Quantum computing program, quantum computing apparatus, and quantum computing method

Abstract

To more reliably and quickly obtain the solution to a radio resource allocation problem.SOLUTION: A quantum calculation program causes a computer to perform a transformation function that uses a binary number to represent the number specific to a channel used in wireless communication and transforms an objective function of a radio resource allocation problem for the channel into the product of binary variables.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a quantum computing program, a quantum computing apparatus, and a quantum computing method. [Background technology]

[0002] By having base stations, access points (APs), and other devices used in wireless communication use different channels, it becomes possible to reduce radio wave interference and increase communication channel capacity. To achieve this, it is necessary to obtain a suitable solution to the problem of allocating suitable channels to each base station, access point, etc., when multiple terminals exist in the service area of ​​the base station, access point, etc. This problem is widely known as the radio resource allocation problem. Examples of literature on techniques for obtaining solutions to the radio resource allocation problem include Non-Patent Document 1 and Non-Patent Document 2. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] K. Kurasawa et al., “A high-speed channel assignment algorithm for dense IEEE 802.11 systems via coherent Ising machine,” IEEE Wireless Communications Letters, vol. 10, no. 8, 2021. [Non-Patent Document 2] K. Saito, A Ikami, and C. Ono, “Evaluating dynamic spectrum allocation using quantum annealing,” IEICE Communications Express, vol. 1, no. 9, 2021.

[0004] Non-Patent Document 1 formulates the radio resource allocation problem as a quadratic unconstrained binary optimization (QUBO) problem and discloses a technique for obtaining a solution using a coherent ising machine. Non-Patent Document 1 discloses that by using a coherent ising machine, it is possible to obtain a solution with a higher effective throughput than other heuristic-based search methods within a certain time regardless of the size of the QUBO problem.

[0005] Non-Patent Document 2 formulates the radio resource allocation problem in a mobile phone network as a QUBO problem and discloses a technique that enables obtaining a solution 2146 times faster than a mathematical programming solver by using a classical computer.

[0006] However, the high speed in obtaining a solution of the coherent ising machine according to Non-Patent Document 1 has not been theoretically proven. Similarly, the high speed in obtaining a solution of the classical annealers of the quantum annealer and the quantum inspired machine according to Non-Patent Document 2 has not been theoretically proven. Furthermore, since both the technique according to Non-Patent Document 1 and the technique according to Non-Patent Document 2 require a large number of binary variables, there is a concern that the search space may be expanded and a solution may not be obtained quickly.

Summary of the Invention

Problems to be Solved by the Invention

[0007] The present invention has been made in view of the above circumstances, and an object thereof is to provide a quantum computing program, a quantum computing device, and a quantum computing method capable of more reliably and quickly obtaining a solution to the radio resource allocation problem.

Means for Solving the Problems

[0008] One aspect of the present invention represents a number unique to a channel used for wireless communication using a binary number, A binary variable is set for each access point, and for each digit when the channel used by the access point is represented in binary, and the evaluation of the channel assignment to the access point is shown using the binary variable. and the objective function of the radio resource allocation problem regarding the channel A function to perform the generation process, and a function to perform quantum computation to derive the value of the binary variable using the objective function,It is a quantum computing program to be executed by a computer.

[0009] The quantum computing program according to one aspect of the present invention applies Grover's adaptive search to the radio resource allocation problem, The aforementioned Product of binary variables The assignment of the channel to the access point is expressed as the product of a subexpression that subtracts the binary variable from 1, or as the product of a combination of the binary variable and a subexpression that subtracts the binary variable from 1. Binary variables that have the possibility of making the value of the objective function smaller than a predetermined threshold value A quantum computing function that executes a quantum computing process for deriving, and the classical computing function that executes a classical computing process for calculating the value of the objective function when the binary variable value is given, and when the value of the objective function when the binary variable [[ID=一三]] value is given is smaller than the predetermined threshold, the predetermined threshold is further value to the value of the objective function when the binary variable New is given, and a repetition processing function that repeats the process of causing the quantum computing function to execute the quantum computing process, causing the classical computing function to execute the classical computing process, and causing the update function to execute the update process until a predetermined condition is satisfied is further executed by the computer.

[0010] ]> value value to Randomly determine the initial variable, which is the initial value of the variable, value and when the initial variable Value is given, use the initial value of the predetermined threshold as the value of the objective function, and in the first quantum computing process to be executed, use the initial value of the predetermined threshold as the predetermined threshold. ]>

[0011] One aspect of the present invention represents the number unique to the channel used for wireless communication using binary numbers, A binary variable is set for each access point, and for each digit when the channel used by the access point is represented in binary, and the evaluation of the channel assignment to the access point is shown using the binary variable. the objective function of the radio resource allocation problem regarding the channel The process to generate is executed, and a quantum computation process is performed to derive the value of the binary variable using the objective function. is a quantum computing device.

[0012] One aspect of the present invention represents the number unique to the channel used for wireless communication using binary numbers, A binary variable is set for each access point, and for each digit when the channel used by the access point is represented in binary, and the evaluation of the channel assignment to the access point is shown using the binary variable.The objective function of the radio resource allocation problem relating to the aforementioned channel is The quantum computation process is performed to generate and derive the value of the binary variable using the objective function. This is a quantum computing method. [Effects of the Invention]

[0013] According to the present invention, it is possible to provide a quantum computing program, a quantum computing device, and a quantum computing method that can more reliably and quickly obtain a solution to the wireless resource allocation problem. [Brief explanation of the drawing]

[0014] [Figure 1] This figure shows an example of the software configuration of a quantum computing device according to an embodiment of the present invention. [Figure 2] This figure shows an example of a number assigned to a channel used in wireless communication according to an embodiment of the present invention, a binary representation of the number, and a representation used in its formulation. [Figure 3] This figure shows an example of the distance between access points according to an embodiment of the present invention. [Figure 4] This figure shows an example of the number of binary variables, the maximum value, and the required number of qubits for the objective function generated by the formulation relating to the comparative example and the objective function generated by the formulation according to the embodiment of the present invention. [Figure 5] This figure shows an example of the relationship between the number of trials and the value of the objective function when a full search is performed for the comparative example. [Figure 6] This figure shows a comparative example and an example of the distribution of solutions to the wireless resource allocation problem according to the embodiment of the present invention. [Figure 7] This figure shows an example of the relationship between the number of access points and the number of required qubits when a full search according to the comparative example is performed and when a Grover adaptive search according to the embodiment of the present invention is performed. [Figure 8] This figure shows an example of the relationship between the number of access points and the number of required qubits when a full search according to the comparative example is performed and when a Grover adaptive search according to the embodiment of the present invention is performed. [Figure 9]This flowchart shows an example of a process performed by a quantum computing device according to an embodiment of the present invention. [Figure 10] This figure shows an example of a quantum circuit when a suitable threshold cannot be set using the quantum computing device according to an embodiment of the present invention. [Figure 11] This figure shows an example of the relationship between the number of trials and the value of the objective function in the case where a full search according to the comparative example is performed, and in the case where a suitable threshold is not set by the quantum computing device according to the embodiment of the present invention, and a Grover adaptive search is performed. [Figure 12] This figure shows an example of the probability of observing each state when no suitable threshold is set in the quantum computing apparatus according to an embodiment of the present invention, and the Grover operator is applied zero times to the qubit representing the value of the objective function. [Figure 13] This figure shows an example of the probability of observing each state when no suitable threshold is set in the quantum computing apparatus according to an embodiment of the present invention, and the Grover operator is applied once to the qubit representing the value of the objective function. [Figure 14] This figure shows an example of the probability of observing each state when no suitable threshold is set in the quantum computing apparatus according to an embodiment of the present invention, and the Grover operator is applied twice to the qubit representing the value of the objective function. [Figure 15] This figure shows an example of the probability of observing each state when no suitable threshold is set in the quantum computing apparatus according to an embodiment of the present invention, and the Grover operator is applied three times to the qubit representing the value of the objective function. [Figure 16] This figure shows an example of a quantum circuit when a suitable threshold is set using a quantum computing device according to an embodiment of the present invention. [Figure 17] This figure shows an example of the probability of observing each state when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied zero times to a qubit representing the value of the objective function. [Figure 18]This figure shows an example of the probability of observing each state when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied once to a qubit representing the value of the objective function. [Figure 19] This figure shows an example of the probability of observing each state when a suitable threshold is set using a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied twice to a qubit representing the value of the objective function. [Figure 20] This figure shows an example of the probability of observing each state when a suitable threshold is set using a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied three times to a qubit representing the value of the objective function. [Modes for carrying out the invention]

[0015] [Embodiment] A quantum computing program, quantum computing apparatus, and quantum computing method according to the embodiment will be described with reference to Figures 1 to 20.

[0016] Figure 1 shows an example of the software configuration of a quantum computing device according to an embodiment of the present invention. As shown in Figure 1, the quantum computing device 1 includes a conversion function 11, a quantum computing function 12, a classical computing function 13, an update function 14, and an iterative processing function 15. The conversion function 11, the quantum computing function 12, the classical computing function 13, the update function 14, and the iterative processing function 15 are all realized by the execution of a quantum computing program 10.

[0017] The conversion function 11 represents the channel-specific number used for wireless communication using binary numbers and performs a formulation that transforms the objective function of the wireless resource allocation problem for the channel into a product of binary variables. For example, the conversion function 11 performs the process described below.

[0018] The channel capacity C between an access point used for wireless communication and a terminal used by a user is expressed by the following equation (1), which includes the bandwidth B of the channel used for wireless communication between the access point and the terminal, the power S of the signal received by the terminal, the power I of interfering radio waves received from other terminals within the service area, and the power n of the channel noise. The logarithmic argument in equation (1) is called the Signal to Interference plus Noise power Ratio (SINR). Equation (1) shows that in order to maximize the channel capacity C, the SINR must be maximized. In other words, equation (1) shows that in order to solve the radio resource allocation problem, the sum of the SINRs must be maximized.

[0019]

number

[0020] Furthermore, the binary variable in the objective function of the wireless resource allocation problem is the number of access points N. AP and the number of channels N CH In that case, it is defined by the following equation (2).

[0021]

number

[0022] S is the total received signal power from access point i to terminal u. iu is a binary variable x ij , transmission signal power P, set of terminals U communicating via access point i i , distance d between access point i and terminal u iu It is expressed by the following equation (3), which includes the damping constant α and the Kronecker delta δ.

[0023]

number

[0024] The total received signal power I of terminals u located within the service area of ​​access point i, received from other terminals. iu This is expressed by the following equation (4).

[0025]

number

[0026] Therefore, the objective function that maximizes the sum of the SINRs of each terminal is expressed by equation (5) from equations (3) and (4). Note that equation (5) is valid under the assumption that the SINR is unaffected by noise power n.

[0027]

number

[0028] The conversion function 11 transforms the wireless resource allocation problem into a minimization problem by taking the reciprocal of both sides of equation (5), which is equation (6).

[0029]

number

[0030] Furthermore, the conversion function 11 adds the constraint represented by the following equation (7) because each access point uses only one channel.

[0031]

number

[0032] In other words, the objective function that maximizes the sum of the SINRs for each terminal is given by equation (8) based on equations (6) and (7). Equation (8) includes a penalty coefficient λ to avoid violating the constraints expressed in equation (7).

[0033]

number

[0034] The conversion function 11 defines the part of equation (6) relating to distance D by the following equation (9).

[0035]

number

[0036] Next, the conversion function 11 represents a channel-specific number used for wireless communication using binary numbers. The conversion function 11 represents the channel-specific number as a binary number, expressing the digit "0" contained in the binary number as "1-x (x=0 or 1)" and the digit "1" contained in the binary number as "x (x=0 or 1)".

[0037] Figure 2 shows an example of a channel number assigned to a wireless communication used according to an embodiment of the present invention, its binary representation, and the representation used in its formulation. Figure 2 shows the number of access points N AP This shows the case where = 4. The left column of Figure 2 shows the numbers assigned to the channels. The middle column of Figure 2 shows the numbers shown in the left column of Figure 2 as binary representations. The right column of Figure 2 shows the binary numbers in the middle column of Figure 2 converted into a product of binary variables. For example, conversion function 11 represents the numbers shown in the left column of Figure 2 as the binary numbers shown in the middle column of Figure 2. Then, conversion function 11 converts the binary numbers shown in the middle column of 2 into a product of binary variables shown in the right column of Figure 2.

[0038] As a result, the conversion function 11 is configured such that the value of the objective function increases when the target channel is selected. Furthermore, with respect to the channel, the number of bits R required for such representation satisfies the following equation (10), and is therefore expressed by the following equation (11).

[0039]

number

[0040]

Number

[0041] In the following description, taking the case where the number N of access points AP = 4 and the number N of channels CH = 3 as an example for explanation. FIG. 3 is a diagram showing an example of the distance between access points according to an embodiment of the present invention. In this case, the above-described distance D shall adopt the distance shown in FIG. 3. Incidentally, in this case, the channel shown in the bottom row of FIG. 2 will be redundant.

[0042] The objective function is represented by the following formula (12) in the case of the formulation according to the comparative example.

[0043]

Number

[0044] On the other hand, the conversion function 11 selects two of the four access points, creates the product of binary variables between the access points shown in the left column of FIG. 3, and multiplies it by the distance D shown in the right column of FIG. 3. For example, the product of the binary variables of access point 1 and access point 2 is represented by the following formula (13).

[0045]

Number

[0046] Next, the conversion function 11 adds up the terms obtained by multiplying the product of the binary variables created between the access points shown in the left column of FIG. 3 by the distance D. For example, the conversion function 11 obtains the following formula (14) by such processing.

[0047]

Number

[0048] The conversion function 11 then has a number of channels N CH =2 R The number of channels is N. CH <2 R It determines whether it is true. The conversion function 11 has a number of channels N. CH =2 R If it is determined that this is the case, then equation (14) is used as the objective function of the wireless resource allocation problem. On the other hand, the conversion function 11 has a number of channels N CH <2 R If this is determined, the remaining channel numbers shown in the bottom row of Figure 2 are converted into a product of binary variables, multiplied by a penalty coefficient λ, and added to equation (14) as a constraint to generate equation (15). The conversion function 11 uses equation (15) as the objective function of the wireless resource allocation problem.

[0049]

number

[0050] The conversion function 11 performs the formulation described above. Figure 4 is a diagram showing an example of the number of binary variables, the maximum value, and the number of required qubits for the objective function generated by the formulation related to the comparative example and the objective function generated by the formulation according to the embodiment of the present invention. The top row of Figure 4 shows an example of the number of binary variables, the maximum value, and the number of required qubits for equation (12), which represents the objective function generated by the formulation related to the comparative example. The bottom row of Figure 4 shows an example of the number of binary variables, the maximum value, and the number of required qubits for equation (15), which represents the objective function generated by the formulation according to the embodiment of the present invention. Referring to Figure 4, it can be seen that equation (15) has a smaller maximum value and fewer required qubits than equation (12). Although equation (15) has a maximum order of 4, unlike equation (12) which has a maximum order of 2, Grover Adaptive Search (GAS) is applicable to objective functions of order 2 or higher, so there is no particular problem.

[0051] The conversion function 11 is used for the number of access points NAP =4, Number of channels N CH If = 4, perform the above formulation to generate the objective function represented by equation (16) below.

[0052]

number

[0053] Figure 5 shows an example of the relationship between the number of trials and the value of the objective function when a brute-force search is performed according to the comparative example. Figure 6 shows an example of the distribution of solutions to the wireless resource allocation problem according to the comparative example and the embodiment of the present invention. Referring to Figure 6, the value of the objective function is thought to converge after about 250 trials, but referring to Figure 5, it converges after about 80 trials. This is thought to be because, as shown in Figure 6, there are 256 total solutions, but only 24 are global optimal solutions, resulting in a high ratio of global optimal solutions to the total number of solutions.

[0054] Next, we will explain the number of qubits required when a brute-force search is performed according to the comparative example and the number of qubits required when a Grover adaptive search according to the embodiment of the present invention is performed. Grover adaptive search involves n binary variables (x1, x2, ..., x) included in the objective function. n This requires n qubits to represent the objective function and m qubits to represent the value of the objective function. m is the smallest integer that satisfies equations (17) and (18). Equation (17) also includes any coefficient k in the objective function.

[0055]

number

[0056]

number

[0057] The objective function generated by the formulation relating to the comparative example contains the number of binary variables expressed in equation (19) and takes the maximum value expressed in equation (20). Furthermore, the objective function generated by the formulation relating to the comparative example is encoded by the number of qubits expressed in equation (21).

[0058]

number

[0059]

number

[0060]

number

[0061] Therefore, the objective function generated by the formulation relating to the comparative example requires the number of qubits expressed by equation (22). Equation (22) includes asymptotic notation "O(·)".

[0062]

number

[0063] N CH =N AP If N is / 4, then equation (22) becomes equation (23). CH =N AP If the value is / 2, then equation (22) becomes equation (24).

[0064]

number

[0065]

number

[0066] The objective function generated by the formulation according to the embodiment of the present invention includes a number of binary variables represented by the following equation (25), and takes the maximum value represented by the following equation (26). Furthermore, the objective function generated by the formulation according to the embodiment of the present invention is encoded by a number of qubits represented by the following equation (27).

[0067]

number

[0068]

number

[0069]

number

[0070] Therefore, the objective function generated by the formulation according to the embodiment of the present invention requires the number of qubits represented by the following equation (28).

[0071]

number

[0072] N CH =N AP If N is / 4, then equation (28) becomes equation (29). CH =N AP If the value is / 2, then equation (28) becomes equation (30).

[0073]

number

[0074]

number

[0075] Figures 7 and 8 show an example of the relationship between the number of access points and the number of required qubits when a full search according to the comparative example is performed and when a Grover adaptive search according to the embodiment of the present invention is performed. Referring to Figures 7 and 8, it can be seen that the objective function generated by the formulation according to the embodiment requires fewer qubits than the objective function generated by the formulation according to the comparative example. Furthermore, Figures 7 and 8 show that the number of qubits that can be reduced increases as the scale of the wireless resource allocation problem increases.

[0076] The quantum computing function 12 randomly determines an initial variable, which is the initial value of a binary variable, and sets the value of the objective function when the initial variable is 0 as the initial value of a predetermined threshold. In the first quantum computing process executed, it uses the initial value of the predetermined threshold as the predetermined threshold. Then, the quantum computing function 12 applies Grover adaptive search to the wireless resource allocation problem and performs a quantum computing process to derive a binary variable that has the potential to make the value of the objective function, which has been transformed into a product of binary variables, smaller than the predetermined threshold.

[0077] Classical computation function 13 performs a classical computation process that calculates the value of the objective function using a classical computer, given a binary variable.

[0078] The update function 14 performs an update process. Specifically, if the value of the objective function given a binary variable is smaller than a predetermined threshold, the update function 14 updates the predetermined threshold to the value of the objective function given a binary variable. On the other hand, if the value of the objective function given a binary variable is greater than or equal to the predetermined threshold, the update function 14 updates the predetermined natural number to an even larger natural number.

[0079] The iterative processing function 15 repeatedly causes the quantum computing function 12 to perform quantum computing, the classical computing function 13 to perform classical computing, and the update function 14 to perform update processing until a predetermined condition is met. The predetermined condition is, for example, that the total number of times the Grover operator is applied is equal to or greater than a predetermined number of times. Alternatively, the predetermined condition is that the query computation time of the classical domain that is not updated to the value of the objective function by the update function 14 is equal to or greater than a predetermined threshold. Alternatively, the predetermined condition is that at least one of these two conditions is met.

[0080] Next, an example of a process performed by the quantum computing device 1 will be described with reference to Figure 9. Figure 9 is a flowchart showing an example of a process performed by the quantum computing device according to an embodiment of the present invention.

[0081] In step S11, the conversion function 11 represents the channel-specific number used for wireless communication using binary numbers and converts the objective function of the wireless resource allocation problem with respect to the channel into a product of binary variables.

[0082] In step S12, the quantum computing function 12 applies Grover adaptive search to the wireless resource allocation problem and derives binary variables that have the potential to make the value of the objective function, which has been transformed into a product of binary variables, smaller than a predetermined threshold.

[0083] In step S13, the classical computation function 13 calculates the value of the objective function using a classical computer, given a binary variable.

[0084] In step S14, the update function 14 determines whether the value of the objective function given a binary variable is less than a predetermined threshold. If the update function 14 determines that the value of the objective function given a binary variable is less than a predetermined threshold (step S15: YES), it proceeds to step S15. On the other hand, if the update function 14 determines that the value of the objective function given a binary variable is greater than or equal to a predetermined threshold (step S15: NO), it proceeds to step S16.

[0085] In step S15, the update function 14 updates the predetermined threshold to the value of the objective function given a binary variable, and proceeds to step S17.

[0086] In step S16, the update function 14 updates the predetermined natural number to an even larger natural number and proceeds to step S17.

[0087] Next, we will explain an example of the results obtained when the quantum computing device 1 determines an initial value of a predetermined threshold and repeatedly performs quantum computing, classical computing, and update processing. In this explanation of the results, the number of access points N AP =3, Number of channels N CH Let's take the case where =3 as an example. Quantum computer 1 randomly initializes the distances between access points and generates an objective function represented by the following equation (31). Then, based on the fact that the binary variable x has the property represented by the following equation (32), quantum computer 1 transforms equation (31) into equation (33).

[0088]

number

[0089]

number

[0090]

number

[0091] The quantum computing function 12 represents the objective function expressed by equation (33) using a quantum circuit. Figure 10 shows an example of a quantum circuit when a suitable threshold is not set by the quantum computing apparatus according to the embodiment of the present invention. For example, the quantum computing function 12 represents the objective function E(x) expressed by equation (33) using the quantum circuit shown in Figure 10. The quantum circuit shown in Figure 10 uses six qubits to represent six binary variables and five qubits to represent the value of the objective function E(x).

[0092] A quantum circuit is a state preparation operator A that constructs the function E(x)-y obtained by subtracting a threshold y from the objective function E(x). y This is applied to the initial state of the objective function E(x). This allows the quantum circuit to have pairs of n binary variables and the value of the objective function. n Generates a superposition of multiple elements.

[0093] Quantum circuits use unitary operators U G It uses quantum gates represented by (θ) and the Inverse Quantum Fourier Transform (IQFT). Unitary operator U G The quantum gate represented by (θ) is the state preparation operator A y The value of the objective function is calculated. When a quantum circuit realizes an integer k, it performs an inverse quantum Fourier transform, leaving only the state that represents a single integer k. In other words, the quantum circuit performs integer addition and subtraction by rotating the phase. The quantum circuit then represents the result of integer addition and subtraction with m=5 bits. Furthermore, the objective function uses qubits representing each of the n=6 variables as control bits, and the unitary operator U is used only when all control bits are 1. G It is represented as a quantum circuit that applies (θ). Therefore, the quantum computing function 12 can search for solutions to higher-order unconstrained binary optimization problems by increasing the number of control bits.

[0094] The quantum circuit uses the oracle operator O to invert and mark the phase θ at which the function E(x)-y is negative, in order to amplify the probability of outputting a negative state among the values ​​of the function E(x)-y calculated in parallel for all combinations of n=6 variables. The phase θ at which the function E(x)-y is negative is the phase θ at which the objective function E(x) is smaller than the threshold y. Furthermore, since the value of the objective function is expressed using two's complement, it can be constructed by applying a Z gate only to the first of m=5 bits. The quantum circuit then uses the Grover diffusion operator D to amplify the probability of outputting a state represented by the marked phase θ. The Grover diffusion operator D inverts each state relative to the average of the states represented by all combinations of n=6 variables. The quantum circuit then applies the Grover operator G L times to state G L A y |0> n+m Outputs.

[0095] The quantum computing function 12 randomly determines an initial variable x0, which is the initial value of a binary variable, and sets the value of the objective function E(x0) given the initial variable x0 as the initial value y0 of a predetermined threshold. In the first quantum computing process to be executed, it uses the initial value y0 of the predetermined threshold as the predetermined threshold.

[0096] In this case, the quantum circuit shown in Figure 10 is included in the objective function E(x), and the Hadamard gate H is applied to the six qubits representing the initialized binary variables to generate an equally probable superposition of (x1, x2, ..., x6). The black circles in Figure 10 represent the control bits. When all the control bits are 1, the unitary operator U is applied to the qubits representing the binary variables. G To apply the effect.

[0097] The first unitary operator U shown in Figure 10 G The quantum gate expressed by (8.2π / 16) corresponds to the first term of the objective function shown in equation (33). The second unitary operator U shown in Figure 10 GThe quantum gate expressed by (11.1π / 16) corresponds to the second term of the objective function shown in equation (33). The third unitary operator U shown in Figure 10 G The quantum gate represented by (-7.4π / 16) corresponds to the third term of the objective function shown in equation (33). The fourth unitary operator U shown in Figure 10 G The quantum gate expressed by (-7.4π / 16) corresponds to the fourth term of the objective function shown in equation (33). The fifth term and subsequent terms of equation (33) are omitted in Figure 10. The quantum circuit shown in Figure 10 calculates the final phase by applying the inverse quantum Fourier transform after the quantum gate has been applied. The quantum circuit shown in Figure 10 then sets the Grover operator G to L i To activate it repeatedly

[0098] The classical computation function 13 performs classical computation. Specifically, the classical computation function 13 uses a classical computer to calculate the value y of the objective function E(x) given the variable x.

[0099] The update function 14 executes the update process. Specifically, the update function 14 checks if the value y of the objective function E(x) given variable x is a predetermined threshold y i If it is less than a predetermined threshold y i The value of the objective function E(x) given the variable x y i+1 The value of the objective function E(x) given the variable x is updated to =y. Meanwhile, the update function 14 determines that the value y of the objective function E(x) is a predetermined threshold y. i If the value is greater than or equal to the given value, the predetermined natural number k is updated to an even larger natural number. For example, the update function 14 updates the predetermined natural number k to a natural number expressed by the following equation (34). The value of λ included in equation (34) is, for example, 8 / 7.

[0100]

number

[0101] The iterative processing function 15 repeatedly causes the quantum computing function 12 to perform quantum computing, the classical computing function 13 to perform classical computing, and the update function 14 to perform update processing until predetermined conditions are met.

[0102] Figure 11 shows an example of the relationship between the number of trials and the value of the objective function when a brute-force search according to the comparative example is performed and when a suitable threshold is not set by the quantum computing apparatus according to the embodiment of the present invention and a Grover adaptive search is performed. The horizontal axis of Figure 11 represents the number of trials. The vertical axis of Figure 11 represents the value of the objective function E(x). The dashed line in Figure 11 shows the relationship between the number of trials and the value of the objective function when a brute-force search according to the comparative example is performed. The solid line in Figure 11 shows the relationship between the number of trials and the value of the objective function when the processing according to the embodiment of the present invention is performed.

[0103] Referring to Figure 11, it can be seen that the process performed by quantum computing device 1 is able to obtain the state that minimizes the objective function E(x) with fewer trials than the exhaustive search in the comparative example. Note that the ability to solve a problem with less query computation by using quantum computing is called quadratic acceleration or quantum acceleration.

[0104] Figures 12 to 15 show the probabilities of observing each of the six binary variable states when the Grover operator G is applied to the qubit representing the value of the objective function E(x). Figures 12 to 15 show only the top 16 states in terms of observed probability.

[0105] Figure 12 shows an example of the probability of observing each state when no suitable threshold is set by the quantum computing apparatus according to the embodiment of the present invention, and the Grover operator is applied 0 times to the qubit representing the value of the objective function. Figure 13 shows an example of the probability of observing each state when no suitable threshold is set by the quantum computing apparatus according to the embodiment of the present invention, and the Grover operator is applied 1 time to the qubit representing the value of the objective function. Figure 14 shows an example of the probability of observing each state when no suitable threshold is set by the quantum computing apparatus according to the embodiment of the present invention, and the Grover operator is applied 2 times to the qubit representing the value of the objective function. Figure 15 shows an example of the probability of observing each state when no suitable threshold is set by the quantum computing apparatus according to the embodiment of the present invention, and the Grover operator is applied 3 times to the qubit representing the value of the objective function.

[0106] Figures 12 to 15 all show that the observed probabilities for all states are not amplified. This is because, although the quantum circuit is functioning correctly, the minimum value of the objective function expressed by equation (33) is 0, and there are no states in which the objective function has a negative value. In other words, the quantum computer 1 needs to set an appropriate threshold that allows for the existence of states in which the objective function has a negative value.

[0107] Figure 16 shows an example of a quantum circuit when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention. In this case, since an appropriate threshold is set, the objective function is the objective function obtained by replacing the first term "8.2" in equation (33) with "7.0". The quantum circuit shown in Figure 16 has the first unitary operator U G Except for (7.0π / 16), it is similar to the quantum circuit shown in Figure 10. The first unitary operator U G (7.0π / 16) corresponds to the first term "7.0" of the objective function in this case.

[0108] Figures 17 to 20 show the probabilities of observing each of the six binary variable states when the Grover operator G is applied to the qubit representing the value of the objective function E(x). Figures 17 to 20 show only the top 16 states in terms of observed probability.

[0109] Figure 17 shows an example of the probability of observing each state when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied 0 times to the qubit representing the value of the objective function. Since Figure 17 shows the probability of observing each state of the six binary variables when the Grover operator G is not applied, it shows that each state is observed with equal probability.

[0110] Figure 18 shows an example of the probability of observing each state when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention and the Grover operator is applied once to a qubit representing the value of the objective function. Figure 18 shows that the probability of observing the state in which the objective function E(x) has its minimum value of -1 is amplified to approximately 0.01 by applying the Grover operator G once.

[0111] Figure 19 shows an example of the probability of observing each state when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied twice to a qubit representing the value of the objective function. Figure 19 shows that the probability of observing the state in which the objective function E(x) has its minimum value of -1 is amplified to approximately 0.01 by applying the Grover operator G twice.

[0112] Figure 20 shows an example of the probability of observing each state when a suitable threshold is set by a quantum computing device according to an embodiment of the present invention, and the Grover operator is applied three times to a qubit representing the value of the objective function. Figure 20 shows that applying the Grover operator G three times only slightly amplifies the probability of observing the state where the objective function E(x) is at its minimum value of -1, suggesting that the number of times the Grover operator G is applied is inappropriate.

[0113] The quantum computing device 1 according to the embodiment has been described above. The quantum computing device 1 includes a conversion function 11, a quantum computing function 12, a classical computing function 13, an update function 14, and an iterative processing function 15.

[0114] The conversion function 11 represents the channel-specific number used for wireless communication using binary numbers and converts the objective function of the wireless resource allocation problem for the channel into a product of binary variables.

[0115] This allows the quantum computer 1 to reduce the number of qubits required to obtain the globally optimal solution to the objective function of the wireless resource allocation problem. Furthermore, this enables the quantum computer 1 to obtain a solution to the wireless resource allocation problem more reliably and quickly.

[0116] The quantum computing function 12 randomly determines initial variables, which are the initial values ​​of binary variables, sets the value of the objective function given the initial variables as the initial value of a predetermined threshold, and uses the initial value of the predetermined threshold as the predetermined threshold in the first quantum computing process to be executed. Then, the quantum computing function 12 applies Grover adaptive search to the wireless resource allocation problem and performs a quantum computing process to derive binary variables that have the potential to make the value of the objective function, which has been transformed into a product of binary variables, smaller than the predetermined threshold. The classical computing function 13 performs a classical computing process to calculate the value of the objective function given binary variables using a classical computer.

[0117] The update function 14 executes the update process. Specifically, if the value of the objective function given a binary variable is smaller than a predetermined threshold, the update function 14 updates the predetermined threshold to the value of the objective function given a binary variable. On the other hand, if the value of the objective function given a binary variable is greater than or equal to a predetermined threshold, the update function 14 updates a predetermined natural number to an even larger natural number. The iterative processing function 15 repeats the process of having the quantum computing function execute quantum computing, the classical computing function execute classical computing, and the update function execute update processing until predetermined conditions are met.

[0118] As a result, the quantum computer 1 can obtain the global optimal solution to the wireless resource allocation problem formulated by the transformation function 11. Furthermore, the quantum computer 1 can obtain a solution even if the coefficients of the objective function of the wireless resource allocation problem formulated by the transformation function 11 include real numbers.

[0119] Embodiments of the present invention have been described above with reference to the drawings. However, the quantum computing program, quantum computing apparatus, and quantum computing method are not limited to the embodiments described above, and at least one of various modifications, substitutions, combinations, and design changes can be made without departing from the spirit of the present invention.

[0120] Furthermore, the effects of the embodiments of the present invention described above are merely examples. Therefore, the embodiments of the present invention may also produce other effects that can be recognized by those skilled in the art from the description of the embodiments above. [Explanation of Symbols]

[0121] 1...Quantum computing device, 10...Quantum computing program, 11...Conversion function, 12...Quantum computing function, 13...Classical computing function, 14...Update function, 15...Iterative processing function

Claims

1. A function that generates an objective function for the wireless resource allocation problem relating to the channel, which represents a unique number for the channel used in wireless communication using binary numbers, sets up a binary variable for each access point and for each digit when the channel used by the access point is represented in binary, and uses the binary variables to show an evaluation of the channel allocation to the access point. A function to perform quantum computation processing to derive the value of the binary variable using the objective function, A quantum computing program that is executed by a computer.

2. A quantum computing function that applies Grover adaptive search to the wireless resource allocation problem and performs quantum computation to derive binary variable values ​​that have the potential to make the value of the objective function, which expresses the allocation of the channels to the access points as a product of the binary variables, a product of subexpressions that subtract the binary variables from 1, or a product of a combination of the binary variables and a subexpression that subtracts the binary variables from 1, smaller than a predetermined threshold, A classical computation function that performs a classical computation process to calculate the value of the objective function using a classical computer when the binary variable values ​​are given, An update function that, when the value of the objective function given the binary variable value is smaller than the predetermined threshold, performs an update process to update the predetermined threshold to the value of the objective function given the binary variable value, A repetitive processing function that repeats the process of causing the quantum computing function to execute the quantum computing process, the classical computing function to execute the classical computing process, and the update function to execute the update process until a predetermined condition is met, A quantum computing program according to claim 1, which causes a computer to perform further operations.

3. The quantum computing function randomly determines an initial variable value which is the initial value of the binary variable, sets the value of the objective function given the initial variable value as the initial value of the predetermined threshold, and in the quantum computing process that is first executed, uses the initial value of the predetermined threshold as the predetermined threshold. The quantum computing program according to claim 2.

4. A unique number for each channel used in wireless communication is represented using binary numbers, a binary variable is set for each access point and for each digit when the channel used by the access point is represented in binary, and a process is executed to generate an objective function for the wireless resource allocation problem relating to the channel, which shows an evaluation of the channel allocation to the access point, using the binary variables. A quantum computation process is performed to derive the value of the binary variable using the aforementioned objective function. Quantum computing device.

5. A unique number for each channel used in wireless communication is represented using binary numbers, a binary variable is established for each access point and for each digit when the channel used by the access point is represented in binary, and an objective function for the wireless resource allocation problem relating to the channel is generated using these binary variables, which shows an evaluation of the channel allocation to the access point. A quantum computation process is performed to derive the value of the binary variable using the aforementioned objective function. Quantum computing methods.

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