Quantum finite power series sum operation method and device and storage medium

Abstract

According to the quantum finite power series and operation method and device and the storage medium, the Qinnine-Nephelium algorithm is combined during circuit design to reduce the multiplication times in the operation process, so that the circuit depth of a quantum circuit is reduced, and the quantum circuit is easier to deploy and implement on a quantum computer. In addition, the device can utilize superposition characteristics and entanglement characteristics of quantum calculation to realize exponential scale calculation which is difficult to realize by a classical calculation method. The whole quantum circuit uses the quantum bit number of the polynomial scale, has the line depth of the polynomial scale and the time complexity, and can support calculation of the power series sum of the number of the exponential scales in one-time operation. And a quantum calculation acceleration scheme is provided for various industrial and practical application scenes using power series estimation and equation solution.

Claims

1. A quantum finite power series and operation method, characterized in that: include: The power series According to Qin Jiushao's algorithm, it can be expressed as ((…(a n x+a n-1 )×x+…+a1)×x+a0; Get the independent variable x and multiple coefficients of the power series, where multiple coefficients are a n 、a n-1 ...a0, convert each coefficient into the corresponding coefficient quantum state, convert at least one independent variable into an independent variable superposition state, the number of quantum bits corresponding to the coefficient quantum state is the same as the number of quantum bits in the independent variable superposition state, both are m; According to the superposition state of the independent variable and the corresponding coefficient quantum state, ((…(a n x+a n-1 )×x+…+a1)×x+a0 are calculated from the inside to the outside.

2. The quantum finite power series and operation method according to claim 1, characterized in that: According to the superposition state of the independent variable and the corresponding coefficient quantum state, ((…(a n x+a n-1 )×x+…+a1)×x+a0, and calculate from the inside out, including: Execute a first n The multiplication operation of x obtains the first result, and the first result + a is executed n-1 The addition operation obtains the second result, and the multiplication operation of the second result × x obtains the third result. n The addition operation of -1 result + a0 obtains the final result.

3. The quantum finite power series and operation method according to claim 1, characterized in that: Any of the coefficients can have multiple values. In this case, the coefficients are converted into corresponding coefficient superposition states. The number of quantum bits corresponding to the coefficient superposition state is the same as the number of quantum bits in the independent variable superposition state, both of which are m. According to the independent variable superposition state and the corresponding coefficient superposition state, ((…(a n x+a n-1 )×x+…+a1)×x+a0, and calculate from the inside to the outside.

4. The quantum finite power series and operation method according to claim 2, characterized in that: The multiplication operation can be expressed as a×b, where a is expressed as (c m-1 ×2 m-1 +…c1×2 1 +c0×2 0 ), so that the multiplication operation is transformed into ((…(a m-1 b×2+a m-2 b)×2+a m-3 b)…+a1b)×2+a0b; where (c m-1 …c1c0) is the binary representation of a.

5. The quantum finite power series and operation method according to claim 1, characterized in that: The multiplication operation in each step uses m auxiliary quantum bits, and the m auxiliary quantum bits are stored in a fourth quantum register. The initial state of the auxiliary quantum bits is 0, and the fourth quantum register contains (n+1)*n*m quantum bits; The coefficient quantum state of each coefficient is stored in the first quantum register, and the first quantum register has a total of m×(n+1) quantum bits; The independent variable superposition state of the independent variable is stored in a second register, and the second register includes m quantum bits; a n The first result obtained by performing the multiplication operation of x and the result of each addition operation are stored in a third register, the third register contains m(n+1) quantum bits and the quantum bits contained in the third register are initially in a 0 state; During the multiplication operation of the second result ×x, the auxiliary quantum bit in the fourth quantum register is called to perform the multiplication operation to obtain the third result, and the third result is stored in the fourth quantum register; then the third result in the fourth quantum register is exchanged to the third register; the third result + a is executed n-2 The fourth result is stored in the third register; Repeat the above steps until the operation is completed.

6. A quantum finite power series and operation device, characterized in that: include: A generating device converts the independent variable x of the power series into a superposition state of independent variables, and converts it into a corresponding coefficient quantum state; A first register, used to store coefficient quantum states; The second register is used to store the superposition state of the independent variable; The third register is used to store a n The multiplication operation of x obtains the first result and the result of each addition operation; The fourth register is used to store auxiliary quantum bits and divide a n The result of a multiplication operation other than x; Operation module, according to ((…(a n x+a n-1 )×x+…+a1)×x+a0, call the coefficient quantum state stored in the first register, the independent variable superposition state stored in the second register, and the first result and the result of the addition operation stored in the third register, calculate the multiplication operation and the addition operation from the inside to the outside, and store the result of the addition operation in the third register; divide a n When performing a multiplication operation other than x, calling the auxiliary quantum bits in the fourth quantum register to perform a multiplication operation, obtaining other multiplication operation results, and storing the other multiplication operation results in the fourth register; The exchange module is used to exchange other multiplication operation results of the fourth register with the specified addition operation results stored in the third register; the specified addition operation result is the result of the addition operation before the multiplication operation corresponding to the other multiplication operation result.

7. An electronic device comprising a memory and a processor, characterized in that: A computer program is stored in the memory, and the processor is configured to run the computer program to perform the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of any method described in claims 1-6 are implemented.

Images