System, Information Processing Method, and Program

Abstract

To provide a system, an information processing method, and a program, capable of reducing processing burdens when valuating derivatives having a plurality of underlying assets.SOLUTION: A system 10 includes a quantum processor 20, wherein the quantum processor 20 executes processing of: applying a quantum algorithm to output a quantum state that retains a value of a market price on each grid as a separate ground-state amplitude, to a partial differential equation regarding a market price valuation of a derivative based on each of a plurality of underlying asset prices, each of a plurality of underlying asset volatilities, a correlation matrix for the plurality of underlying asset prices, and a risk-free interest rate; and calculating a current price of the derivative using a quantum circuit for generating a first quantum state embedded with the current value on each grid at any point in time obtained from executing the quantum algorithm from maturity to any point in time, and a quantum circuit for generating a second quantum state embedded with probability distributions of the plurality of underlying asset prices at any point in time.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a system, an information processing method, and a program.

Background Art

[0002] Conventionally, research has been conducted on evaluating the fair value of derivatives using quantum algorithms. For example, Non-Patent Document 1 below describes research on evaluating the fair value of derivatives by applying a quantum algorithm to a method using partial differential equations (PDE approach).

Prior Art Documents

Non-Patent Documents

[0003]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, in the conventional technology, there is still room for improvement in reducing the processing load when evaluating derivatives having a plurality of underlying assets.

[0005] The present invention has been made in view of such circumstances, and an object thereof is to provide a system, an information processing method, and a program capable of reducing the processing load when evaluating derivatives having a plurality of underlying assets.

Means for Solving the Problems

[0006] A system according to one aspect of the present disclosure includes a quantum processor, and the quantum processor applies a partial differential equation related to the mark-to-market of a derivative based on each of the prices of a plurality of underlying assets, each of the volatilities of the plurality of underlying assets, the correlation matrix of the prices of the plurality of underlying assets, and the risk-free interest rate, to a quantum algorithm that outputs a quantum state that holds the mark-to-market values at each grid as the amplitudes of separate basis states, and executes the quantum algorithm from the expiration time to any time point within a period from the current time to a predetermined future time point to generate a first quantum state embedded with the mark-to-market at each grid at the future time point obtained thereby, and uses a quantum circuit that generates a second quantum state embedded with the probability distribution of the prices of the plurality of underlying assets at any time point, estimates the inner product of the first quantum state and the second quantum state, calculates the expected value of the discounted mark-to-market of the derivative at any time point based on this estimate, and outputs the current mark-to-market of the derivative based on the calculated expected value.

Advantages of the Invention

[0007] According to the present invention, it is possible to reduce the processing load when evaluating a derivative having a plurality of underlying assets.

Brief Description of the Drawings

[0008]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Modes for Carrying Out the Invention

[0009] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. The same elements are denoted by the same reference numerals, and redundant descriptions will be omitted.

[0010] FIG. 1 is a diagram showing an overview of a system 10 according to an embodiment of the present disclosure. The system 10 includes a client computer 500, a server computer 600, and a quantum processor 20. The client computer 500 and the server computer 600 are composed of general-purpose classical computers, as will be described in detail later. The quantum processor 20 may be a quantum computer having a plurality of physical qubits and performing quantum operations by performing gate operations on the qubits.

[0011] The client computer 500 is connected to the server computer 600 via a communication network such as the Internet. The server computer 600 is connected to the quantum processor 20 via a communication network such as a LAN (Local Area Network). A user of the client computer 500 indirectly sends a command to the quantum processor 20 by operating the client computer 500 and executes a quantum operation using the quantum processor 20. Note that the configuration of the system 10 is not limited to that shown in this application example. For example, the quantum processor 20 may be connected to the client computer 500 via a communication network such as a LAN without going through the server computer 600.

[0012] The system 10 according to this embodiment applies a quantum algorithm that outputs a quantum state that holds the value of the current price in each grid as the amplitude of a separate basis state to a partial differential equation related to the current price evaluation of derivatives with the price of each of a plurality of underlying assets, the volatility of each of the plurality of underlying assets, the correlation matrix of the prices of the plurality of underlying assets, and the risk-free interest rate as parameters, and determines the current price of the derivative. In this case, for example, the system 10 may receive from the user a specification of the type of the underlying asset to be evaluated through the client computer 500 by the server computer 600, transfer information regarding the received type of the underlying asset to the quantum processor 20, and output the current price of the derivative determined by the quantum processor 20 to the client computer 500 via the server computer 600.

[0013] Specifically, first, the system 10 refers to the prices S t =(S 1,t , ···, S d,t ) of d underlying assets, and it is required to calculate the current price V(0, S0) of the option price V(t, S Pay ), where a payoff f T (S t ) occurs at the expiration T of the option contract, under the partial differential equation shown in [Equation 1] below. Here, σ i is the volatility of S i,t , ρ ij is the correlation of the fluctuations of S i,t and S j,t , and r is the risk-free interest rate.

Equation

[0014] Boundary conditions shown in, for example, [Equation 2], [Equation 3], and [Equation 4] are set for the partial differential equation shown in [Equation 1].

Equation

Equation

Mathematics

[0015] When the variable transformations shown in [Mathematics 5], [Mathematics 6], and [Mathematics 7] are performed, [Mathematics 1] is transformed as shown in [Mathematics 8].

Mathematics

Mathematics

Mathematics

Mathematics

[0016] By introducing a discrete approximation to the differentiation with respect to the variable x, the linear ordinary differential equation shown in [Mathematics 9] is obtained.

Mathematics

[0017] By integrating both sides of [Mathematics 9] with respect to τ, [Mathematics 10] is obtained.

Mathematics

[0018] Y ~→ (τ) represents the option price on the discrete grid {X (i) gr} i=1 , ···, Ngr As shown in [Mathematics 11], the grid is divided into n i + 1 equal parts in each X i direction, where [l i , u i := logU i , l i := logL i ) (where l gr , u i , u i(excluding). The number of grids is N gr := n d gr It becomes like this.

Number

[0019] The matrix F in [Number 9] is obtained by discretizing the differentiation by X in [Number 8], and is an N gr × N gr matrix.

Number

[0020] D 1st is an n gr × n gr matrix.

Number

[0021] D 2nd is an n gr × n gr matrix.

Number

[0022] I is an n gr × n gr identity matrix.

[0023] C(τ) is expressed as shown in [Number 15]. Hereinafter, it is assumed that C(τ) does not depend on τ.

Number

[0024] [Number 16] is N grIt shows a system of linear equations in (q + 1) dimensions. Here, q := m(k + 1)+2p + 1, where m, k, and p are arbitrary positive integers, and h t is a positive constant, and γ → :=(γ,...,γ)T ∈ R Ngr is a vector formed by arranging the positive constant γ, and e → i is a (q + 1)-dimensional unit vector with only the i-th component being 1 and the others being 0.

[0025]

Number

[0026] The solution of [Equation 16] is described as in [Equation 17]. At this time, Y ~→ (τ ter ) is the approximate solution when [Equation 9] is solved up to τ t = mh ter after discrete approximation in the time direction by the time step width h t (>0), and is close to the solution Y ~→ (τ ter ) of [Equation 9].

[0027]

Number

[0028] Then, the quantum processor 20 generates a quantum state |Ψ ~→ (τ ter ) that is close to the quantum state |Ψ mod > in which Y ~ mod >(τ) of [Equation 18] is amplitude-encoded. Here, in [Equation 18], |Ψ gar > is a quantum state reflecting the values of Y ter from τ = 0 to τ = τ ~→ (τ), which is unnecessary information when obtaining the option's current price in this embodiment.

[0029] [Number]

[0030] Here, when obtaining the option price at the current time t = 0 (corresponding to τ = T), for example, the following procedure can be considered. First, for τ ter = T, find Y ~→ (T). Y ~→ (T) includes the option fair value when the price of the underlying asset takes various values at t = 0. Among them, obtain the option fair value corresponding to the actual current price S → 0. That is, for the x → corresponding to S → on the spatial grid point as x →(k) , it is only necessary to find the k-th component Y ~→ (T, x ~→ ). Therefore, the quantum processor 20 generates the quantum state |Ψ →(k) > with τ ter = T and reads the amplitude of a certain computational basis state corresponding to Y mod (T, x ~→ ). However, in this case, there are the following problems. That is, when the number of grids is large, this amplitude becomes very small. Therefore, a large amount of computational effort is required to read this amplitude from |Ψ →(k) >. Note that even when using the method described in Non-Patent Document 1, although the details are different, since a quantum state with the option fair value at each grid point at time t = 0 amplitude-encoded is generated, the above-mentioned problem of computational effort occurs. mod >

[0031] Therefore, in this embodiment, the quantum processor 20 calculates the derivative fair value V0 as the expected value E[e ter V(t -γtter , S ter (t → ))] shown in [Equation 19] at the time point t ter . For example, the quantum processor 20 uses the linear ordinary differential equation shown in [Equation 9] with T - t ter (hereinafter this is τter Y obtained by solving until (let it be) ~→ (τ ter ) and the discrete grid {X of the price of the original asset at time t as shown in [Equation 20] ter (i) gr} i= 1, ···, Ngr A vector p having the above distribution probability as a component → Calculate the inner product with, and approximate V0 to e -rT p → ·Y ~→ (τ ter )([Equation 25] described later). Note that t ter is the time when the spread of the distribution of the price of the original asset generally reaches the boundary of [Equation 3] and [Equation 4]. Here, it is assumed that positive real numbers A0, A1, …, A d exist and the condition f pay (S → ) ≦ Σ d i=1 A i S i + A0 is satisfied.

Equation

Equation

[0032] To realize the above equation as a quantum algorithm, do as follows. First, the quantum processor 20 constructs a quantum circuit U ~ mod > for generating |Ψ Ψmod > from the initial state |0>|0>. Next, the quantum processor 20 constructs a quantum circuit U Π for generating the quantum state |Π> as shown in [Equation 21] from the initial state |0>|0>.

Equation

[0033] Next, the quantum processor 20 is in the quantum state |Ψ ~ mod ​Outputs an estimated value E1 of the inner product of |Π> and |Ψ>. This is done by estimating the amplitude of |0>|0> in U Ψ ~ mod and the inverse circuit U of UΠ + Π using the state U generated by + Π U Ψ ~ mod |0>|0> by quantum amplitude estimation. Note that the inner product takes a value close to the inner product <Π|Ψ shown in [Equation 22]. mod >

Number

[0034] Note that any known method can be used to generate the quantum state |Π> and the quantum state |Ψ ~ mod >

[0035] Next, the quantum processor 20 outputs an estimated value E2 of the probability of observing any of p(k + 2)+1,..., p(k + 3)+1 in the first register when measuring |Ψ ~ mod > by quantum amplitude estimation. Note that the probability takes a value close to [Equation 23].

Number

[0036] Finally, the quantum processor 20 calculates the value shown in [Equation 24] and uses this as the estimated value of the option current market price. The value shown in [Equation 24] is close to [Equation 25] and is an approximation of the derivative current market price.

Number

Number

[0037] When the quantum processor 20 executes the above-described algorithm under an appropriate calculation setting, the derivative fair price can be obtained with an error of at most ε, and the computational load is shown in [Equation 26]. Also, assume relational expressions as shown in [Equation 27] and [Equation 28]. In this case, the parameters included in [Equation 26] satisfy the relational expression as shown in [Equation 29].

Equation

Equation

Equation

Equation

[0038] Figure 2 is an image diagram showing the spread of the price distribution of the underlying asset. As shown in the figure, as time elapses from the current time point t (= 0), the spread of the price distribution of the underlying asset gradually increases. As shown in the figure, at time t ter the spread of the price distribution of the underlying asset generally coincides with the boundary of the boundary conditions shown in [Equation 2], [Equation 3], and [Equation 4]. On the other hand, when numerically solving [Equation 1], [Equation 2], [Equation 3], and [Equation 4], the derivative fair price at each grid point set within the boundary is obtained. Therefore, obtaining the derivative present value as the expected value of the discounted derivative fair price at time t ter corresponds to using the numerical solution results without excess or deficiency. In the above-described quantum algorithm, Y amplitude-encoded in |Ψ ~ mod (τ ~→ (τ ter) The information will be utilized without excess or deficiency. In contrast, the method described in Non-Patent Document 1 creates a quantum state in which the derivative fair value at time t = 0 is amplitude-encoded and extracts only one of its amplitudes, which requires a great deal of computational effort. In the method of Non-Patent Document 1 and the classical finite difference method, the computational effort increases in the form of O(exp(poly(d))) with respect to the number of underlying assets d, while in this method, since there is no such factor as shown in [Equation 26], it becomes possible to increase d.

[0039] <Example of configuration> FIG. 3 is a block diagram showing a client computer 500 according to an embodiment. The client computer 500 includes, for example, one or more processing units (CPUs) 502, one or more network communication interfaces 508, a memory 504, and one or more communication buses 514 for interconnecting these components.

[0040] The client computer 500 includes, for example, a user interface 506 including a display 510 and a keyboard and / or a mouse 512. The display 510 is an example of an output device, and the output device may be a device that outputs sound such as a speaker.

[0041] The memory 504 is, for example, a high-speed random access memory such as DRAM, SRAM, DDRRAM, or a random access solid-state storage device. The memory 504 may be, for example, a non-volatile memory such as a magnetic disk recording device, an optical disk recording device, or a flash memory device. The memory 504 may be one or more storage devices installed remotely from the CPU 502. The memory 504 stores, for example, programs, modules, data structures, or subsets thereof.

[0042] The operating system 516 includes, for example, procedures for processing various basic system services and executing tasks using hardware.

[0043] The network communication module 518 connects, for example, the client computer 500 to other computers via one or more communication networks. The one or more communication networks include, for example, the Internet, other wide area networks, local area networks, and metropolitan area networks.

[0044] The quantum processor control module 520 receives, for example, an input of information for configuring logical qubits by the quantum processor 20 via the keyboard and / or mouse 512, and transmits it to the server computer 600. For example, the information for configuring logical qubits includes at least one of the types of a plurality of underlying assets or the prices of a plurality of underlying assets, the type of derivative, boundary conditions, and the like. The quantum processor control module 520 locally caches, for example, data items received from the keyboard and / or mouse 512 and calculation results by the quantum processor 20 in the memory 504. The quantum processor control module 520 outputs the calculation result (e.g., the current market price of the derivative) by the quantum processor 20 to an output device to notify the user.

[0045] The client application 522 includes, for example, a web browser and the like.

[0046] One or more processing devices (CPUs) 502 read and execute modules from the memory 504. One or more processing devices (CPUs) 502 execute, for example, the network communication module 518 stored in the memory 504. One or more processing devices (CPUs) 502 execute the quantum processor control module 520 stored in the memory 504.

[0047] The quantum processor control module 520 may be a stand-alone application stored in the memory 504 of the client computer 500. Examples of stand-alone applications include, for example, quantum processor control applications. The quantum processor control module 520 may also be an add-on or plug-in to another application, or a plug-in to a web browser application or an email application.

[0048] FIG. 4 is a block diagram showing a server computer 600 according to an embodiment. The server computer 600 includes, for example, one or more processing units (CPUs) 602, one or more network communication interfaces 608, a memory 604, and one or more communication buses 610 for interconnecting these components.

[0049] The server computer 600 includes, for example, a user interface 606 including a display and a keyboard and / or a mouse. The server computer 600 may omit the user interface 606.

[0050] The memory 604 is, for example, a high-speed random access memory such as DRAM, SRAM, DDRRAM, or a random access solid-state storage device. The memory 604 may also be a non-volatile memory such as a magnetic disk recording device, an optical disk recording device, or a flash memory device. The memory 604 may be one or more storage devices installed remotely from the CPU 602. The memory 604 stores, for example, programs, modules, data structures, or subsets thereof.

[0051] The operating system 612 processes, for example, various basic system services and executes tasks using the hardware.

[0052] The network communication module 614 connects, for example, the server computer 600 to other computers via one or more communication networks. The one or more communication networks include, for example, the Internet, other wide area networks, local area networks, and metropolitan area networks.

[0053] The quantum processor control module 616 receives, for example, information for configuring logical qubits from the client computer 500 by the quantum processor 20 and controls the quantum processor 20. As an example, when the quantum processor control module 616 acquires the types of a plurality of underlying assets from the client computer 500, it may refer to and acquire the prices of the underlying assets corresponding to the plurality of underlying assets, the volatilities of the underlying assets, the correlation matrix of the prices of the underlying assets, and the low-risk interest rates from a predetermined platform for managing the prices of each underlying asset. The quantum processor control module 616 outputs the prices of the underlying assets corresponding to the acquired plurality of underlying assets, the volatilities of the underlying assets, the correlation matrix of the prices of the underlying assets, and the low-risk interest rates to the quantum processor 20. Note that the quantum processor 20 only needs to acquire the prices of the underlying assets corresponding to the plurality of underlying assets from the quantum processor control module 616. For example, at least some of the parameters such as the volatilities of the underlying assets corresponding to the plurality of underlying assets, the correlation matrix of the prices of the underlying assets, and the low risk may be set in advance.

[0054] Also, when the quantum processor control module 616 acquires the type of derivative from the client computer 500, it specifies the boundary condition corresponding to the acquired type of derivative and outputs the specified boundary condition to the quantum processor 20. The quantum processor control module 616 may specify the boundary condition by referring to the related information associating the type of derivative with the boundary condition. This related information may be stored in the memory 604. For example, the related information is information associating the first boundary condition in the case of a European call option, the second boundary condition in the case of a put option, the third boundary condition in the case of a barrier option, and the like.

[0055] The quantum processor 20 refers to the prices of the underlying assets corresponding to a plurality of underlying assets obtained from the quantum processor control module 616, the volatilities of the underlying assets, the correlation matrix of the prices of the underlying assets, and the low-risk interest rate. The quantum processor 20 sets an arbitrary time point t within a predetermined period up to a predetermined future time point after the current time point. Here, as a critical value to which this embodiment is applied, a time point at which the spread of the price distribution of the underlying asset generally coincides with the boundary value of the boundary condition of the partial differential equation may be set. Also, as an optimal value in this embodiment, a time point at which the spread of the price distribution of the underlying asset coincides with the boundary value of the boundary condition of the partial differential equation may be set. Then, the quantum processor 20 solves, retroactively from the time point corresponding to the maturity, a linear ordinary differential equation obtained by discretely approximating the partial differential equation regarding the current value of the derivative, and outputs the inner product of a vector having the current value of the derivative on the discrete grid as a component and a vector having the distribution probability on the discrete grid of the price of the underlying asset at time point t. By executing a quantum algorithm for obtaining the current value of the derivative as the expected value of the discounted current value of the derivative at time point t. The expected value of the discounted current value of the derivative may have its value set as the current value of the derivative, or its value may be corrected by a predetermined method (such as adding a correction term or an offset) and set as the current price of the derivative.

[0056] The quantum processor control module 616 acquires information regarding the current value of the derivative determined by the quantum processor 20 from the quantum processor 20, and transmits the acquired information to the client computer 500 that is the source of information regarding the types of the plurality of underlying assets. The client computer 500 controls to display the acquired information regarding the current value of the derivative on the display 510.

[0057] <Operation Explanation> Next, the operation of the system 10 according to this embodiment will be described. FIG. 5 is a flowchart showing an example of the processing of the system 10 according to this embodiment.

[0058] First, the server computer 600 receives, through the client computer 500, specifications such as the type of derivative and the type of underlying asset to be evaluated (step S10). Note that, depending on the design of the system 10, the necessary input parameters may be changed.

[0059] Next, the server computer 600 controls the quantum processor 20 based on the information regarding the type of derivative and the type of underlying asset received from the client computer 500 (step S11).

[0060] Next, the quantum processor 20 refers to the price of the underlying asset, the volatility of the underlying asset, the correlation matrix of the prices of the underlying assets, and the risk - free interest rate corresponding to the type of derivative and the type of underlying asset specified in the previous step S10 (step S12).

[0061] Next, the quantum processor 20 sets an arbitrary point in time t after the current time, and calculates the current time value of the derivative by executing a quantum algorithm that outputs the inner product of a vector having, as components, the time value of the derivative on a discrete grid obtained by solving, backward from the time point corresponding to the maturity, a linear ordinary differential equation obtained by discretely approximating the partial differential equation regarding the time value of the derivative, and a vector having, as components, the distribution probability on the discrete grid of the price of the underlying asset at time t, as the expected value of the discounted time value of the derivative at time t (step S13).

[0062] Next, the quantum processor 20 outputs the current time value of the derivative determined in the previous step S13 to the server computer 600 (step S14).

[0063] Then, the server computer 600 outputs the current time value of the derivative output from the quantum processor 20 to the client computer 500 that was the source of the specification such as the type of underlying asset (step S15).

[0064] As a result, the system 10 according to the present embodiment can reduce the processing load when evaluating derivatives having a plurality of underlying assets by achieving both the computational speedup in comparison with classical algorithms brought about by the quantum algorithm for solving differential equations and the efficient readout of the information on the derivative fair value amplitude-encoded in the quantum state output by the algorithm. Further, according to the method of the present embodiment, since the amount of calculation does not increase in a form such as O(exp(poly(d))) due to an increase in the number d of a plurality of underlying assets, the number d can be increased.

[0065] Note that the disclosed technology is not limited to the above-described embodiments, and can be implemented in various other forms without departing from the gist of the disclosed technology. Therefore, the above embodiments are merely illustrative in every respect and should not be construed restrictively. For example, each of the above-described processing steps can be arbitrarily changed in order or executed in parallel as long as there is no contradiction in the processing content.

[0066] The program of the embodiments of the present disclosure may be provided in a state stored in a computer-readable storage medium. The storage medium can store the program in a "non-transitory tangible medium". The program includes, by way of non-limiting example, software programs and computer programs. Further, the system 10 of the present disclosure is preferably constructed in a system in a financial institution such as a bank or a securities company. For example, the server computer 600 is a server of a financial institution, and the client computer 500 is a computer used by an employee of the financial institution. For example, when an employee designates a predetermined derivative using the client computer 500, the server computer 600 identifies the prices, volatilities, correlations, and risk-free interest rates of a plurality of underlying assets referred to by this derivative, and instructs the quantum processor 20 to execute a process of calculating the current market price of the derivative using the prices, volatilities, correlations, and risk-free interest rates of the plurality of underlying assets. This calculation result is output to the client computer 500 via the server 600 computer. Note that the server computer 600 and the client computer 500 may be formed as an integrated computer.

Explanation of Signs

[0067] 10…System, 20…Quantum processor, 500…Client computer, 502…CPU, 504…Memory, 506…User interface, 508…Network communication interface, 510…Display, 512…Keyboard / mouse, 514…Communication bus, 516…Operating system, 518…Network communication module, 520…Quantum processor control module, 530…Client application, 600…Server computer, 602…CPU, 604…Memory, 606…User interface, 608…Network communication interface, 610…Communication bus, 612…Operating system, 614…Network communication module, 616…Quantum processor control module.

Claims

1. A system comprising: a quantum processor, wherein the quantum processor applies a quantum algorithm that outputs a quantum state that holds the value of the time value at each grid as the amplitude of a separate basis state to a partial differential equation regarding the time value evaluation of a derivative based on each of the prices of a plurality of underlying assets, each of the volatilities of the plurality of underlying assets, the correlation matrix of the prices of the plurality of underlying assets, and the risk-free interest rate, uses a quantum circuit that generates a first quantum state in which the time value of each grid at an arbitrary point in time obtained by executing the quantum algorithm from the expiration time to an arbitrary point in time within a period from the current time to a predetermined future time is embedded, and a quantum circuit that generates a second quantum state in which the probability distribution of the prices of the plurality of underlying assets at the arbitrary point in time is embedded, estimates the inner product between the first quantum state and the second quantum state, and calculates the expected value of the discounted time value of the derivative based on the estimation, and outputs the current time value of the derivative based on the expected value, and executes a process.

2. The quantum processor estimates the inner product between the first quantum state and the second quantum state by quantum amplitude estimation. The system according to claim 1.

3. The predetermined future time is a time when the spread of the distribution of the prices of the underlying assets substantially coincides with the boundary value of the boundary condition of the partial differential equation. The system according to claim 1 or 2.

4. The arbitrary point in time is the future time. The system according to claim 3.

5. The boundary condition is changed according to the type of the derivative. The system according to claim 3 or 4.

6. A computer that inputs the plurality of underlying assets and outputs, as parameters, each of the prices of the plurality of underlying assets corresponding to the plurality of underlying assets, each of the volatilities of the plurality of underlying assets, the correlation matrix of the prices of the plurality of underlying assets, and the risk-free interest rate to the quantum processor, wherein the computer acquires the determined current time value of the derivative and outputs it to an output device. The system according to any one of claims 1 to 5.

7. An information processing method executed by a system including a quantum processor, wherein the quantum processor Apply a quantum algorithm that outputs a quantum state that holds the value of the time value in each grid as the amplitude of a separate basis state to the partial differential equation for the fair value evaluation of derivatives based on each of the prices of a plurality of underlying assets, each of the volatilities of the plurality of underlying assets, the correlation matrix of the prices of the plurality of underlying assets, and the risk-free interest rate. Using a quantum circuit that generates a first quantum state embedded with the time value of each grid at an arbitrary point in time obtained by executing the quantum algorithm from the expiration time to an arbitrary point in time within a period from the current time to a predetermined future time, and a quantum circuit that generates a second quantum state embedded with the probability distribution of the prices of a plurality of underlying assets at the arbitrary point in time. Estimate the inner product of the first quantum state and the second quantum state, and based on the estimation, calculate the expected value of the discounted fair value of the derivative at the arbitrary point in time. Output the current fair value of the derivative based on the expected value. Information processing method.

8. On a quantum processor included in a system. Apply a quantum algorithm that outputs a quantum state that holds the value of the time value in each grid as the amplitude of a separate basis state to the partial differential equation for the fair value evaluation of derivatives based on each of the prices of a plurality of underlying assets, each of the volatilities of the plurality of underlying assets, the correlation matrix of the prices of the plurality of underlying assets, and the risk-free interest rate. Using a quantum circuit that generates a first quantum state embedded with the time value of each grid at an arbitrary point in time obtained by executing the quantum algorithm from the expiration time to an arbitrary point in time within a period from the current time to a predetermined future time, and a quantum circuit that generates a second quantum state embedded with the probability distribution of the prices of a plurality of underlying assets at the arbitrary point in time. Estimate the inner product of the first quantum state and the second quantum state, and based on the estimation, calculate the expected value of the discounted fair value of the derivative at the arbitrary point in time. Output the current fair value of the derivative based on the expected value. Program for causing the execution of the process.

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