted and the channel access authorization key is generated: the information control party first performs single quantum bit computational basis measurement and Bell state basis measurement, obtains the channel control right, and associates the target quantum state amplitude and phase parameter information to the entangled quantum bit system of the operation execution party and the receiving agent party; then sends the Bell state measurement result to the target operation execution party to help it reconstruct the target quantum state; the single quantum bit computational basis measurement result is reserved as the authorization key for subsequent control of the receiving agent party;

[0009] The second stage is accurate recovery of the target quantum state. The operation executor performs preset quantum operation sequences and dynamic correction operations according to the classical information feedback, so as to realize remote accurate recovery of the target quantum state. The preset quantum operation sequences include Hadamard gate operation and double-qubit CNOT gate operation.

[0010] The third stage is target quantum operation execution and induced quantum state teleportation. The operation executor first implements target quantum operation on the reconstructed target quantum state to prepare an induced quantum state. Then, Bell state base joint measurement is performed to teleport quantum information part of the target operation induced state to a quantum bit of the receiving agent. Finally, the measurement result is transmitted through a classical channel. It is worth noting that although all information of the target operation induced quantum state has been transmitted through entanglement association and classical communication, the receiving agent cannot accurately reconstruct the target operation induced quantum state without the channel access authorization key.

[0011] The fourth stage is controlled output of the target operation induced quantum state. The information controller, as an authorized subject, has the decision-making right of target output state reconstruction. When the authorization is granted, the information controller transmits the channel access authorization key to the receiving agent through the classical channel. The receiving agent can accurately reconstruct the target operation induced state by performing corresponding dynamic transformation operation based on the key. If the authorization is denied, the task is automatically terminated. This mechanism shows that the accurate reconstruction of the target operation induced quantum state is essentially controlled by the authorization decision of the information controller.

[0012] Further, the expression of the five-qubit cluster state is:

[0013]

[0014] wherein, represents the characteristic expression of the five-qubit cluster state, and the subscript marks different quantum bits; |0> and |1> represent two mutually orthogonal standard computational basis state vectors in quantum information, which can correspond to specific states of a quantum physical system, such as representing the electron spin upward |↑> and spin downward |↓> states in an electron spin system, the horizontal polarization |H> and vertical polarization |V> states in an optical system, and two different atomic energy levels in a superconducting quantum circuit system; Π represents a product symbol; σ (1,1) = |0><0| - |1><1| is a Pauli operation, the subscript k = 1, …, 5, L generally refers to the quantum bit label on which the Pauli operation acts, has no object, and only represents a mathematical symbol, which is defined as The target quantum state is an arbitrary single-qubit state.

[0015] Further, the first stage operation of the module two includes the following steps:

[0016] S I -1: The information controller performs single-qubit computational basis measurement on his qubit 1. The measurement result is directly related to the specific form of quantum channel state collapse, which constitutes the authorization key of the subsequent receiving agent control;

[0017] S I -2: The information controller performs joint Bell state basis measurement on his qubit 4 and target qubit t. This measurement realizes the quantum-classical information separation of the target quantum state, in which the quantum information component has been associated with the qubit of the operation executor, and the classical information component has been encoded as the Bell state basis measurement result.

[0018] S I -3: The information controller encodes his Bell state basis measurement result as 2-bit classical information and transmits it to the operation executor through the classical channel to realize the measurement result disclosure and complete the first stage of information transmission.

[0019] Further, the single-qubit computational basis is composed of two standard state vectors {|0>, |1>}, while the Bell state basis is composed of four mutually orthogonal and complete two-qubit state vectors

[0020]

[0021]

[0022]

[0023]

[0024] Further, the authorization key of the information controller is associated with the computational basis measurement result of qubit 1, and their corresponding relationship is:

[0025] Single-qubit computational basis measurement result of the information controller

[0026] Further, the corresponding relationship between the Bell state basis measurement result of the information controller and the 2-bit classical information encoding is:

[0027] Bell state basis measurement result of the information controller

[0028] Further, the second stage operation of the module two includes the following steps:

[0029] S II ​-1: The operation executor respectively implements single-qubit Hadamard gate operation on its quantum bits 3 and 5. The operation converts the computational basis {|0>, |1>} into the orthogonal basis {|+>, |->}, significantly improves the transmission capacity and entanglement resource availability of the quantum channel, and optimizes the entanglement characteristics of the quantum channel.

[0030] S II -2: The operation executor performs two-qubit CNOT gate operation (quantum bit 5 as master quantum bit and quantum bit 3 as controlled quantum bit) on its quantum bits 3 and 5, further optimizes the quantum channel into a configuration that adapts to the target operation requirements through entanglement association.

[0031] S II -3: The operation executor implements dynamic correction operation on its quantum bit 5, thereby realizing remote recovery of the target quantum state.

[0032] Further, the single-qubit Hadamard gate quantum operator is defined as:

[0033]

[0034] wherein, H = (1 / √2) (σx-σz) represents the characteristic expression of the Hadamard gate operator, σ (0,1) = |0><1|+|1><0| and σ (1,1) = |0><0|-|1><1| are two Pauli operations.

[0035] Further, the expressions of the orthogonal basis are respectively:

[0036]

[0037] Further, the two-qubit CNOT gate operator is:

[0038]

[0039] wherein quantum bit x is the master quantum bit and quantum bit y is the passive quantum bit; σ (0,0) = |0><0|+|1><1| and σ (0,1) = |0><1|+|1><0| respectively represent the unit operation and a Pauli operation.

[0040] Further, the dynamic correction operation is associated with the 2-bit classical information sent by the information controller, and the corresponding relationship is:

[0041]

[0042] Further, the dynamic correction operation operator wherein, denotes modulo 2 addition, i.e. When (m, n) takes different values, the corresponding dynamic correction operations are also different; specifically, when (m, n) takes (0, 0), (0, 1), (1, 0), (1, 1) respectively, the corresponding dynamic correction operations are where is the unit operator, and are three different Pauli operations.

[0043] Further, the third stage operation of the module two comprises the following steps:

[0044] S III -1: The operation executor performs the target quantum operation on his qubits 5, realizing the remote operation on the target quantum state. At this time, the target operation induces the quantum state to be generated, but it still needs to be transmitted to the receiving agent through further operation;

[0045] S III -2: The operation executor performs joint Bell state basis measurement on his qubits 3 and 5, so that the quantum information associated with the target operation induced quantum state is non-locally transmitted to the qubits of the receiving agent through the entanglement channel.

[0046] S III -3: The operation executor encodes his Bell state basis measurement results as 2-bit classical information and transmits them to the receiving agent through the classical channel to realize the disclosure of the measurement results and complete the information transmission of the third stage. At this time, the receiving agent has collected the quantum information associated with the target operation induced quantum state and the classical information, but he still cannot accurately reconstruct because he does not have the channel access authorization key of the information controller.

[0047] Further, the correspondence between the Bell state basis measurement results of the operation executor and the 2-bit classical information encoding is as follows:

[0048]

[0049] Further, the fourth stage operation of the module two comprises the following steps:

[0050] S IV -1: The information controller decides whether to authorize the receiving agent to reconstruct the target operation induced quantum state. If it decides to authorize, the next operation is performed; if it refuses to authorize, the action is automatically terminated.

[0051] S IV -2: The information controller transmits the authorization key to the receiving agent through the classical channel.​

[0052] S IV -3: The receiving agent performs a dynamic transformation operation on its qubit 2, reconstructs the target operation-induced quantum state, and realizes the target operation acting on the remote target quantum state under the authorization of the information controller and finally completes the output on the receiving agent's qubit.

[0053] Further, the dynamic transformation operation is not only associated with the 2-bit classical information passed by the operation executor, but also associated with the information controller's authorization key, and the corresponding relationship between them is:

[0054]

[0055] Further, the dynamic transformation operation operator is denoted as modulo 2 addition, i.e. And When (i,j,l) takes different values, the corresponding dynamic transformation operation is also different; specifically, when (i,j,l) takes (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1) respectively, the corresponding dynamic correction operation is where

[0056] Further, the method for controllable remote execution of single-qubit arbitrary target quantum operation splits the quantum state information into multiple sub-information, so that each receiver can only obtain one part. The information controller and the receiving agent are equivalent to the target operation receiving team, and only when the team members cooperate with each other can they obtain secure and complete quantum-classical receiving information, so as to accurately reconstruct the target operation-induced quantum state on their certain qubit. Even if part of the team members are dishonest, they cannot individually steal or leak confidential quantum information.

[0057] The beneficial effects of the present application are as follows: the present application uses a one-dimensional five-qubit cluster state as a quantum channel, wherein qubits 3 and 5 are allocated to an operation executor, qubits 1 and 4 are allocated to an information controller, and qubit 2 is allocated to a receiving agent, thereby realizing the distributed storage of information by using limited quantum resources; the information controller performs qubit measurement and classical information transmission, including single-qubit computational basis measurement and Bell state basis measurement, so that the measured quantum information part is kept on the qubits of the operation executor and the receiving agent; the operation executor performs a series of quantum operations according to the received classical information and transmits the results to the receiving agent through classical information, wherein the operation executor can perform any quantum operation without directly contacting the target qubit; the information controller and the receiving agent cooperate to finally realize the target quantum operation on the qubits of the receiving agent, and if they do not cooperate, neither the information controller nor the receiving agent can individually obtain and reconstruct the complete target operation-induced output state information, thereby ensuring the safe, accurate and controllable remote execution of the target quantum operation. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 is a technical route diagram of single-qubit arbitrary target operation remote controllable execution of the present application;

[0059] Figure 2 is a quantum resource population diagram provided by an embodiment of the present application;

[0060] Figure 3 is a quantum operation flow provided by an embodiment of the present application Figure 1 ;

[0061] Figure 4 is a quantum operation flow provided by an embodiment of the present application Figure 2 ;

[0062] Figure 5 is a quantum operation flow provided by an embodiment of the present application Figure 3 ;

[0063] Figure 6 is a quantum operation flow provided by an embodiment of the present application Figure 4 . DETAILED DESCRIPTION

[0064] The subject matter described herein will now be discussed with reference to example implementations. It should be understood that discussions of these implementations merely walk through the features and / or arrangements that can be utilized in connection with the subject matter described herein and can be modified in various ways. Each of the various implementations can omit, substitute, or add various procedures or components as desired. Additionally, features described in relation to one example can also be combined in other examples.

[0065] Disclosed in at least one embodiment of the present application is a method for controllable remote execution of single quantum bit arbitrary target quantum operation, the technical implementation route of which is shown in the accompanying drawings of the specification Figure 1 , and characterized in comprising the following two core modules.

[0066] Core module one: quantum channel construction (see the accompanying drawings of the specification Figure 2 ).

[0067] In the present application, there are three legitimate participants: Anne, Bob and Chris. Anne is the executor of the single quantum bit target operation , Bob is the information controller, and Chris is the receiving agent. Bob and Chris jointly form a remote receiving team designated by Anne. The specific form of the target quantum operation is unknown to anyone, and Anne wants to execute the target operation on the single quantum bit target state |ζ> at two agents. Since Anne does not fully trust either of the two agents, she must ensure that neither Bob nor Chris has the ability to accurately act on the target state |ζ> with the target operation and ultimately obtain the target operation induced state , and only the two of them can complete the quantum task by cooperating with each other.

[0068] The core of the present application is to construct an optimized quantum channel through quantum entanglement resources. Specifically, the quantum entanglement resource used is a one-dimensional five-qubit cluster state, which has higher entanglement robustness and low decoherence compared to other entanglement resources such as GHZ state and W state, and its expression is:

[0069]

[0070] In the formula, denotes the characteristic expression of the five-qubit cluster state, and the subscript marks different quantum bits; |0> and |1> denote two mutually orthogonal standard computational basis vectors in quantum information, which can correspond to specific states of a quantum physical system, such as representing electron spin up |↑> and spin down |↓> states in an electron spin system, representing photon horizontal polarization |H> and vertical polarization |V> states in an optical system, and representing two different atomic energy levels in a superconducting quantum circuit system; Π represents the product symbol; σ (1,1) = |0><0| - |1><1| is a Pauli operation, and the subscript k = 1, …, 5 represents the quantum bit label on which the Pauli operation acts, denotes the computational symbol, which is defined as The quantum bit population structure of the entanglement resource is That is, the quantum bits 3 and 5 belong to the memory of Anne, the quantum bits 1 and 4 belong to the memory of Bob, and the quantum bit 2 belongs to the memory of Chris. The specific population mode of the entanglement resource is designed based on the deep analysis of quantum information security transmission, and can realize the three-party secure partition of quantum information in the target quantum state and the target quantum operation, so that any single agent cannot independently obtain complete quantum information. This design provides high-security quantum channel support for controllable execution of remote quantum operations. Among them, the high-quality quantum resource and the optimized entanglement population configuration are the physical basis for the feasibility of the scheme, and are also the core innovation point that distinguishes it from the prior art.

[0071] For ease of description, the quantum bits (3, 5), (1, 4) and 2 are marked as (a1, a2), (b1, b2) and c respectively in the embodiment. According to this marking method, the one-dimensional five-qubit cluster state can be re-expressed as:

[0072]

[0073] Among them, is a direct expression of the five-qubit cluster state characteristics, and the subscripts mark different quantum bits held by the three parties, wherein the quantum bits a1, a2 represent two quantum bit marks held by Anne, b1, b2 represent two quantum bit marks held by Bob, and c represents one quantum bit mark held by Chris; |0> and |1> represent two mutually orthogonal standard computational basis vectors in quantum information, which can correspond to specific states of a quantum physical system, such as representing the electron spin upward |↑> and spin downward |↓> states in an electron spin system, the horizontal polarization |H> and vertical polarization |V> states in an optical system, and two different atomic energy levels in a superconducting quantum circuit system; σ (1,1) = |0><0| - |1><1| is a Pauli operation, represents the Pauli operation σ (1,1) acting on the quantum bits c, a1, b2, a2 respectively.

[0074] In addition, the quantum bit t corresponding to the target quantum state |ζ> belongs to the quantum memory of Bob, and its specific expression is:

[0075] |ζ> t = (cosθ|0> + e iδ sinθ|1>) t ;

[0076] Among them, |ζ> tLet θ represent the characteristic expression of the target quantum state on qubit t, θ∈[0,π / 2], δ∈[0,π / 2], cosθ and sinθ represent the amplitude parameters of the target quantum state, and e iδ The phase parameter represents the target quantum state. This quantum state can characterize any form of single-qubit state, demonstrating the versatility of the method proposed in this invention.

[0077] Core Module Two: Quantum Information Processing (See the instruction manual appendix) Figure 3 ).

[0078] The quantum information processing method provided in this embodiment of the invention comprises four ordered stages and a total of twelve operational steps. The technical features and specific implementation process of each stage will be described in detail through embodiments and accompanying drawings.

[0079] Phase 1: Target quantum state transfer and channel access authorization key generation (see instruction manual appendix) Figure 4 ).

[0080] This stage of the operation is performed by the information control party. Its core technology lies in decomposing the target qubit information into quantum and classical components and establishing a monitoring and control mechanism for the receiving agent. The operational process mainly includes:

[0081] The information controller performs a single-qubit measurement on its held qubit b1, and the measurement result constitutes the classical control conditions for the receiving agent.

[0082] The information controller performs Bell state measurements on its own qubit b2 and target qubit t to achieve nonlocal transmission of the quantum information part of the target quantum state to the target operation executor, and simultaneously acquires classical correlation information characterizing the features of the target quantum state;

[0083] The information controller sends the classical information corresponding to the Bell state measurement results to the target quantum operation executor to assist it in obtaining complete information about the target quantum state.

[0084] The specific operational steps and technical characteristics of this stage are as follows:

[0085] Step S-1: Bob performs a single-qubit computational basis on his qubit b2 ( The measurement is performed on the quantum channel and the result is encoded into an authorization key for the subsequent control receiving agent to access the quantum channel.

[0086] The single-qubit computing base in this invention Bob's single-qubit computational basis measurement causes the initial five-qubit cluster state to collapse with equal probability into one of the following two states, as follows:

[0087]

[0088] wherein, denote the characteristic expressions of the two collapsed forms of the five-qubit cluster state resulting from the measurement, is the result of the single-qubit computational basis measurement performed by Bob on his qubit b1, denotes the direct product symbol, is the characteristic expression of the corresponding collapsed state of the remaining four qubits c, a1, b2, a2; specifically, when the result of the single-qubit computational basis measurement applied by Bob on his qubit b1 is |0>, the remaining four qubits c, a1, b2, a2 collapse correspondingly into the quantum state In this case, the collapsed form of the five-qubit cluster state can be expressed as whereas when the result of the single-qubit computational basis measurement applied by Bob on his qubit b1 is |1>, the remaining four qubits c, a1, b2, a2 collapse correspondingly into the quantum state In this case, the collapsed form of the five-qubit cluster state can be expressed as The expression for

[0089]

[0090] wherein, denotes modulo-2 addition, i.e. whereas

[0091] When l = 0,

[0092]

[0093] When l = 1,

[0094]

[0095] The importance of this step lies in the fact that it creates a conditionally dependent quantum state, i.e. the subsequent state of the quantum system depends on the measurement result of Bob This dependency is crucial for achieving supervisory control over the receiving agent Chris, ensuring that Chris cannot complete the quantum task alone. From an information security perspective, this step establishes the first security barrier for the entire process.

[0096] Obviously, after Bob's measurement, the quantum channel state connecting Anne, Bob, and Chris collapses into a four-qubit entangled state The specific form of this collapsed state depends on the result of Bob's single-qubit computational basis measurement With respect to this measurement, only Bob knows the result at present, while Anne and Chris do not know it. This directly leads to the fact that Chris cannot complete the quantum task alone in the last stage without the help of Bob. In this sense, it can be considered that the single-qubit measurement of Bob is essentially a supervisory control operation on Chris. Therefore, Bob encodes the single-qubit measurement result as an authorization key for Chris to access the quantum channel. The corresponding relationship is as follows:

[0097]

[0098] Step S-2: Bob performs a Bell state basis measurement on his qubit pair (b2, t).

[0099] The Bell state basis measurement is an important operation in quantum information processing, and its basis vectors are composed of four mutually orthogonal Bell states, that is, where

[0100]

[0101] The physical meaning of the Bell state basis measurement of Bob is that it can decompose the target quantum state information into quantum information part and classical information part, and the quantum information part has been transmitted to the target operation executor Anne through the quantum channel, and the classical information part is determined by the Bell basis measurement result, and its value directly reflects the collapse of the entangled state.

[0102] Specifically, before the Bell state basis measurement of Bob, the overall quantum state of the composite system composed of qubits (a1, a2, b2, c, t) is:

[0103]

[0104] wherein, denotes the quantum state characteristic expression of the overall composite system composed of qubits (a1, a2, b2, c, t), is the characteristic expression of the corresponding collapsed state of the remaining four qubits c, a1, b2, a2 of the cluster state caused by the single-qubit measurement of Bob on his qubit b1, |ζ t is the characteristic expression of the target quantum state on the qubit t.

[0105] Under the Bell state basis framework, the quantum state of the composite system can be re-expressed in the following form:

[0106]

[0107] wherein, denotes the quantum state of the composite system of qubits (a1, a2, b2, c, t), and ∑ denotes the summation symbol, denotes the possible measurement outcomes of the Bell-state basis measurement on the qubit pair (b2, t), denotes the corresponding collapsed state of the rest of the system qubits (c, a1, a2), which is expressed as:

[0108]

[0109] wherein, is the characteristic expression of the corresponding collapsed state of the rest of the system qubits (c, a1, a2) caused by the Bell-state basis measurement on the qubit pair (b2, t), and denote the amplitude and phase parameters of the collapsed state, which are specifically expressed as:

[0110]

[0111]

[0112] It is not difficult to see that the Bell-state basis measurement by Bob completely destroys the quantum channel connecting Anne and Bob, and the quantum information hidden in qubit t is completely transmitted to the composite state of qubits (a1, a2, c). At this time, the quantum state of the entire system evolves into:

[0113]

[0114] wherein, denotes the possible measurement outcomes of the Bell-state basis measurement on the qubit pair (b2, t), denotes the corresponding collapsed state of the rest of the system qubits (c, a1, a2). Specifically, when the Bell-state basis measurement result of Bob is , then the rest of the system qubits (c, a1, a2) correspondingly collapse into or When the Bell-state basis measurement result of Bob is , then the rest of the system qubits (c, a1, a2) correspondingly collapse into or When the Bell-state basis measurement result of Bob is , then the rest of the system qubits (c, a1, a2) correspondingly collapse into or When the Bell-state basis measurement result of Bob is , then the rest of the system qubits (c, a1, a2) correspondingly collapse into or

[0115] Step S-3: Bob announces his Bell state measurement result to Anne by sending two classical bits of information (m, n).

[0116] Bob and Anne have agreed beforehand that the two classical bits of information (m, n) correspond to the Bell state measurement result

[0117] This step establishes a classical communication channel, enabling Bob to pass his measurement result to Anne. The classical information (m, n) is crucial for Anne's subsequent operations, but with only this information, Anne cannot obtain the complete quantum state. Similarly, without this classical information, Anne cannot correctly perform subsequent operations. This mutual dependence of quantum information and classical information is another embodiment of the security mechanism of the present invention.

[0118] Second stage: Precise recovery of target quantum state (see the accompanying drawings Figure 4 ).

[0119] This stage of operation is implemented by the target quantum operation performer Anne, and its technical core lies in using the quantum bit resources deployed by Anne's network nodes and the received classical information to perform a corresponding sequence of quantum operations to complete the precise reconstruction of the target quantum information. The operation process mainly includes:

[0120] The operation performer performs single-qubit gate operations on quantum bits a1 and a2 to change the computational basis of the quantum bits;

[0121] The operation performer performs a controlled-NOT gate operation on its quantum bit pair (a1, a2) to evolve the quantum channel state into a form more suitable for target operations;

[0122] The operation performer performs a corresponding Pauli operation on its quantum bit a3 to reconstruct the target quantum state on the quantum bits.

[0123] The specific operation steps and technical features of this stage are as follows:

[0124] Step S-4: Anne performs a Hadamard gate operation on her quantum bits a1 and a2, respectively

[0125] The Hadamard gate operator is defined as: where σ (0,1) = |0><1| + |1><0|, σ (1,1)|0><0|-|1><1| are two different Pauli operations. The Hadamard gate operation is a basic gate operation in quantum communication and quantum computation, which can transform the computational basis state into the orthogonal basis state, and vice versa. In the present application, this operation transforms the quantum state between the computational basis and the orthogonal basis, and prepares for the subsequent quantum operation. Physically, it is equivalent to performing rotation on the quantum bit, which changes the representation basis vector of the quantum state.

[0126] After Anne's operation, the quantum channel state evolves into:

[0127]

[0128] where, is the characteristic representation of the evolved quantum state of the quantum bit system (c, a1, a2) after Anne's two Hadamard gate operations, respectively represent the Hadamard gate operation on quantum bits a1, a2.

[0129] Step S-5: Anne performs a controlled NOT gate operation

[0130] The controlled NOT gate operator is defined as that is, when the quantum state of quantum bit a2 is |0>, the operation σ (0,0) is performed on quantum bit a1, and when the quantum state of quantum bit a2 is |1>, the operation σ (0,1) is performed on quantum bit a1; where σ (0,0) = |0><0| + |1><1| and σ (0,1) = |0><1| + |1><0| represent the unit operation and a Pauli operation, respectively. The controlled NOT gate is a basic two-qubit entanglement operation, which evolves the quantum channel state into a form more suitable for target operations. In the present application, this operation establishes a specific correlation between quantum bits a1 and a2, and prepares for the subsequent Bell state measurement. From the perspective of quantum information, this step adjusts the entanglement structure of the quantum system and optimizes the information transmission path.

[0131] The controlled NOT gate operation changes the quantum channel state into:

[0132]

[0133] where, is the characteristic representation of the evolved quantum state of the quantum bit system (c, a1, a2) after Anne's two Hadamard gate operations, After the action, the characteristic expression of the state evolution of the quantum bit system (c, a1, a2). At this point, the quantum channel state evolves into two direct product states, and the initial quantum information part of the quantum bit t has been completely transmitted to Anne's quantum bit a2. Subsequently, according to the classical information (m, n) sent by Bob, Anne can successfully reconstruct the quantum state of the target quantum bit t on her own quantum bit a2 by performing appropriate operations.

[0134] Step S-6: Anne performs a corresponding dynamic correction operation on her quantum bit a2

[0135] The dynamic correction operation here is a set of basic single quantum bit unitary operations, including wherein, denotes the inverse operation of the unit operation, and denote the inverse operations of the three different Pauli operations respectively. The specific dynamic recovery operation to be performed depends on the classical information (m, n) sent by Bob. The purpose of this step is to accurately reconstruct the initial target quantum state |ζ> on Anne's quantum bit a2, in preparation for performing the target operation.

[0136] After Anne's dynamic correction operation, the state evolution of the quantum bit group (a1, a2, c) is:

[0137]

[0138] wherein, is the characteristic expression of the state evolution of the quantum bit group (a1, a2, c) after Anne's dynamic correction operation, denotes the single quantum bit unitary operation performed on quantum bit a2 denotes a mathematical representation of the characteristic expression. denotes the single quantum bit unitary operation performed on quantum bit c denotes that at this time the target quantum state |ζ> has been reconstructed on quantum bit a2.

[0139] Third stage: target quantum operation execution and induced quantum state teleportation (see the description accompanying Figure 5 ).

[0140] This stage operation is still implemented by the target quantum operation execution party Anne, and its technical core lies in completing the target quantum operation execution and inducing the teleportation of quantum state information; its operation process mainly includes:

[0141] The operation executor executes a target quantum operation on its quantum bit a2 to obtain an induced quantum state, and realizes remote operation on the target quantum state;

[0142] The operation executor performs Bell state basis measurement on its quantum bit pair (a1, a2) to realize information decomposition of the target operation induced quantum state, and synchronously obtains classical correlation information representing characteristics of the induced state through quantum entanglement characteristics, and non-local transmits quantum information of the induced state to the receiving agent;

[0143] The operation executor completes the third stage of information transmission by sending 2-bit classical information to the receiving agent to announce the measurement result, but at this time the receiving agent cannot independently obtain the information of the target operation induced quantum state.

[0144] The specific operation steps and technical features of this stage are as follows:

[0145] Step S-7: Anne executes a target quantum operation on her quantum bit a2.

[0146] This is the key step of the entire method. After Anne's operation, the target quantum operation acts on the target quantum state |ζ> to construct the induced quantum state However, at this time it only resides on quantum bit a2, not on the quantum bit of any remote agent, so further operations are needed to successfully share the target operation induced quantum state by the two agents according to the controllable quantum operation target. That is, the next task is to non-local transmit the target operation induced quantum state to the quantum bit of the receiving agent.

[0147] Step S-8: Anne measures her quantum bit pair (a1, a2) with a Bell state basis.

[0148] Note that before Anne's measurement, the quantum state of the remaining quantum bit system (a1, a2, c) is:

[0149]

[0150] where, represents the characteristic expression of the quantum bit system (a1, a2, c) state before Anne's Bell state measurement, represents the entangled state expression of the quantum bit pair (a1, c) at this time, represents the target quantum operation of Anne acting on the reconstructed target quantum state |ζ> of quantum bit a2 to obtain the target operation induced quantum state.

[0151] In fact, in the Bell basis framework, this quantum state can be rewritten as

[0152]

[0153] where, denotes the possible measurement results of Anne's Bell basis measurement on her quantum bit pair (a1, a2), |Υ i,j,l > c denotes the collapsed state of quantum bit c corresponding to Anne's Bell basis measurement, which can be expressed as:

[0154]

[0155] where, and respectively constitute part of the quantum state of quantum bit c at this time, where the quantum information part is exactly the same as the target operation-induced state, part is a single-qubit unitary operation. From the above formula, it is easy to see that Anne's Bell basis measurement causes quantum bit c to also collapse, and the correspondence between Anne's measurement results and the collapsed state is Note that the state of quantum bit c at this time is not only related to l, but also related to i and j. Therefore, only by knowing the exact value of (i, j, l) can Chris reconstruct the target operation-induced quantum state

[0156] This step is similar to the Bell basis measurement performed by Bob in the first stage, which aims to transfer the quantum information on a2, i.e., the result of the target operation to quantum bit c held by Chris through quantum teleportation. This measurement causes the quantum information and classical information to be separated again, and Anne's measurement results will affect the quantum state that Chris eventually obtains.

[0157] Step S-9: Anne announces her measurement results to Chris by sending 2-bit classical information (i, j).

[0158] Similar to step S-3, this step establishes a classical communication channel between Anne and Chris. The classical information (i, j) is necessary for Chris to perform the recovery operation in the fourth stage. It should be noted that even if Chris receives Anne's classical information, he cannot independently complete the output of the target operation-induced quantum state, because the complete representation of the collapsed state of quantum bit c at Chris's network node at this time also depends on the classical correlation information possessed by the information controller Bob.

[0159] Fourth stage: target operation induces controlled output of quantum state (see description of the figure 2) Figure 6 ).

[0160] This stage operation is jointly implemented by information controller Bob and receiving agent Chris, the core of its technology is to ensure that only through cooperation can the quantum task be completed, thereby ensuring the security of quantum information; its operation process mainly includes:

[0161] Information controller decides whether to continue or terminate the operation;

[0162] Information controller sends the single-qubit measurement result in step S-1 to receiving agent;

[0163] Receiving agent performs dynamic transformation operation on the quantum bit c it holds Finally, the controllable remote execution of the target quantum operation is realized.

[0164] The specific operation steps and technical features of this stage are as follows:

[0165] Step S-10: Bob decides whether to perform information transmission.

[0166] Based on the preset security assistance condition, Bob decides whether to assist Chris in obtaining all the information of the target operation induced quantum state. If yes, Bob performs the next step of information transmission operation; otherwise, the process is terminated.

[0167] Step S-11: Bob tells Chris his measurement result by sending a 1-bit classical information (1).

[0168] This step establishes a classical communication channel between Bob and Chris. Bob sends the single-qubit measurement result he obtained in step S-1 to Chris. Bob and Chris agree in advance that the classical information (1) corresponds to the measurement result |l> of Bob's quantum bit b1, and this information is one of the necessary conditions for Chris to perform the correct dynamic transformation operation, which embodies the characteristic that information controller and receiving agent must cooperate to recover the complete information.

[0169] Step S-12: According to the classical information of Anne and Bob, Chris performs the corresponding dynamic transformation operation on his quantum bit c

[0170] Chris's dynamic transformation operation is parameterized and uniquely determined by the Pauli operator The implementation is entirely dependent on the accuracy of the classical information (i, j) provided by Anne and the authorized key (l) passed by Bob. This design highlights the necessity of three-party (Anne-Bob-Chris) collaborative quantum operations. From the perspective of quantum information theory, this process is essentially the conversion of Chris's quantum bit state into the final result of the target operation acting on the target quantum state through the optimal local unitary operation.

[0171] Dynamic transformation operation performed by Chris Convert the quantum bit c state to:

[0172]

[0173] where, represents the single-qubit unitary operation ; and represents the quantum state |Υ i,j,l > on which this inverse operation is applied to the quantum bit c; according to the principles of quantum mechanics, After Chris completes the above dynamic transformation operation, Anne's single-qubit arbitrary target operation has been successfully executed on Chris's quantum bit c, and the output is exactly the target operation-induced quantum state This marks the completion of the designed controllable remote single-qubit arbitrary target operation process of the invention. Thus, based on shared entangled resources, combined with quantum local operations and classical communication, the invention has achieved the controllable remote execution of arbitrary single-qubit target operations in a deterministic manner. The completion of this quantum task not only accurately realizes the expected quantum information processing goal, but also builds an efficient and reliable remote quantum control system through rigorous theoretical design and technical implementation.

[0174] Based on the above example framework, we now quantize the key parameters to provide more specific technical implementation details. In the example, Anne, as the central node, has the right to execute the target quantum operation U = R Z (π / 3)·H. In this target quantum operation, H represents a Hadamard gate operation, and R Z (π / 3) represents a π / 3 radian rotation operation around the Z axis of the Bloch sphere, i.e., a Hadamard gate operation followed by a π / 3 radian rotation operation around the Z axis of the Bloch sphere. Bob and Chris, as two remote receiving terminals, need to collaborate to jointly output the target quantum operation U = R Z(π / 3)·H and acts on their target quantum state. The initial target quantum state |ζ> is stored in Bob's qubit; the five-qubit cluster state is distributed among the three parties in the manner described earlier. The operational flow according to the present application is executed as follows:

[0175] 1. Bob performs a single-qubit measurement and encodes the measurement result, generating a channel access authorization key l = 0;

[0176] 2. Bob performs a Bell state measurement, obtaining a classical information result (m, n) = (0, 1), and sends it to Anne;

[0177] 3. Anne performs a corresponding sequence of quantum operations, including Hadamard gate operations, controlled NOT gate operations, dynamic recovery operations Target quantum operation U = R Z (π / 3)·H and Bell state measurement, obtaining a classical information result (i, j) = (1, 0), and sending it to Chris;

[0178] 4. Bob decides whether to authorize the receiving proxy party to output the target operation-induced quantum state;

[0179] 5. Bob sends the channel access authorization key l = 0 to Chris;

[0180] 6. Chris performs a dynamic transformation operation

[0181] Finally, the target operation U = R is successfully implemented on Chris's qubit Z remote execution of (π / 3)·H.

[0182] The security of the present application is based on the following aspects:

[0183] (1) Quantum information and classical information are divided into multiple parts and distributed among different participants. Any single participant cannot obtain complete information alone.

[0184] (2) Only when all participants cooperate according to the specified protocol can the quantum task be completed. This ensures that even if some participants are dishonest, they cannot individually steal or leak quantum information.

[0185] (3) Quantum measurement leads to the collapse of quantum states, and once the measurement is completed, part of the original quantum state information is lost. This irreversibility provides a physical layer of security for information security.

[0186] (4) Only quantum resources are not enough, the correct classical information is also important for the successful implementation of remote quantum operation. The security mechanism of this quantum-classical hybrid increases the security of the system.

[0187] The target quantum operation realized by the present application can be used as a key to remotely activate or drive some important collective actions, such as multi-level joint control or launch of quantum missiles in the military field, multi-battlefield synchronous encryption or decryption of quantum communication networks, multi-unit cooperative activation or dormancy of quantum defense systems; multi-party joint sealing or disassembly of quantum contracts in the commercial field, multi-platform synchronous execution or revocation of quantum transactions, multi-agency cooperative authorization or revocation of quantum intellectual property rights; multi-bank joint activation or freezing of quantum currencies in the financial field, multi-country real-time clearing or interception of quantum payment systems, multi-market intelligent triggering or termination of quantum investment strategies; multi-department joint start or pause of quantum production lines in the industrial field, multi-node cooperative optimization or interruption of quantum supply chains, multi-region intelligent allocation or isolation of quantum energy networks, etc.

[0188] From the practical point of view, the core quantum operation and measurement techniques used in the present application have been realized and applied in the experimental platforms of various quantum systems, which provides sufficient technical support for the practical operability of the method. Specifically, the double-qubit controlled-NOT operation, the Pauli operation, the Hadamard gate operation, and the single-qubit projection measurement and Bell state joint measurement techniques involved in the present application not only have clear corresponding in various quantum system theoretical models, but also have been verified and applied in ion trap system, optical integrated circuit system, cavity QED system and superconducting quantum circuit system, etc. a variety of representative quantum system experimental platforms.

[0189] Ion trap system for its high coherence and controllability, optical system for its fast operation speed and low noise characteristics, and cavity QED system for its strong coupling characteristics, and superconducting quantum circuit system for its high integration and strong expansion and fast control characteristics, all of which make the experimental implementation of the present application possible. In addition, the five-qubit cluster state used to construct the quantum channel in the present method can be prepared in many ways in experiments. The maturity and development of these experimental techniques provide a solid foundation for the experimental implementation of the present method.

[0190] In summary, the present application provides a method for controllable remote execution of single-qubit arbitrary target quantum operation based on five-qubit cluster state, which utilizes the sharing mechanism of quantum information to ensure the safe transmission of quantum information, and has the advantages of efficient use of quantum resources, strong universality and realization of certainty, and has a wide application prospect in the field of quantum information processing such as quantum communication, quantum computing and quantum cryptography. Its typical application scenarios include but are not limited to national security field, financial security field, commercial secret field and industrial control field. Since the measurement and operation of quantum state are relatively mature technologies, the present application is applicable to various quantum communication and computing platforms such as superconducting quantum circuit, ion trap, optical integrated circuit and cavity QED.

[0191] Figures 2-6 The dashed box is used to define the local spatial distribution of the three user nodes; the solid line channel constitutes a classical communication link, and the arrow identifies the transmission path of classical information; the dot represents a quantum bit entity; the square corresponds to a single-qubit measurement device, the rectangle represents a Bell state measurement device; the triangle marks a single-qubit target operation; the ellipse represents a controlled non-gate operation; the dashed and solid circles represent Pauli operations and single-qubit Hadamard gate operations, respectively; the operation units on each quantum bit are implemented in the order of layer-by-layer expansion from inside to outside.

[0192] The above describes the embodiments of the present application, but the embodiments are not limited to the specific implementation described above, which is only illustrative and not restrictive. Those skilled in the art can make more forms of equivalent embodiments under the inspiration of the embodiments, which are all within the protection scope of the embodiments.

Claims

1. A method for controllably performing a single qubit arbitrary target quantum operation remotely, characterized in that, The application relates to a quantum information processing method and device. The quantum channel construction comprises using a one-dimensional five-quantum-bit cluster state as a quantum channel, wherein quantum bit 3 and 5 are allocated to a target operation execution party, quantum bit 1 and 4 are allocated to an information control party, and quantum bit 2 is allocated to a receiving agent party; the distributed storage of the entangled resource enables quantum information to be securely transmitted among the three parties, and provides optimized quantum channel support for controllable execution of remote quantum operation; a target quantum state is loaded to quantum bit t of the information control party; The quantum information processing comprises a first stage, a second stage, a third stage and a fourth stage. In the first stage, target quantum state transmission and channel access authorization key generation: the information control party firstly performs single quantum bit computational basis measurement and Bell state basis measurement, obtains the channel control right, and associates the amplitude and phase parameter information of the target quantum state to the entangled quantum bit system of the operation execution party and the receiving agent party; then the Bell state measurement result is sent to the target operation execution party to help the target operation execution party to reconstruct the target quantum state; the single quantum bit computational basis measurement result is reserved as an authorization key for subsequent control of the receiving agent party; In the second stage, target quantum state accurate recovery: the operation execution party performs a preset quantum operation sequence and dynamic correction operation according to the classical information feedback, and realizes remote accurate recovery of the target quantum state; the preset quantum operation sequence comprises a Hadamard gate operation and a double quantum bit CNOT gate operation; In the third stage, target quantum operation execution and induced quantum state teleportation: the operation execution party firstly implements target quantum operation on the reconstructed target quantum state to prepare an induced quantum state; then performs Bell state basis joint measurement to teleport the quantum information part of the target operation induced state to the quantum bit of the receiving agent party; finally, the measurement result is transmitted through a classical channel; it is worth noting that although the whole information of the target operation induced quantum state has been transmitted through entanglement association and classical communication, the receiving agent party cannot accurately reconstruct the target operation induced quantum state without the channel access authorization key; the quantum information part comprises amplitude and phase; In the fourth stage, controlled output of the target operation induced quantum state: the information control party, as an authorized subject, has the decision-making right of target output state reconstruction; when the authorization permission is given, the information control party transmits the channel access authorization key to the receiving agent party through the classical channel, and the receiving agent party can accurately reconstruct the target operation induced state by performing corresponding dynamic transformation operation based on the key; if the authorization is denied, the task is automatically terminated; the mechanism shows that the accurate reconstruction of the target operation induced quantum state is essentially controlled by the authorization decision of the information control party.

2. The method of claim 1, wherein, The expression of the five-quantum-bit cluster state is as follows: where |C V > 12345 denotes the five-qubit cluster state characteristic expression, the subscript marks different qubits; |0> and |1> denote two mutually orthogonal standard computational basis state vectors in quantum information, which can correspond to specific states of a quantum physical system, such as representing the electron spin upward |↑> and spin downward |↓> states in an electron spin system, respectively, or corresponding to the photon horizontal polarization |H> and vertical polarization |V> states in an optical system, respectively, or representing two different atomic energy levels in a superconducting quantum circuit system; Π denotes the product symbol; σ (1,1) = |0><0|-|1><1| is a Pauli operation, the subscript k = 1, …, 5, L generally refers to the qubit label on which the Pauli operation acts; σ (1,1) denotes the computational symbol, which is defined as σ (1,1) = 1; the target quantum state is an arbitrary single-qubit state.

3. The method of claim 1, wherein, The first stage operation comprises the following steps: S I -1: the information controller performs a single-qubit computational basis measurement on its qubit 1; the measurement result directly correlates to the specific form of the quantum channel state collapse, constituting the authorization key for the subsequent docking with the receiving agent's control; S I -2: the information controller performs a joint Bell state basis measurement on its qubits 4 and the target qubit t; this measurement implements quantum-classical information separation of the target quantum state, with the quantum information component having been teleported onto the operator's qubits and the classical information component being the Bell state basis measurement result; S I -3: The information controller encodes his Bell state basis measurement result into 2 bits of classical information and transmits it to the operation performer via a classical channel.

4. The method of claim 3, wherein, The single quantum bit computational basis is composed of two standard state vectors {0>, 1>}, while the Bell state basis is composed of four mutually orthogonal and complete two quantum bit state vectors {|B 0,0 >,|B 0,1 >, B 1,0 >, B 1,1}. The authorization key of the information control party is associated with the computational basis measurement result of quantum bit 1, and the corresponding relationship is as follows: The corresponding relationship between the Bell state basis measurement result of the information control party and the 2-bit classical information coding is as follows: Information controller's single qubit computational basis measurement result |l> (l = 0, 1) Authorized key l; The second stage operation comprises the following steps: Bell state basis measurement result |B of the information controller m,n (m, n = 0, 1) 2-bit classical information encoding (m, n).

5. The method of claim 1, wherein, ​ S II -1: The operation executor respectively implements single-qubit Hadamard gate operations on its qubits 3 and 5; the operations transform the computational basis states {|0>, |1>} into the orthogonal basis states {|+>, |-}>; S II -2: The operation executor performs a two-qubit CNOT gate operation on its qubits 3 and 5, further optimizing the quantum channel by reforming the entanglement correlation to a configuration that fits the needs of the target operation; the two-qubit CNOT gate operation contains qubit 5 as the master qubit and qubit 3 as the controlled qubit; S II -3: The operation performer implements a dynamic correction operation on its qubits 5.

6. The method of controllably performing a single qubit arbitrary target quantum operation at a remote location according to claim 5, wherein, The single quantum bit Hadamard gate quantum operator is defined as: where H denotes the Hadamard gate operator characteristic representation, σ (0,1) = |0><1| + |1><0| and σ (1,1) = |0><0| - |1><1| are two Pauli operations, respectively. The expression of the orthogonal ground state is: and The two quantum bit CNOT gate operator is: N x，y =|0> x <0|②σ y (0，0) +|1> x <1|②σ y (0，1) ; where the qubit x is the control qubit; the qubit y is the target qubit; and σ (0,0) = |0><0| + |1><1| and σ (0,1) = |0><1| + |1><0| represent the identity operation and a Pauli operation, respectively. The dynamic correction operation is associated with the 2-bit classical information sent by the information controller, and the corresponding relationship is: 2 bits of classical information (m, n) delivered by the information controller Dynamic correction operation 7. The method of claim 1, wherein, The third stage operation includes the following steps: S III -1: the operation performer executes the target quantum operation on its qubits 5; at this point the target operation-induced state has been generated, but it still needs to be teleported to the receiving proxy by the operation; S III -2: The operation executor performs joint Bell state basis measurement on its qubits 3 and 5, causing the target operation to induce state-correlated quantum information to be non-locally transmitted via the entanglement channel to the qubits of the receiving proxy. S III -3: The operation executor encodes his Bell state basis measurement result as 2-bit classical information and transmits it to the receiving agent through the classical channel; at this time, although the receiving agent has collected the quantum information and classical information of the target operation-induced state correlation at the same time, it still cannot successfully output it due to the lack of channel access authorization key from the information controller.

8. The method of claim 1, wherein, The fourth stage operation includes the following steps: S IV -1: The information controller decides whether to authorize the receiving agent to reconstruct the target operation-induced quantum state; if authorization is decided, the next step is performed; if authorization is refused, the task is automatically terminated. S IV -2: The information controller passes the authorization key to the receiving agent over a classical channel; S IV -3: The receiving agent performs a dynamic transformation operation on its qubits 2, reconstructing the target operation-induced quantum state, enabling the target operation to act on the remote target quantum state under the authorization of the information controller and ultimately completing the output on the receiving agent's qubits.

9. The method of claim 8, wherein, The dynamic conversion operation is not only associated with the 2-bit classical information transmitted by the operation executor, but also associated with the authorization key transmitted by the information controller, and the corresponding relationship between them is:

10. The method of claim 9, wherein the method is controllable to remotely perform a single qubit arbitrary target quantum operation. By splitting the quantum state information into multiple sub-information, each receiver can only obtain one part; The information controller and the receiving agent are equivalent to the target operation receiving team. Only when the team members cooperate with each other can they obtain safe and complete quantum-classical receiving information, so as to accurately reconstruct the target output state on their quantum bit. Even if part of the members in the team are dishonest, they cannot steal or leak the secret quantum information alone.

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