Estimation Method and Device for Classical Capacity of Quantum Channel, Electronic Device and Medium

Abstract

The present disclosure provides a method, apparatus, electronic device, computer-readable storage medium, and computer program product for estimating the classical capacity of a quantum channel, relating to the field of computers, and particularly to the field of quantum computer technologies. The implementation solution is as follows: determining m first quantum states of m qubits, each of the m first quantum states including adjustable parameters; initializing the adjustable parameters in the m first quantum states; iteratively executing the following operations multiple times to minimize a loss function: based on the m first quantum states determined by the parameters, determining m probability values of an ensemble when there is a maximum value of the Holevo capacity of the quantum channel through a semidefinite programming method; optimizing the adjustable parameters in the m first quantum states by minimizing the loss function based on the m probability values, the loss function being determined based on the Holevo information; and determining the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel.

Description

Technical Field

[0001] The present disclosure relates to the field of computers, and more particularly to the field of quantum computer technology. Specifically, it relates to a method, apparatus, electronic device, computer-readable storage medium, and computer program product for estimating the classical capacity of a quantum channel. Background Art

[0002] Information transmission exists in all aspects of social production and life. Daily telephone and email communications are all processes of classical information transmission. Nowadays, quantum computer technology is developing rapidly, and the use of quantum technology for information transmission has also attracted great interest from researchers. In information theory, the transmission of information is characterized by a channel, and the capacity of the channel represents the maximum rate at which information can be reliably transmitted using that channel. In quantum information theory, the transmission of information is characterized by a quantum channel, and its classical capacity represents the maximum rate at which classical information can be reliably transmitted using that quantum channel. Currently, calculating the classical capacity of a quantum channel mostly involves mathematical simplification and operations, and there are few systematic solutions for general quantum channels. Summary of the Invention

[0003] The present disclosure provides a method, apparatus, electronic device, computer-readable storage medium, and computer program product for estimating the classical capacity of a quantum channel.

[0004] According to an aspect of the present disclosure, there is provided a method for estimating the classical capacity of a quantum channel, including: determining m first quantum states of n qubits, where n is the number of qubits of the quantum channel, m is the number of quantum states in a preset ensemble, and m and n are positive integers, and each of the m first quantum states includes adjustable parameters; initializing the adjustable parameters in the m first quantum states; iteratively performing the following operations multiple times to minimize a loss function: based on the m first quantum states determined by the parameters, determining m probability values of the ensemble when the Holevo information of the quantum channel has a maximum value through a semidefinite programming method, where the m probability values correspond one-to-one to the m first quantum states, and the Holevo information is determined based on the ensemble; optimizing the adjustable parameters in the m first quantum states by minimizing the loss function based on the m probability values, where the loss function is determined based on the Holevo information; and determining the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel.

[0005] According to another aspect of the present disclosure, there is provided an information transmission method based on a quantum channel, including: obtaining an ensemble corresponding to the Holevo information of the quantum channel; obtaining classical information to be transmitted to encode the classical information onto corresponding quantum states in the ensemble; transmitting the encoded quantum states through the quantum channel to obtain transmitted quantum states; and decoding the transmitted quantum states to obtain the transmitted classical information, wherein the ensemble corresponding to the Holevo information is optimized based on the method described above.

[0006] According to another aspect of the present disclosure, there is provided an apparatus for estimating the classical capacity of a quantum channel, including: a first determination unit configured to determine m first quantum states of n qubits, where n is the number of qubits of the quantum channel and m is the number of quantum states in a preset ensemble, and m and n are positive integers, and each of the m first quantum states includes adjustable parameters; an initialization unit configured to initialize the adjustable parameters in the m first quantum states; an iteration unit configured to iteratively perform the following operations multiple times to minimize a loss function: based on the m first quantum states determined by the parameters, determining m probability values of the ensemble when the Holevo information of the quantum channel has a maximum value through a semidefinite programming method, where the m probability values correspond one-to-one to the m first quantum states, and the Holevo information is determined based on the ensemble; optimizing the adjustable parameters in the m first quantum states by minimizing the loss function based on the m probability values, where the loss function is determined based on the Holevo information; and a second determination unit configured to determine the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel.

[0007] According to another aspect of the present disclosure, there is provided an information transmission apparatus based on a quantum channel, including: an acquisition unit configured to acquire an ensemble corresponding to the Holevo information of the quantum channel; an encoding unit configured to acquire classical information to be transmitted to encode the classical information onto corresponding quantum states in the ensemble; a transmission unit configured to transmit the encoded quantum states through the quantum channel to obtain transmitted quantum states; and a decoding unit configured to decode the transmitted quantum states to obtain the transmitted classical information, wherein the ensemble corresponding to the Holevo information is optimized based on the method described above.

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

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

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

[0011] According to one or more embodiments of the present disclosure, a classical capacity estimation method applicable to a general quantum channel optimizes the parameters describing the input ensemble by combining the gradient descent method and semidefinite programming, and efficiently obtains an estimation result of the Holevo capacity of the quantum channel with less computing resources.

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

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

[0014] Figure 1 A flowchart of a method for estimating the classical capacity of a quantum channel according to an embodiment of the present disclosure is shown;

[0015] Figure 2 A flowchart of an information transmission method based on a quantum channel according to an embodiment of the present disclosure is shown;

[0016] Figure 3 A structural block diagram of an apparatus for estimating the classical capacity of a quantum channel according to an embodiment of the present disclosure is shown;

[0017] Figure 4 A structural block diagram of an information transmission apparatus based on a quantum channel according to an embodiment of the present disclosure is shown; and

[0018] Figure 5 A structural block diagram of an exemplary electronic device capable of implementing the embodiments of the present disclosure is shown. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] The following describes exemplary embodiments of the present disclosure with reference to the accompanying drawings. Various details of the embodiments of the present disclosure are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope of the present disclosure. Similarly, descriptions of well-known functions and structures are omitted in the following description for clarity and conciseness.

[0020] In the present disclosure, unless otherwise specified, the terms “first,” “second,” etc. are used to describe various elements and are not intended to limit the positional relationship, timing relationship, or importance relationship of these elements. Such terms are only used to distinguish one element from another. In some examples, the first element and the second element may refer to the same instance of the element, and in certain cases, based on the context description, they may also refer to different instances.

[0021] In the descriptions of the various examples in the present disclosure, the terms used are only for the purpose of describing specific examples and are not intended to be limiting. Unless the context clearly indicates otherwise, if the number of elements is not specifically limited, the element may be one or more. In addition, the term “and / or” used in the present disclosure covers any one of the listed items and all possible combinations.

[0022] Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0023] So far, various different types of computers in use are based on classical physics as the theoretical basis for information processing, and are called traditional computers or classical computers. Classical information systems use the physically easiest-to-implement binary data bits to store data or programs. Each binary data bit is represented by 0 or 1, called a bit or a byte, as the smallest information unit. Classical computers themselves have inevitable weaknesses: one is the most basic limit of energy consumption in the computing process. The minimum energy required for logic elements or storage units should be several times that of kT to avoid malfunction due to thermal fluctuations; the second is information entropy and heat generation energy consumption; the third is that when the wiring density of computer chips is very large, according to the Heisenberg uncertainty relation, when the uncertainty of the electron position is very small, the uncertainty of the momentum will be very large. The electrons are no longer bound, and there will be a quantum interference effect, which will even damage the performance of the chip.

[0024] A quantum computer is a type of physical device that follows the properties and laws of quantum mechanics to perform high-speed mathematical and logical operations, store, and process quantum information. When a device processes and computes quantum information and runs quantum algorithms, it is a quantum computer. Quantum computers follow unique quantum dynamics laws (especially quantum interference) to achieve a new mode of information processing. For parallel processing of computational problems, quantum computers have an absolute speed advantage over classical computers. The transformation implemented on each superposition component by a quantum computer is equivalent to a classical computation. All these classical computations are completed simultaneously and are superimposed according to a certain probability amplitude to give the output result of the quantum computer. This kind of computation is called quantum parallel computing. Quantum parallel processing greatly improves the efficiency of quantum computers, enabling them to complete tasks that classical computers cannot, such as the factorization of a very large natural number. Quantum coherence is essentially utilized in all quantum super-fast algorithms. Therefore, quantum parallel computing using quantum states instead of classical states can achieve computing speeds and information processing capabilities that are incomparable to classical computers, while saving a large amount of computing resources.

[0025] Nowadays, with the rapid development of quantum computer technology, information transmission based on quantum technology has gradually moved from theory to reality. In communication theory, the transmission of information is characterized by a channel, and the capacity of the channel represents the maximum rate at which information can be reliably transmitted using this channel. In quantum information theory, the transmission of information is characterized by a quantum channel. That is, the quantum channel is the main research object of information transmission, while classical information is one of the most common forms of information.

[0026] The classical capacity of a quantum channel represents the maximum rate at which classical information can be reliably transmitted using this quantum channel. A quantum channel 's classical capacity is shown by formula (1):

[0027]

[0028] where, represents the quantum channel composed of the tensor product of n quantum channels , represents the Holevo capacity of the quantum channel .

[0029] It should be noted that the Holevo capacity has superadditivity, that is, for two quantum channels and In terms of Therefore, according to formula (1), the form of formula (2) can be obtained.

[0030]

[0031] That is, a quantum channel Khorevo capacity The classical capacity of the channel is given by The lower bound.

[0032] Therefore, the quantum channel can be estimated by The classical capacity is estimated by using the Khorev capacity of the α-Horlevo ...

[0033]

[0034] Among them, {pj, ρj} are several quantum states ρ j The ensemble consists of , S(ρ) = -Tr[ρ log2 ρ] is the von Neumann entropy of the quantum state ρ. The quantum state ρ can be mathematically represented by a density matrix, and Tr represents the trace of the matrix. The Hollevo capacity gives a lower bound on the classical capacity of a quantum channel, which represents the maximum rate at which the channel can reliably transmit classical information without using quantum entanglement resources. It can be seen that calculating the Hollevo capacity of a quantum channel is to find an ensemble so that the Hollevo information of the quantum channel in this ensemble has the maximum value. In other words, the Hollevo capacity of a quantum channel can be called the maximum value of its Hollevo information.

[0035] Typically, a parameterized quantum circuit (PQC) can be implemented on a quantum computer or simulated on a classical computer to obtain the quantum states in the ensemble and their corresponding probability distributions. Machine learning methods are then used to optimize these parameters to obtain an estimate of the Hollevo capacity of the quantum channel, which serves as a lower bound for the classical capacity of the channel. However, since both the quantum states and probability distributions of the input ensemble need to be parameterized, when the channel dimension is high (such as a multi-qubit channel), the large number of training parameters introduced is detrimental to optimizing the training model, which can easily lead to the model's inability to accurately estimate the Hollevo capacity of the quantum channel.

[0036] Therefore, according to an embodiment of the present disclosure, a method for estimating the classical capacity of a quantum channel is provided. Figure 1 FIG. 4 shows a flow chart of a method for estimating the classical capacity of a quantum channel according to an embodiment of the present disclosure, as shown in FIG. Figure 1As shown, method 100 includes: determining a first quantum state of m n - qubit states, where n is the number of qubits of the quantum channel, m is the number of quantum states in a preset ensemble, and m and n are positive integers, and each of the m first quantum states includes adjustable parameters (step 110); initializing the adjustable parameters in the m first quantum states (step 120); iteratively performing the following operations multiple times to minimize a loss function (step 130): based on the m first quantum states determined by the parameters, determining m probability values of the ensemble when the Holevo information of the quantum channel has a maximum value through a semidefinite programming method, where the m probability values correspond one - to - one with the m first quantum states, and the Holevo information is determined based on the ensemble (step 1301); optimizing the adjustable parameters in the m first quantum states by minimizing the loss function based on the m probability values, where the loss function is determined based on the Holevo information (step 1302); and determining the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel (step 140).

[0037] According to an embodiment of the present disclosure, a classical capacity estimation method applicable to a general quantum channel optimizes the parameters describing the input ensemble through a combination of the gradient descent method and semidefinite programming, and efficiently obtains an estimation result of the Holevo capacity of the quantum channel using less computational resources.

[0038] In the present disclosure, based on the principle of quantum computing, a parameterization method for an arbitrary quantum state is innovatively designed. Taking a single - qubit state as an example, each quantum state |ψ> requires two parameters θ0, θ1 ∈ (0, π].

[0039] Specifically, parameterization can be performed according to formula (4):

[0040] |ψ> = cos(θ0)|0> + [cos(θ1) + i sin(θ1)]sin(θ0)|1> Formula (4)

[0041] where |0> and |1> are single - bit computational basis states, |0> = [1, 0] T and |1> = [0, 1] T , and i is the imaginary unit. Based on |ψ>, the density matrix ρ(θ1, θ2) = |ψ><ψ| of this quantum state can be constructed, as shown in formula (5) specifically:

[0042]

[0043] Among them, <ψ| represents the conjugate transpose of |ψ>. By adjusting the parameters θ0 and θ1, different quantum states ρ(θ1, θ2) can be obtained. More generally, if the number of quantum states of the input ensemble is m and the dimension of each quantum state is d, then m*(2d - 2) parameters are required to parameterize the m quantum states respectively.

[0044] For any pure quantum state of n qubits, it can be parameterized based on formula (6):

[0045]

[0046] Among them, and are variable parameters, is in decimal representation, and β k satisfies the recursive property, that is, β1 = 0, Exemplarily, when n = 2, the parameterized quantum state is specifically shown in formula (7):

[0047]

[0048] Among them, the parameters are There are a total of 6 parameters, namely θ0, θ1, and θ2.

[0049] According to some embodiments, determining the first quantum state of m n - qubits includes: determining the initial quantum state of m n - qubits; and determining the parameterized quantum circuit of m n - qubits to apply the parameterized quantum circuit of the m n - qubits to the corresponding initial quantum states respectively to obtain m first quantum states.

[0050] In some examples, a parameterized quantum circuit can also be used for quantum state parameterization. A parameterized quantum circuit usually consists of several single - qubit rotation gates and controlled - NOT gates (CNOT gates). The rotation angles of the several single - qubit rotation gates form a vector θ = [θ0,..., θ k , that is, the adjustable parameters. The quantum state ρ can be regarded as the quantum state obtained by a parameterized quantum circuit U(θ) acting on an initial quantum state ρ init where θ is the parameter of the parameterized quantum circuit. The initial state ρ init can usually be taken as |0><0| in quantum computing.

[0051] In some embodiments, the initial quantum state ρ init can be |0><0| for easy preparation, and its mathematical form is a matrix with the first element in the upper left corner being 1 and the remaining elements all being 0:

[0052]

[0053] However, it can be understood that other forms of initial quantum states are also acceptable and are not restricted herein.

[0054] According to some embodiments, the loss function is determined based on the following formula (8):

[0055]

[0056] where ρ j is the j-th first quantum state, j = 1, 2,..., m, is the quantum state obtained after the quantum channel acts on the quantum state ρ j , p j is the probability value corresponding to the j-th first quantum state, and S() represents the von Neumann entropy. That is, in order to find an ensemble ε = {p j , ρ j} such that the value of the function is maximized, the loss function can be taken to be equal to so that this ensemble can be found by minimizing the loss function. Alternatively, other forms of loss functions are also possible and are not restricted herein.

[0057] According to some embodiments, the adjustable parameters in the m first quantum states are adjusted by the gradient descent method to minimize the loss function.

[0058] It can be understood that it is also possible to adjust the parameters in the parameterized circuit by any other suitable optimization method, which is not restricted herein. Moreover, minimizing the loss function does not mean finding the absolute minimum of the loss function. As long as the minimum value of the loss function can be approximately obtained under experimental conditions or within the allowable error, it is sufficient.

[0059] In an exemplary embodiment according to the present disclosure, the capacity of the quantum channel is estimated. First, in step 1, the number m of quantum states in the ensemble is determined, and this m value can be set arbitrarily. However, it can be understood that the larger the m value, the more accurate the estimated capacity of the quantum channel may be, but at the same time, the required computational amount will also be larger. Exemplarily, the quantum states of the ensemble are initialized: according to the dimension d of the quantum channel, the number m of quantum states included in the ensemble is determined as m = d to d 2 . Then, m*(2d - 2) parameters θ := {θ j} are randomly initialized and used to parameterize the quantum states of the ensemble, denoted as ρ j .

[0060] In step 2, the output state j after each ρ in the ensemble passes through the channel is calculated. Optimize the ensemble parameters:

[0061] In step 3, for the quantum state determined by the current parameters Use the technique of semidefinite programming to solve the following convex optimization problem to obtain the probability distribution of the ensemble

[0062]

[0063] Then, for the obtained probability distribution, use the gradient descent method to optimize the parameters of the quantum state in the ensemble The loss function is:

[0064]

[0065] Repeat steps 2 - 3 to minimize the loss function. When the set number of iterations is reached, stop the optimization and record the value of the objective function at this time as The corresponding ensemble is Output As the Holevo capacity estimate of this scheme for the quantum channel That is, the estimated value of the lower bound of its classical capacity. At the same time, the ensemble ε* is the input ensemble corresponding to obtaining this estimated value.

[0066] In the embodiments according to the present disclosure, a parameterized quantum circuit is used and the parameters therein are optimized to obtain an estimated value of the Holevo capacity of a quantum channel as an estimated value of the classical capacity of the quantum channel, where the method according to the embodiments of the present disclosure is flexible enough and has no restrictions on the input quantum channel. That is, for any quantum channel, the method according to the embodiments of the present disclosure can be implemented and give its estimated value of the Holevo capacity, having universality.

[0067] Moreover, in the embodiments according to the present disclosure, steps 1 - 3 can be implemented on near - term quantum devices or can be completed by classical computer simulation. In both cases, the estimation of the Holevo capacity of the input quantum channel can be completed. When the method described in this embodiment runs on a quantum device, the input quantum channel to be estimated should be a physically implemented and usable quantum channel; when the method described in this embodiment runs on a classical computer for simulation, the input quantum channel to be estimated should be the mathematical form corresponding to the physical quantum channel for simulation calculation.

[0068] In an exemplary application, estimate the depolarizing channel (Depolarizing channel) and its tensor - product channels using the method described in the embodiments of the present disclosure. The depolarizing channel is a common single - qubit quantum channel, and its Holevo capacity has been proven to satisfy additivity, that is For a quantum channel When the input state is a quantum state described by a density matrix ρ, the output state can be expressed as where {K i} is called the Kraus operator. Among them,

[0069]

[0070] where p ∈ [0, 1],

[0071]

[0072] are the conjugate transposes of K0, K1, K2, and K3 respectively.

[0073] We implemented this scheme based on the PaddlePaddle and QuantumLever platforms, and estimated the Holevo capacity for the depolarizing channel with p = 0.2 and its tensor product channel In the experiment, the number of ensemble quantum states selected was m = d 2 = 2 2n (n = 1, 2, 3). Table 1 shows the comparison between the Holevo capacity estimation values given by this scheme and the theoretical values.

[0074]

[0075] Table 1

[0076] It can be seen from the experimental results that the Holevo capacity estimation error given by this scheme for the depolarizing channel and its tensor product channel is as low as 10 -9 . This demonstrates that this scheme achieves a high-precision estimation of the lower bound of the classical information capacity of the above quantum channels.

[0077] In an exemplary application, the advantage of optimizing the loss function by the gradient descent method combined with semidefinite programming (GD + SDP) in this scheme is demonstrated. For the depolarizing channel with p = 0.2 and its tensor product channel We estimated the Holevo capacity of the channel using this scheme (GD + SDP) and the scheme using only the gradient descent method (GD) respectively.

[0078] The same number of iterations (60 times) was set for the two optimization schemes, and the error magnitudes of the Holevo capacity estimations given by the two schemes compared with the theoretical values were compared. The experimental data is shown in Table 2.

[0079]

[0080] Table 2

[0081] According to the data in Table 2, after 60 iterations are completed, the estimation error of the Holevo capacity given by the present scheme (GD+SDP) is 1 to 3 orders of magnitude lower than that of the scheme that only uses the gradient descent method (GD). Therefore, the present scheme combines semi-definite programming with the gradient descent method, which improves the optimization efficiency of the algorithm.

[0082] After obtaining the capacity estimate of the quantum channel, classical information can be transmitted through this quantum channel based on this estimate. When transmitting classical information through this quantum channel, first, the classical information needs to be encoded into a quantum state, and then this quantum state is transmitted through this quantum channel. Finally, the receiving party decodes the obtained quantum state to obtain the classical information.

[0083] Therefore, as Figure 2 shown, according to an embodiment of the present disclosure, there is also provided an information transmission method 200 based on a quantum channel, including: obtaining an ensemble corresponding to the Holevo information of the quantum channel (step 210); obtaining classical information to be transmitted to encode the classical information onto the corresponding quantum state in the ensemble (step 220); transmitting the encoded quantum state through the quantum channel to obtain the transmitted quantum state (step 230); and decoding the transmitted quantum state to obtain the transmitted classical information (step 240). The ensemble corresponding to the Holevo information is optimized based on the method described in any one of the above embodiments.

[0084] Exemplarily, in the last step of the method described in the above embodiment, an ensemble ε corresponding to the Holevo capacity of the input quantum channel is obtained. * . Therefore, when transmitting classical information, the classical information can be first encoded onto the corresponding quantum state in the ensemble to complete the encoding process before transmission. Since the Holevo information of this quantum channel is the maximum value at this ensemble, that is, the estimated value of the Holevo capacity of this quantum channel, and the Holevo capacity represents the maximum rate at which classical information can be reliably transmitted through this quantum channel without using quantum entanglement resources. Therefore, by encoding the classical information to be transmitted onto the quantum state of this ensemble, reliable and efficient transmission of this classical information can be achieved.

[0085] According to some embodiments, for the quantum states in this ensemble, an optimal scheme for distinguishing them can be calculated through semi-definite programming as a scheme for decoding the transmitted quantum state. Semi-definite programming has an efficient classical algorithm. Therefore, according to the output of the method described in the above embodiment, a scheme for transmitting classical information through the estimated quantum channel can be conveniently obtained, and this scheme can reach the estimated Holevo capacity, which has high practicability.

[0086] According to an embodiment of the present disclosure, as Figure 3As shown, an estimation device 300 for the classical capacity of a quantum channel is further provided, including: a first determination unit 310 configured to determine a first quantum state of m n-qubit systems, where n is the number of qubits of the quantum channel, m is the number of quantum states in a preset ensemble, and m and n are positive integers, and each of the m first quantum states includes adjustable parameters; an initialization unit 320 configured to initialize the adjustable parameters in the m first quantum states; an iteration unit 330 configured to iteratively perform the following operations multiple times to minimize a loss function: based on the m first quantum states determined by the parameters, determining m probability values of the ensemble when the Holevo information of the quantum channel has a maximum value through a semidefinite programming method, where the m probability values correspond one-to-one to the m first quantum states, and the Holevo information is determined based on the ensemble; optimizing the adjustable parameters in the m first quantum states by minimizing the loss function based on the m probability values, where the loss function is determined based on the Holevo information; and a second determination unit 340 configured to determine the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel.

[0087] Here, the operations of the above units 310-340 of the estimation device 300 for the classical capacity of the quantum channel are respectively similar to the operations of steps 110-140 described above, and will not be elaborated here.

[0088] According to an embodiment of the present disclosure, as Figure 4 shown, an information transmission device 400 based on a quantum channel is further provided, including: an acquisition unit 410 configured to acquire an ensemble corresponding to the Holevo information of the quantum channel; an encoding unit 420 configured to acquire classical information to be transmitted and encode the classical information onto corresponding quantum states in the ensemble; a transmission unit 430 configured to transmit the encoded quantum states through the quantum channel to obtain transmitted quantum states; and a decoding unit 440 configured to decode the transmitted quantum states to obtain transmitted classical information. The ensemble corresponding to the Holevo information is optimized based on the method described in any of the above embodiments.

[0089] Here, the operations of the above units 410-440 of the information transmission device 400 based on the quantum channel are respectively similar to the operations of steps 210-240 described above, and will not be elaborated here.

[0090] According to an embodiment of the present disclosure, an electronic device, a readable storage medium, and a computer program product are further provided.

[0091] Refer to Figure 5, a block diagram of an electronic device 500 that can be a server or a client of the present disclosure will now be described. It is an example of a hardware device that can be applied to various aspects of the present disclosure. The electronic device is intended to represent various forms of digital electronic computer devices, such as, for example, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as, for example, personal digital assistants, cellular telephones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely exemplary and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0092] As Figure 5 shown, the electronic device 500 includes a computing unit 501 that can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 502 or a computer program loaded from a storage unit 508 into a random access memory (RAM) 503. In the RAM 503, various programs and data required for the operation of the electronic device 500 can also be stored. The computing unit 501, the ROM 502, and the RAM 503 are connected to each other via a bus 504. An input / output (I / O) interface 505 is also connected to the bus 504.

[0093] Multiple components in the electronic device 500 are connected to the I / O interface 505, including: an input unit 506, an output unit 507, a storage unit 508, and a communication unit 509. The input unit 506 can be any type of device that can input information into the electronic device 500. The input unit 506 can receive input digital or character information, and generate key signal inputs related to the user settings and / or function controls of the electronic device, and can include, but is not limited to, a mouse, a keyboard, a touch screen, a trackpad, a trackball, a joystick, a microphone, and / or a remote control. The output unit 507 can be any type of device that can present information, and can include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. The storage unit 508 can include, but is not limited to, magnetic disks, optical disks. The communication unit 509 allows the electronic device 500 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks, and can include, but is not limited to, a modem, a network card, an infrared communication device, a wireless communication transceiver, and / or a chipset, such as a Bluetooth device, an 802.11 device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0094] The computing unit 501 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 501 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 501 executes the various methods and processes described above, such as method 100 or 200. For example, in some embodiments, method 100 or 200 can be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 508. In some embodiments, part or all of the computer program can be loaded and / or installed onto the electronic device 500 via the ROM 502 and / or the communication unit 509. When the computer program is loaded into the RAM 503 and executed by the computing unit 501, one or more steps of method 100 or 200 described above can be executed. Alternatively, in other embodiments, the computing unit 501 can be configured to execute method 100 or 200 in any other suitable manner (e.g., by means of firmware).

[0095] Various embodiments of the systems and techniques described above in this document can be implemented in digital electronic circuitry, integrated circuit systems, field-programmable gate arrays (FPGA), application-specific integrated circuits (ASIC), application-specific standard products (ASSP), systems-on-a-chip (SOC), complex programmable logic devices (CPLD), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special or general-purpose programmable processor that receives data and instructions from a storage system, at least one input device, and at least one output device, and transmits the data and instructions to the storage system, the at least one input device, and the at least one output device.

[0096] The program code for implementing the methods of the present disclosure can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when the program codes are executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program codes can be executed entirely on the machine, partially on the machine, as a stand-alone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0097] In the context of this disclosure, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0098] In order to provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer. Other kinds of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, speech input, or tactile input).

[0099] The systems and techniques described herein can be implemented in a computing system including backend components (e.g., as a data server), or a computing system including middleware components (e.g., an application server), or a computing system including frontend components (e.g., a user computer having a graphical user interface or a web browser through which the user can interact with an implementation of the systems and techniques described herein), or a computing system including any combination of such backend components, middleware components, or frontend components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), and the Internet.

[0100] A computer system can include a client and a server. The client and the server are generally remote from each other and typically interact through a communication network. The client-server relationship is generated by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, or a server of a distributed system, or a server incorporating a blockchain.

[0101] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and no limitations are imposed herein.

[0102] Although embodiments or examples of the present disclosure have been described with reference to the accompanying drawings, it should be understood that the above methods, systems, and devices are merely exemplary embodiments or examples, and the scope of the present invention is not limited by these embodiments or examples, but is only defined by the authorized claims and their equivalent scope. Various elements in the embodiments or examples can be omitted or replaced by their equivalent elements. In addition, the steps can be executed in an order different from that described in the present disclosure. Further, the various elements in the embodiments or examples can be combined in various ways. Importantly, with the evolution of technology, many of the elements described herein can be replaced by equivalent elements that emerge after the present disclosure.

Claims

1. A method for estimating the classical capacity of a quantum channel, comprising: Determining m first quantum states of n qubits, where n is the number of qubits of the quantum channel, m is the number of quantum states in a preset ensemble, m and n are positive integers, and each of the m first quantum states includes adjustable parameters; Initializing the adjustable parameters in the m first quantum states; Iteratively performing the following operations multiple times to minimize a loss function: Based on the m first quantum states determined by the parameters, determining m probability values of the ensemble when the Holevo information of the quantum channel has a maximum value through a semidefinite programming method, where the m probability values correspond one-to-one to the m first quantum states, and the Holevo information is determined based on the ensemble; Optimizing the adjustable parameters in the m first quantum states by minimizing the loss function based on the m probability values, where the loss function is determined based on the Holevo information; And Determining the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel.

2. The method according to claim 1, wherein, Determining m first quantum states of n qubits includes: Determining m initial quantum states of n qubits; and Determining a parameterized quantum circuit of m n qubits, and respectively applying the parameterized quantum circuits of m n qubits to the corresponding initial quantum states to obtain m first quantum states.

3. The method according to claim 1, wherein Determining the loss function based on the following formula: where ρ j is the j-th first quantum state, j = 1, 2, …, m, is the quantum state obtained after the quantum channel acts on the quantum state ρ j , p j is the probability value corresponding to the j-th first quantum state, and S() represents the von Neumann entropy.

4. The method according to claim 1, wherein Adjusting the adjustable parameters in the m first quantum states by the gradient descent method to minimize the loss function.

5. An information transmission method based on a quantum channel, comprising: Obtaining the ensemble corresponding to the Holevo information of the quantum channel; Obtaining classical information to be transmitted, and encoding the classical information onto the corresponding quantum state in the ensemble; Transmitting the encoded quantum state through the quantum channel to obtain a transmitted quantum state; And Decoding the transmitted quantum state to obtain the transmitted classical information, where The ensemble corresponding to the Holevo information is optimized based on the method according to any one of claims 1-4.

6. The method according to claim 5, wherein Determining a way to distinguish the transmitted quantum state through semidefinite programming, and decoding the transmitted quantum state based on the determined way.

7. An apparatus for estimating the classical capacity of a quantum channel, comprising: A first determination unit configured to determine m first quantum states of n qubits, where n is the number of qubits of the quantum channel, m is the number of quantum states in a preset ensemble, m and n are positive integers, and each of the m first quantum states includes adjustable parameters; An initialization unit configured to initialize the adjustable parameters in the m first quantum states; An iteration unit configured to iteratively perform the following operations multiple times to minimize a loss function: Based on the determined m first quantum states of the parameters, the m probability values of the ensemble when the Holevo information of the quantum channel has a maximum value are determined by the semidefinite programming method, where the m probability values correspond one-to-one to the m first quantum states, and the Holevo information is determined based on the ensemble; Based on the m probability values, the adjustable parameters in the m first quantum states are optimized by minimizing the loss function, where the loss function is determined based on the Holevo information; and A second determination unit, configured to determine the Holevo information of the quantum channel obtained after minimizing the loss function as an estimated value of the classical capacity of the quantum channel.

8. The device according to claim 7, wherein The first determination unit includes: A first determination subunit, configured to determine m initial quantum states of n qubits; and A second determination subunit, configured to determine a parameterized quantum circuit of m n qubits, and apply the parameterized quantum circuits of the m n qubits to the corresponding initial quantum states respectively to obtain m first quantum states.

9. The apparatus according to claim 7, wherein The loss function is determined based on the following formula: where ρ j is the j-th first quantum state, j = 1, 2, …, m, is the quantum state obtained after the quantum channel acts on the quantum state ρ j , p j is the probability value corresponding to the j-th first quantum state, and S() represents the von Neumann entropy.

10. The device according to claim 7, wherein, The adjustable parameters in the m first quantum states are adjusted by the gradient descent method to minimize the loss function.

11. An information transmission device based on a quantum channel, comprising: An acquisition unit, configured to acquire the ensemble corresponding to the Holevo information of the quantum channel; An encoding unit, configured to acquire the classical information to be transmitted and encode the classical information onto the corresponding quantum state in the ensemble; A transmission unit, configured to transmit the encoded quantum state through the quantum channel to obtain the transmitted quantum state; and A decoding unit, configured to decode the transmitted quantum state to obtain the transmitted classical information, where The ensemble corresponding to the Holevo information is optimized based on the method according to any one of claims 1-4.

12. The apparatus according to claim 11, wherein, The method for distinguishing the transmitted quantum state is determined by semidefinite programming, and the transmitted quantum state is decoded based on the determined method.

13. An electronic device, comprising: At least one processor; and A memory communicatively connected to the at least one processor; wherein The memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute the method according to any one of claims 1-6.

14. A non-transitory computer-readable storage medium storing computer instructions, wherein, The computer instructions are used to cause the computer to execute the method according to any one of claims 1-6.

15. A computer program product comprising a computer program, wherein, The computer program, when executed by a processor, implements the method according to any one of claims 1-6.

Images