Quantum communication method and quantum communication system

Abstract

The application provides a quantum communication method and a quantum communication system, the method comprising: in the case that a quantum transmitter transmits quantum information, encoding the quantum information by using a first invariant quantum neural network to obtain encoded quantum information, wherein the quantum information is generated according to to-be-transmitted information transmitted by the quantum transmitter, and the first invariant quantum neural network is generated based on an invariant gate set generated based on a symmetric group and a quantum channel containing parameters; transmitting the encoded quantum information by using a quantum channel, decoding the transmitted quantum information by using a second invariant quantum neural network to obtain decoded quantum information; and processing the decoded quantum information by using a quantum receiver to obtain the to-be-transmitted information.

Description

Technical Field

[0001] This invention relates to the field of quantum communication technology, and more specifically, to a quantum communication method and a quantum communication system. Background Technology

[0002] In recent years, quantum technology has developed rapidly, with quantum communication being one of the most important research directions. Similar to classical communication, quantum communication transmits information from a source to a destination through a transmission channel. However, the difference lies in the transmission medium: the quantum channel is the transmission medium itself, and the content transmitted within it is a quantum state. The concept of quantum communication was proposed long ago, with applications such as quantum teleportation, quantum encrypted communication, and quantum key distribution. These technologies utilize special properties of quantum mechanics to achieve more secure and efficient communication methods. Quantum channel coding refers to the process of encoding the quantum information transmission channel in quantum communication. Unlike classical communication, the information transmitted in quantum communication is no longer quantum information composed of classical bits, but rather quantum information composed of qubits (also known as quantum states). Therefore, specific encoding methods are required to protect and transmit these quantum states.

[0003] However, existing variational quantum algorithms have certain limitations in solving quantum channel coding problems, and their coding performance and fidelity are unsatisfactory. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide a quantum communication method and a quantum communication system.

[0005] One aspect of this invention provides a quantum communication method, comprising:

[0006] When quantum information is transmitted at a quantum transmitter, the quantum information is encoded using a first invariant quantum neural network to obtain encoded quantum information. The quantum information is generated based on the information to be transmitted transmitted by the quantum transmitter, and the first invariant quantum neural network is generated based on an invariant gate set generated based on a symmetric group and a parameterized quantum channel.

[0007] The encoded quantum information is transmitted using a quantum channel, and the transmitted quantum information is decoded using a second invariant quantum neural network to obtain the decoded quantum information.

[0008] The decoded quantum information is processed using a quantum receiver to obtain the information to be transmitted.

[0009] According to an embodiment of the present invention, either the first invariant quantum neural network or the second invariant quantum neural network is trained in the following manner:

[0010] The set of basic gates is processed using the equivalent transformation method to obtain the above-mentioned invariant gate set, wherein the above-mentioned basic gate set includes multiple basic gates;

[0011] Based on the above set of invariant gates and the above parameterized quantum channel, an initial quantum neural network is generated;

[0012] The initial quantum neural network is iteratively updated using the gradient descent algorithm to obtain the invariant quantum neural network.

[0013] According to an embodiment of the present invention, the set of basic gates is processed using an equivalent transformation method to obtain the aforementioned set of invariant gates, including:

[0014] The Twilring method is used to transform each of the above basic gates into elements that satisfy the invariance of the above symmetry group, resulting in multiple initial invariant gates;

[0015] By merging multiple initial invariant gates as described above, multiple target invariant gates are obtained.

[0016] Based on multiple objective invariant gates, generate the set of invariant gates mentioned above.

[0017] According to an embodiment of the present invention, the above-described initial invariant gate The calculation is as follows:

[0018]

[0019] Among them, U k It is a symmetric group The k-th element is represented by the unitary matrix in the Hilbert space where the quantum circuit resides, g i Let N be the i-th basic gate, and N be the symmetry group. The number of elements.

[0020] According to an embodiment of the present invention, an initial quantum neural network is generated based on the above-described set of invariant gates and the above-described parameterized quantum channel, comprising:

[0021] Generate Hermitian and unitary operators based on the above set of invariant gates;

[0022] Based on the Hermitian operator, the unitary operator, and the initial parameterized quantum circuit described above, generate the target quantum circuit;

[0023] Based on the aforementioned target quantum circuit and parameter control noise, a parameterized quantum channel is generated.

[0024] Based on the aforementioned parameterized quantum channel, the aforementioned initial quantum neural network is generated.

[0025] According to an embodiment of the present invention, the above-mentioned set of invariant gates is: in, For the objective-invariant gate, the Hermitian operator and the unitary operator are V, respectively. j and W j The target quantum circuit U(θ) is shown in the first formula below, and the initial quantum neural network is shown in the second formula below:

[0026]

[0027] Where θ is the control parameter. The parameter control noise is used for the j-th layer in the initial quantum neural network.

[0028] According to an embodiment of the present invention, the parameter control noise is shown in the first formula below, and the parameter control noise includes bit flip noise, phase flip noise, and depolarization noise, and the bit flip noise is shown in the second formula below:

[0029]

[0030] Among them, V l Let p be the Hermitian operator, p be the control parameter for bit-flipping noise, ρ be an arbitrary single-bit quantum state, I be the identity matrix, and X be the Pauli-X matrix.

[0031] According to an embodiment of the present invention, the initial quantum neural network described above is iteratively updated using a gradient descent algorithm to obtain the invariant quantum neural network described above, comprising:

[0032] Based on the initial quantum neural network and the target quantum channel described above, an intermediate quantum neural network is generated;

[0033] The target loss value is obtained by calculating the above intermediate quantum neural network using the target loss function;

[0034] The target loss value and control parameters are iteratively processed using the gradient descent algorithm described above to obtain the updated control parameters;

[0035] Based on the updated control parameters and the intermediate quantum neural network, the invariant quantum neural network is generated.

[0036] According to an embodiment of the present invention, the target loss function is as follows:

[0037]

[0038] Where ψ represents a quantum pure state, For intermediate quantum neural networks, θ d and θ e These are control parameters.

[0039] Another aspect of the present invention provides a quantum communication system, comprising:

[0040] A quantum transmitter is used to generate quantum information based on the information to be transmitted.

[0041] A channel coding device is used to encode the quantum information using a first invariant quantum neural network when the quantum information is transmitted at the quantum transmitter to obtain encoded quantum information. The first invariant quantum neural network is generated based on an invariant gate set generated by a symmetric group and a parameterized quantum channel.

[0042] A quantum channel is used to transmit the encoded quantum information to a channel decoding device.

[0043] The aforementioned channel decoding device is used to decode the transmitted quantum information using a second invariant quantum neural network to obtain the decoded quantum information.

[0044] The quantum receiver is used to process the decoded quantum information to obtain the information to be transmitted.

[0045] According to embodiments of the present invention, the structure of an invariant quantum neural network is optimized using symmetry groups. Under the condition of good symmetry, the complexity of the quantum gates and the number of control parameters used in the network can be greatly reduced, thereby improving the encoding effect in the quantum communication process and thus improving the fidelity of quantum communication. Attached Figure Description

[0046] The above and other objects, features and advantages of the present invention will become more apparent from the following description of embodiments of the invention with reference to the accompanying drawings, in which:

[0047] Figure 1 A flowchart of a quantum communication method according to an embodiment of the present invention is shown;

[0048] Figure 2 A schematic diagram illustrating the generation of an invariant quantum neural network according to an embodiment of the present invention is shown;

[0049] Figure 3 A schematic diagram of a quantum communication system according to an embodiment of the present invention is shown. Detailed Implementation

[0050] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the invention. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the invention for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0051] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0052] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0053] When using expressions such as "at least one of A, B, and C", they should generally be interpreted in accordance with the meaning that is commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B, and C, etc.).

[0054] Figure 1 A flowchart of a quantum communication method according to an embodiment of the present invention is shown.

[0055] According to embodiments of the present invention, such as Figure 1 As shown, the quantum communication method includes operations S101 to S103.

[0056] In operation S101, when quantum information is transmitted at the quantum transmitter, the quantum information is encoded using the first invariant quantum neural network to obtain the encoded quantum information. The quantum information is generated based on the information to be transmitted from the quantum transmitter, and the first invariant quantum neural network is generated based on the invariant gate set generated based on the symmetry group and the parameterized quantum channel.

[0057] In operation S102, the encoded quantum information is transmitted using a quantum channel, and the transmitted quantum information is decoded using a second invariant quantum neural network to obtain the decoded quantum information.

[0058] In operation S103, the decoded quantum information is processed by the quantum receiver to obtain the information to be transmitted.

[0059] According to an embodiment of the present invention, in the process of quantum channel coding, the channel coding operation and the channel decoding can be regarded as two quantum operations. The purpose of quantum channel coding is to make these two quantum operations and the channel together constitute an identity channel id (i.e., without changing the state of the input quantum state).

[0060] According to an embodiment of the present invention, the quantum state transmitted by the information source Alice (i.e., the quantum transmitter) is first encoded through the channel to obtain a new quantum state, and then the quantum information is transmitted through the quantum channel. The information receiver Bob (i.e., the quantum receiver) will perform channel decoding operation on the quantum state through the quantum channel to obtain the final quantum state information, i.e. the information to be transmitted.

[0061] Figure 2 A schematic diagram illustrating the generation of an invariant quantum neural network according to an embodiment of the present invention is shown.

[0062] According to embodiments of the present invention, such as Figure 2 As shown, either the first invariant quantum neural network or the second invariant quantum neural network is trained in the following way:

[0063] The set of basic gates is processed using the equivalent transformation method to obtain the set of invariant gates, where the set of basic gates includes multiple basic gates;

[0064] Generate an initial quantum neural network based on the invariant gate set and the parameterized quantum channel;

[0065] The initial quantum neural network is iteratively updated using the gradient descent algorithm to obtain an invariant quantum neural network.

[0066] According to an embodiment of the present invention, the basic components of a quantum neural network are Hermitian operators and unitary operators as shown in formulas (1) and (2). The set of these basic components is called the set of basic gates. Basic gate g n It can be a Pauli door or other door operation.

[0067] According to an embodiment of the present invention, after obtaining the basic gate set, the invariant gate set is obtained using the following method.

[0068] According to embodiments of the present invention, such as Figure 2 As shown, by processing the set of basic gates using the equivalent transformation method, we obtain the set of invariant gates, including:

[0069] The Twilring method is used to transform each basic gate into an element that satisfies the invariance of the symmetry group, resulting in multiple initial invariant gates. Among them, the initial invariant gate The calculation is shown in formula (1):

[0070]

[0071] Among them, U k It is a symmetric group The k-th element is represented by the unitary matrix in the Hilbert space where the quantum circuit resides, g i Let N be the i-th basic gate, and N be the symmetry group. The number of elements;

[0072] Multiple initial invariant gates are merged to obtain multiple target invariant gates;

[0073] Generate a set of invariant gates based on multiple objective invariant gates.

[0074] According to an embodiment of the present invention, a new set of gates is constructed. Merging identical elements in the set forms an invariant gate set. in, The target invariant gate is then used. Subsequently, based on the set of invariant gates and the parameterized quantum channel, an initial quantum neural network is generated.

[0075] The specific method for generating the initial quantum neural network is as follows:

[0076] Generate Hermitian operators V based on the invariant gate set. j Heyou Calculator W j ;

[0077] Based on the Hermitian operator, the unitary operator, and the initial parameterized quantum channel, the target quantum circuit is generated, where the target quantum circuit U(θ) is as shown in formula (2):

[0078]

[0079] Based on the target quantum circuit and parameter control noise, an initial quantum neural network is generated, as shown in formula (3):

[0080]

[0081] Where θ is the control parameter. The parameter control noise is used for the j-th layer in the initial quantum neural network.

[0082] According to an embodiment of the present invention, the target quantum circuit U(θ) is a unitary operator controlled by a series of parameters θ, possessing the desirable property of reversibility. However, such operations also have certain limitations. For example, if the initial state is a quantum pure state, a mixed state cannot be prepared through a neural network of this structure, thus this structure cannot accomplish the task of preparing a thermal state. A more general quantum operation is a completely positive definite and trace-preserving (CPTP) operation. Most existing methods use the addition of auxiliary bits to complete a local CPTP operation, but this method requires additional auxiliary bits, which is unacceptable when existing quantum bit resources are scarce.

[0083] According to an embodiment of the present invention, the present invention constructs a parameter-controlled CPTP operation through formula (3) without the need to use additional auxiliary bits.

[0084] According to an embodiment of the present invention, the parameter control noise is as shown in formula (4), and the parameter control noise includes bit flip noise, phase flip noise, and depolarization noise. The bit flip noise is as shown in formula (5):

[0085]

[0086] Among them, V l Let M be the Hermitian operator, p be the number of unitary operators in the hybrid unitary quantum channel, p be the control parameter for bit-flipping noise, ρ be an arbitrary single-bit quantum state, I be the identity matrix, and X be the Pauli-X matrix.

[0087] According to an embodiment of the present invention, during the channel coding process, a first invariant quantum neural network is used to encode quantum information to obtain encoded quantum information, wherein... It is a group (i.e., a symmetric group) formed by the symmetries satisfied by the channel, as shown in formula (6):

[0088]

[0089] in, For the target quantum channel.

[0090] According to embodiments of the present invention, such as Figure 2 As shown, the gradient descent algorithm is used to iteratively update the initial quantum neural network to obtain an invariant quantum neural network, including:

[0091] Based on the initial quantum neural network and the target quantum channel, an intermediate quantum neural network is generated;

[0092] The target loss value is obtained by calculating the intermediate quantum neural network using the target loss function;

[0093] The gradient descent algorithm is used to iteratively process the target loss value and control parameters to obtain the updated control parameters;

[0094] Based on the updated control parameters and the intermediate quantum neural network, an invariant quantum neural network is generated.

[0095] According to an embodiment of the present invention, the initial quantum neural network is first determined according to formula (3). and ε(θ) e ),in, Then according to and ε(θ) e and target quantum channel Generate intermediate quantum neural networks

[0096] According to an embodiment of the present invention, the target loss value is calculated using the target loss function shown in formula (7):

[0097]

[0098] Where ψ represents a quantum pure state, For intermediate quantum neural networks, θ d and θ e These are control parameters.

[0099] According to an embodiment of the present invention, the gradient descent algorithm is then used for iteration as shown below:

[0100] First, randomly initialize the control parameter θ. (0) ;

[0101] Then repeat the following steps for round T;

[0102] The initial parameter for each round is θ. t ;

[0103] Estimate the gradient of the loss function at this point using the finite difference method:

[0104]

[0105] in and and θ t The difference lies in the j-th parameter, specifically denoted as θ. + →θ j +δ,θ - →θ j -δ.

[0106] Update parameter θ based on gradient value (t+1):

[0107]

[0108] Where η is the learning rate, which can be preset. It is the gradient information of the current point.

[0109] The loop terminates if either condition is met; otherwise, it repeats the above steps. This allows the output of approximately optimal parameters θ. ＊ That is, the updated control parameter θ ＊ =θ d +θ e Finally, θ is determined based on the actual situation. d and θ e The specific values ​​are obtained to derive the invariant quantum neural network.

[0110] According to an embodiment of the present invention, after obtaining the invariant quantum neural network, the maximum fidelity can be calculated based on the qubits transmitted by the quantum transmitter and the qubits received by the quantum receiver. The calculation of the maximum fidelity is as follows:

[0111]

[0112] According to an embodiment of the present invention, a fidelity threshold can be set, for example, 80%. If the maximum fidelity is less than the fidelity threshold, the invariant quantum neural network can be retrained or the gradient descent algorithm can be used to find the optimal parameters.

[0113] According to embodiments of the present invention, this method constructs a parametric quantum channel by adding freely controllable parameter control noise to a parametric quantum circuit, without requiring additional auxiliary bit resources. Furthermore, this method utilizes symmetry to optimize the structure of the quantum neural network. With good symmetry, the complexity of the network's quantum gates and the number of control parameters used can be greatly reduced. Simultaneously, as the number of parameters decreases, the vanishing gradient phenomenon can be avoided during training.

[0114] Figure 3 A schematic diagram of a quantum communication system according to an embodiment of the present invention is shown.

[0115] According to embodiments of the present invention, such as Figure 3 As shown, the quantum communication system includes:

[0116] A quantum transmitter is used to generate quantum information based on the information to be transmitted.

[0117] A channel coding device is used to encode quantum information using a first invariant quantum neural network when quantum information is transmitted at a quantum transmitter, thereby obtaining encoded quantum information. The first invariant quantum neural network is generated based on an invariant gate set generated from a symmetric group and a parameterized quantum channel.

[0118] A quantum channel is used to transmit encoded quantum information to a channel decoding device.

[0119] A channel decoding device is used to decode transmitted quantum information using a second invariant quantum neural network to obtain decoded quantum information.

[0120] The quantum receiver is used to process the decoded quantum information to obtain the information to be transmitted.

[0121] According to embodiments of the present invention, this method constructs a parametric quantum channel by adding freely controllable parameter control noise to a parametric quantum circuit, without requiring additional auxiliary bit resources. Furthermore, this method utilizes symmetry to optimize the structure of the quantum neural network. With good symmetry, the complexity of the network's quantum gates and the number of control parameters used can be greatly reduced. Simultaneously, as the number of parameters decreases, the vanishing gradient phenomenon can be avoided during training.

[0122] The embodiments of the present invention have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of the invention. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of the invention is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of the invention, and all such substitutions and modifications should fall within the scope of the invention.

Claims

1. A quantum communication method, characterized in that, include: When quantum information is transmitted at a quantum transmitter, the quantum information is encoded using a first invariant quantum neural network to obtain encoded quantum information. The quantum information is generated based on the information to be transmitted transmitted by the quantum transmitter, and the first invariant quantum neural network is generated based on an invariant gate set generated based on a symmetric group and a parameterized quantum channel. The encoded quantum information is transmitted using a quantum channel, and the transmitted quantum information is decoded using a second invariant quantum neural network to obtain the decoded quantum information. The decoded quantum information is processed using a quantum receiver to obtain the information to be transmitted; Either the first invariant quantum neural network or the second invariant quantum neural network is trained in the following manner: The set of basic gates is processed using the equivalent transformation method to obtain the set of invariant gates, wherein the set of basic gates includes multiple basic gates; Based on the invariant gate set and the parameterized quantum channel, an initial quantum neural network is generated; The initial quantum neural network is iteratively updated using the gradient descent algorithm to obtain the invariant quantum neural network; The generation of the initial quantum neural network based on the invariant gate set and the parameterized quantum channel includes: Hermitian and unitary operators are generated based on the set of invariant gates. Based on the Hermitian operator, the unitary operator, and the initial parameterized quantum circuit, generate the target quantum circuit; The initial quantum neural network is generated by controlling noise according to the target quantum circuit and parameters.

2. The method according to claim 1, characterized in that, The invariant gate set is obtained by processing the basic gate set using the equivalent transformation method, including: The Twilring method is used to transform each of the basic gates into elements that satisfy the invariance of the symmetry group, resulting in multiple initial invariant gates; Multiple initial invariant gates are merged to obtain multiple target invariant gates; The set of invariant gates is generated based on the plurality of target invariant gates.

3. The method according to claim 2, characterized in that, The initial invariant gate The calculation is shown in formula (1): （1） in, It is a symmetric group The The element is represented by a unitary matrix in the Hilbert space where the quantum circuit resides. For the i-th basic gate, It is a symmetric group The number of elements.

4. The method according to claim 1, characterized in that, The set of invariant gates is as follows: ,in, For the objective-invariant gate, the Hermitian operator and the unitary operator are respectively and The target quantum circuit As shown in formula (2), the initial quantum neural network is as shown in formula (3): （2） （3） in, For control parameters, The parameter control noise is used for the j-th layer in the initial quantum neural network.

5. The method according to claim 1, characterized in that, The parameter control noise is shown in formula (4), and the parameter control noise includes bit flip noise, phase flip noise, and depolarization noise. The bit flip noise is shown in formula (5). （4） （5） in, For Hermitian operators, These are the control parameters for bit flip noise. It is an arbitrary single-bit quantum state. It is an identity matrix. It is the Pauli-X matrix.

6. The method according to claim 1, characterized in that, The initial quantum neural network is iteratively updated using the gradient descent algorithm to obtain the invariant quantum neural network, including: Based on the initial quantum neural network and the target quantum channel, an intermediate quantum neural network is generated; The target loss value is obtained by calculating the intermediate quantum neural network using the target loss function; The target loss value and control parameters are iteratively processed using the gradient descent algorithm to obtain updated control parameters; The invariant quantum neural network is generated based on the updated control parameters and the intermediate quantum neural network.

7. The method according to claim 6, characterized in that, The target loss function is shown in Equation (6): （6） in, For quantum pure state, This is an intermediate quantum neural network. and These are control parameters.

8. A quantum communication system, characterized in that, include: A quantum transmitter is used to generate quantum information based on the information to be transmitted. A channel coding device is used to encode the quantum information using a first invariant quantum neural network when the quantum information is transmitted at the quantum transmitter to obtain encoded quantum information. The first invariant quantum neural network is generated based on an invariant gate set generated based on a symmetric group and a parameterized quantum channel. A quantum channel is used to transmit the encoded quantum information to a channel decoding device; The channel decoding device is used to decode the transmitted quantum information using a second invariant quantum neural network to obtain the decoded quantum information. A quantum receiver is used to process the decoded quantum information to obtain the information to be transmitted. Either the first invariant quantum neural network or the second invariant quantum neural network is trained in the following manner: The set of basic gates is processed using the equivalent transformation method to obtain the set of invariant gates, wherein the set of basic gates includes multiple basic gates; Based on the invariant gate set and the parameterized quantum channel, an initial quantum neural network is generated; The initial quantum neural network is iteratively updated using the gradient descent algorithm to obtain the invariant quantum neural network; The generation of the initial quantum neural network based on the invariant gate set and the parameterized quantum channel includes: Hermitian and unitary operators are generated based on the set of invariant gates. Based on the Hermitian operator, the unitary operator, and the initial parameterized quantum circuit, generate the target quantum circuit; The initial quantum neural network is generated by controlling noise according to the target quantum circuit and parameters.

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