Quantum Tensor Fourier Transform for Multi-Dimensional Data
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Solution Overview
Problem
Classical computing methods for performing multi-dimensional Fourier transforms are inefficient and impossible to perform directly in quantum computing systems due to the inherent differences in qubit encoding, leading to slow and resource-intensive data processing.
Innovation Solution
Implementing quantum manipulation operations in a quantum computing system to transform physical quantum representations of multi-dimensional tensor data objects into their Fourier transforms, allowing parallel processing of different portions of the data, thereby conserving processing time and resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical computing methods are used to perform multi-dimensional Fourier transforms, then the transform can be performed with established algorithms, but the processing time and resource consumption become extremely inefficient and slow
Solution Approach 1:
The patent replaces the classical mechanical computing system with a quantum computing system. Specifically, it uses quantum states (qubits) to represent tensor data and applies quantum Fourier transform operations instead of classical FFT algorithms. This substitution leverages quantum superposition and entanglement to achieve exponential speedup in Fourier transform computations, directly resolving the contradiction between reliable computation and processing speed.
2Productivity
If quantum computing systems are used to perform Fourier transforms, then processing speed can be improved through parallel operations, but the system complexity and difficulty of implementation increase
Solution Approach 1:
The patent segments the quantum Fourier transform process into distinct modular components: (1) quantum state preparation circuits that encode classical tensor data into quantum states, (2) quantum Fourier transform gate sequences that perform the actual transformation, and (3) measurement circuits that extract results. This segmentation makes the complex quantum system more manageable and implementable while preserving the parallel processing speedup.
Solution Approach 2:
The patent introduces intermediary classical computing components that bridge the quantum and classical domains. These include classical pre-processing modules that prepare input data, quantum-classical interface layers that transfer data between domains, and post-processing modules that interpret quantum measurement results. These intermediaries reduce the complexity burden on the quantum system itself while maintaining high processing speed.
3Productivity
If quantum representations are used to encode multi-dimensional tensor data, then parallel processing of different data portions is enabled, but the encoding and manipulation operations become more complex
Solution Approach 1:
The patent transitions data from classical dimensional representation to quantum dimensional representation. Classical tensor data with explicit indices is encoded into quantum states where indices become quantum numbers associated with qubit basis states. This dimensional change enables parallel processing because quantum superposition allows multiple index values to coexist simultaneously, and quantum entanglement allows correlations between different tensor dimensions to be represented efficiently.
Solution Approach 2:
The patent changes the fundamental parameters of data representation from classical bits to quantum bits (qubits). This parameter change enables parallel processing through quantum superposition, where a single quantum state can represent multiple classical configurations simultaneously. The complexity of encoding is managed through systematic mapping rules that translate classical tensor indices into quantum basis states.
Data Source
AI summary
Various embodiments of the present disclosure provide systems and methods for generally generating and transforming physical quantum representations of multi-dimensional tensor data objects. Specifically, various embodiments enable the rapid and efficient generation of a physical quantum representation representing the Fourier transform of a multi-dimensional tensor data object based at least in part on manipulating another physical quantum representation of the multi-dimensional tensor data object itself via quantum manipulation operations. Information may be extracted from the generated physical quantum representation to determine the Fourier transform of the multi-dimensional tensor data object. Accordingly, various embodiments may comprise quantum manipulation operations for a tensor-form quantum Fourier transform (TQFT) for a multi-dimensional tensor data object. Various embodiments for the TQFT are advantageously comprehensive, versatile, and applicable to any quantum representation form for a multi-dimensional tensor data object. The TQFT may be performed in any quantum computing system and/or simulated quantum computing system.