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Method for realizing quantum circuit design through quantum Haar wavelet transformation

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

Inactive Publication Date: 2017-09-12
GUANGXI NORMAL UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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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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  • Method for realizing quantum circuit design through quantum Haar wavelet transformation
  • Method for realizing quantum circuit design through quantum Haar wavelet transformation
  • Method for realizing quantum circuit design through quantum Haar wavelet transformation

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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 through quantum Haar wavelet transformation, and belongs to the field of quantum information processing. According to the method, the existing quantum Fourier transform implementing technology is perfected and improved, and implementing circuits of two pieces of multi-layer quantum Haar wavelet transformation and two pieces of multi-layer quantum Haar wavelet inverse transformation are established separately by using extended tensor product and basic quantum bit gate (comprising quantum bit controlled door and single quantum bit gate). Based on analysis of the complex rates of the implementing circuits of the quantum Haar wavelet transformation and the quantum Haar wavelet inverse transformation, the complex rates of the implementing circuits of the two pieces of multi-layer quantum Haar wavelet transformation and the two pieces of multi-layer quantum Haar wavelet inverse transformation are Theta(n2) for one data set with 2n elements, and other typical and rapid Haar wavelet transformation cannot achieve the aim. The method is suitable for the fields of algorithms such as compression, denoising, encryption and decryption of images of actual information processing application, and has important significance in popularization of perfection and application of a quantum computing theory.

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