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A method of quantum haar wavelet transform to realize quantum circuit design

A technology of wavelet transform and circuit design, applied in computing, instruments, complex mathematical operations, etc., can solve the problems of high complexity in electronic circuit design

Inactive Publication Date: 2021-04-20
GUANGXI NORMAL UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0022] The present invention provides a method for quantum Haar wavelet transform to realize quantum circuit design, which solves the problem of high complexity of electronic circuit design realized by conventional Haar wavelet transform

Method used

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  • A method of quantum haar wavelet transform to realize quantum circuit design
  • A method of quantum haar wavelet transform to realize quantum circuit design
  • A method of quantum haar wavelet transform to realize quantum circuit design

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Embodiment 1

[0083] A method of quantum Haar wavelet transform to realize quantum circuit design, combining quantum computing with classical Haar wavelet transform technology to obtain quantum Haar wavelet transform; using quantum Haar wavelet transform to design the first multi-layer quantum Quantum circuits for Haar wavelet transform.

[0084] Assume is k layer 2 n The Haar wavelet transform of the element, is k-1 layer 2 n-1 The Haar wavelet transform of the element, then the classical multi-layer quantum Haar transform can be defined as:

[0085]

[0086] in is a uniform shuffled permutation matrix, H and I 2 yes figure 1 Medium single-qubit gates, Yes 2 The n times tensor product.

[0087] According to the principle of extended tensor product operation, we get And substituting it into formula (1), the iterative formula of the first multi-layer quantum Haar transform is designed as:

[0088]

[0089] where H and I 2 yes figure 1 Medium single-qubit gates, is t...

Embodiment 2

[0104] A method of quantum Haar wavelet transform to realize quantum circuit design, combining quantum computing with classical Haar wavelet transform technology to obtain quantum Haar wavelet transform; using quantum Haar wavelet transform to design the first multi-layer quantum Quantum circuits for Haar wavelet inverse transform.

[0105] The formula (2) is inversely calculated, and the first multi-layer quantum Haar wavelet inverse transform iteration formula is obtained as:

[0106]

[0107] where H and I 2 yes figure 1 Medium single-qubit gates, is the tensor product operation symbol, Yes 2 The n times tensor product, is a uniform shuffling permutation matrix, and the corresponding quantum circuit is as image 3 shown. is k layer 2 n The inverse Haar wavelet transform of the element, is k-1 layer 2 n-1 The Haar wavelet inverse transform of the element, the initial value of the iteration is:

[0108]

[0109] According to formula (5), when k=n-1, the ...

Embodiment 3

[0118] A method of quantum Haar wavelet transform to realize quantum circuit design, combining quantum computing with classical Haar wavelet transform technology to obtain quantum Haar wavelet transform; using quantum Haar wavelet transform to design the second multi-layer according to the principle of extended tensor product operation Quantum Circuits for Quantum Haar Wavelet Transform.

[0119] suppose is k layer 2 n The Haar wavelet transform of the element, is k-1 layer 2 n-1 The Haar wavelet transform of the element, then the classical multi-layer quantum Haar transform can be defined as:

[0120]

[0121] in is a uniform shuffled permutation matrix, H and I 2 yes figure 1 Medium single-qubit gates, Yes 2 The n times tensor product. According to the principle of extended tensor product operation, Can be reduced to the equivalent tensor product Will Substituting formula (6), the iterative formula of the second multi-layer quantum Haar transform is des...

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Abstract

The invention provides a method for realizing quantum circuit design by quantum Haar wavelet transform, which belongs to the field of quantum information processing. Gates (including qubit controlled gates and single-qubit gates), respectively construct two multi-layer quantum Haar wavelet transforms and two multi-layer quantum Haar inverse wavelet transform implementation circuits. From the analysis of the circuit complexity of quantum Haar wavelet transform and quantum Haar inverse wavelet transform, it can be seen that for a 2 n element data set, the complexity of the circuit of 2 multilayer quantum Haar wavelet transform and 2 multilayer quantum Haar inverse wavelet transform is Θ(n 2 ), which cannot be achieved by other classical fast Haar wavelet transforms. It is suitable for many practical information processing applications in the fields of image compression, denoising, encryption and decryption, and is of great significance to the improvement of quantum computing theory and the promotion of applications.

Description

technical field [0001] The invention relates to the field of quantum information processing, in particular to a method for realizing quantum circuit design through quantum Haar wavelet transform. Background technique [0002] Quantum computing is the product of the combination of quantum mechanics and computer science. The parallelism, superposition and measurement uncertainty of quantum computing are fundamental to the superiority of quantum computers over classical computers. [0003] Quantum wavelet transform is the core algorithm of quantum information processing. Quantum Haar wavelet transform is a compact, second-order, orthogonal wavelet transform, which has a wide range of applications in the field of information processing. For example, quantum Haar wavelet transform plays an important role in algorithms such as image coding, edge detection, and image watermarking. . [0004] In classical computing, an information unit is represented by a bit (Bit), which has only...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/14
CPCG06F17/148
Inventor 黎海生夏海英宋树祥范萍
Owner GUANGXI NORMAL UNIV