Tensor Network Quantum Image Encoding Circuit
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Solution Overview
Problem
Near-term quantum computers face challenges in efficiently loading image data due to limited gate fidelity and the need for sparse data representation, which can result in information loss and complexity in image processing tasks.
Innovation Solution
A method for encoding grayscale image data into a quantum state using a matrix product state representation, implemented with a system of N qubits where N=log2(NxNy), and applying quantum circuits with CNOT gates to efficiently load the image data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If sparse data representation (unary amplitude encoding or product state encoding) is used, then the number of qubits and gates is reduced, but information loss occurs and image processing capability deteriorates
Solution Approach 1:
The patent changes the encoding parameter from sparse representation to dense amplitude encoding, where the quantum state amplitudes directly represent image pixel values. This allows N qubits to encode M pixels with M=2^N, achieving dense packing of information without compression losses while maintaining manageable circuit complexity through the specific encoder architecture.
2Loss of information
If dense data representation is used, then image information is preserved, but the number of gates scales with data size making it infeasible for near-term quantum computers
Solution Approach 1:
The patent segments the image data into blocks and processes each block independently through the quantum encoder. The encoder is applied to multiple smaller blocks rather than the entire image at once, reducing the gate complexity for each encoding operation while preserving the complete image information through concatenation of block encodings.
Solution Approach 2:
The patent transitions from encoding individual pixels sequentially to encoding blocks of pixels in parallel across multiple qubit registers. This dimensional reorganization allows the system to handle larger images by distributing the encoding burden across multiple quantum registers, reducing the depth and complexity of individual encoding circuits.
3Device complexity
If compression techniques (PCA, variational auto-encoders, spatial averaging) are applied, then data can be loaded with fewer qubits, but critical image features like edges are lost
Solution Approach 1:
The patent creates a quantum copy of the complete classical image data through amplitude encoding, where each pixel value is represented as an amplitude in the quantum state. This copying process preserves all original image information without compression, allowing the quantum system to access the full-resolution image for processing tasks that require precise feature detection.
Data Source
AI summary
A method for data loading of an image in quantum machine learning includes encoding, in N qubits, an input (pxy, x, y) of a grayscale image having Nx pixels on the x-axis and Ny pixels on the y-axis in a matrix product state using a plurality of tensors, wherein N=log2(NxNy), 1≤x≤Nx, 1≤y≤Ny, 0<pxy≤1, and x, y∈, and applying, on the N qubits, quantum circuits implementing the plurality of tensors, each of the quantum circuit comprising CNOT gates.