Quantum Gate Fractional Fourier-Kravchuk Transform
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current implementations of quantum Fourier-Kravchuk transforms (QKTs) are difficult to scale up and have fixed fractionality, limiting their applicability in signal processing, especially for non-periodic signals, and the computational time is comparable to discrete Fourier transforms (DFTs) without efficient reduction in operations.
Innovation Solution
A method utilizing a single quantum gate with exchange interaction, implemented by a beam splitter, to perform the fractional quantum Fourier-Kravchuk transform on d-level quantum states (qudits), where the interaction is governed by a specific Hamiltonian and the evolution operator generates the transform, allowing for adjustable fractionality and efficient processing of input data sequences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If waveguide-based implementations are used, then quantum Fourier-Kravchuk transform can be realized, but the fractionality is fixed and scaling is difficult
Solution Approach 1:
The patent replaces waveguide-based mechanical/optical systems with a quantum gate system governed by a specific Hamiltonian with exchange interaction. This substitution enables adjustable fractionality through the evolution parameter θ while maintaining scalability, as the quantum gate can be implemented with standard quantum computing components rather than fixed waveguide structures.
Solution Approach 2:
The invention changes the controlling parameter from fixed waveguide length to an adjustable evolution parameter θ in the quantum gate. By varying θ, the fractionality α can be continuously adjusted according to α = θ/(2π), providing adaptability without requiring physical restructuring of the system.
2Productivity
If traditional quantum KTs are used, then transform can be performed, but computational time is comparable to DFT without efficient reduction
Solution Approach 1:
The patent segments the complex transform operation into a single quantum gate operation governed by a specific Hamiltonian. By encoding the entire fractional quantum Fourier-Kravchuk transform into one gate with evolution parameter θ, the computational complexity is reduced from multiple sequential operations to a single unified operation, achieving constant-time processing.
Solution Approach 2:
The quantum gate with exchange interaction serves as a universal operator that can perform different fractional transforms by adjusting the evolution parameter θ. This single gate structure can implement any fractionality α = θ/(2π), making it a multi-functional device that eliminates the need for multiple specialized components.
3Adaptability or versatility
If d-level quantum states are used, then higher dimension transformation is enabled, but encoding and detection complexity increases
Solution Approach 1:
The patent introduces an intermediary quantum gate system that mediates between the qudit input states and the measurement apparatus. The quantum gate with exchange interaction transforms the high-dimensional quantum states in a controlled manner, allowing standard quantum detectors to measure the output without directly handling the complexity of high-dimensional state preparation and analysis.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables constant-time information processing for qudit data encoding, reducing computational time significantly and allowing for transformation of large data sequences, which is not possible with waveguide-based implementations, and extends the transform to higher dimensions by using orthogonal spectral or polarization modes independently.
Implementation Method 1
physical systems realizing the Hong-Ou-Mandel (HOM) quantum interference can be used to calculate the quantum fractional Fourier-Kravchuk transform with a single quantum gate
Implementation Method 2
the interaction of two independent modes a and b in the quantum gate is governed by the following Hamiltonian wherein H0 is the free quantum oscillator energy and HI - the interaction Hamiltonian where g corresponds to the exchange interaction strength
Implementation Method 3
the quantum gate is implemented by a beam splitter and the input data are encoded as superposition of multiphoton Fock states that interfere on the beam splitter
Data Source
Figure 1
Figure 2
Figure 3a~3f
AI summary
The present invention relates to a method of performing a fractional quantum Fourier-Kravchuk transform (QKT), characterised in that input data sequence is encoded in quantum amplitudes of a d-level (qudit) state which is processed by a quantum gate implementing an exchange interaction, and the result is read out by means of quantum detectors located behind this device,The invention relates also to a device, in particular a quantum computer, configured to implement said method.