Image Analysis-Synthesis Using the Quantum Fourier Transform

Abstract –This paper introduces a hybrid two-dimensional Quantum Fourier Transform (2D hybrid QFT) method for image analysis and synthesis. The QFT and Inverse QFT (IQFT) functions enable analysis-synthesis implementation using frequency spectrum-based selection approaches. We study the resolution and precision of the QFT by comparing its outputs against classical two-dimensional Fast Fourier Transform (FFT) techniques, using pixel-level Signal to Noise Ratio (SNR) as a metric. Formative and summative assessments have been deployed  as a exercise in a senior-level Digital Signal Processing (DSP) course, and two National Science Foundation (NSF) workforce development programs. Preliminary evaluation results are presented in this paper.

 

Evaluation Question:

  1. What is the fundamental building block of quantum computing?
    1. Bit
    2. Qubit
    3. Byte
    4. Duobinary
    5. All of the above
    6. None of the above
  1. Quantum computing can solve certain types of problems faster than classical computing. What is a key factor contributing to this potential speed advantage?
    1. Higher clock speed
    2. Larger memory capacity
    3. Quantum entanglement and superposition
    4. Advanced cooling systems
    5. All of the above
    6. None of the above
  1. Which of these noise types are typically observed in quantum computing?
    1. Bit flip
    2. Amplitude damping
    3. Depolarizing noise
    4. Measurement Error
    5. All of the above
    6. None of the above
  1. What is the computational complexity of the QFT algorithm, where N =2^n, and “n” is the number of qubits?
    1. O(n^2)
    2. O(n log n)
    3. O(n)
    4. O(2^n)
    5. None of the above
  1. What is the role of normalization in computing the QFT?
    1. To ensure the sum of the squares of all probability amplitudes equals 1
    2. To reduce the computational complexity
    3. To improve the image quality
    4. To remove noise from the image
    5. None of the above
  1. What is the first step in computing the 2D FFT of an image?
    1. Create symmetry in the spatial domain
    2. Compute the magnitude spectrum of odd indexed components
    3. Apply the FFT to each row or each column of the image matrix
    4. Normalize the image data w.r.t. the maximum magnitude
    5. None of the above
  2. In which part of the image do you find the zero frequency component after a 2D FFT shift?
    1. Corners
    2. Center
    3. Top-left corner
    4. Bottom-right corner
  1. What does a peak in the frequency domain represent?
    1. A noise artifact
    2. A frequency component with high power
    3. A region of high spatial intensity in the original image
    4. A frequency component with low power
    5. None of the above
  1. What method is used to select a subset of L QFT components in a manner that maximizes the power of the signal?
    1. Select the Highest L frequency magnitude components.
    2. Select the L frequency magnitude components in a random manner
    3. Select every other frequency magnitude component until L components are selected
    4. Select the First L frequency magnitude components and Highest L frequency magnitude components.
    5. None of the above
  1. What happens to the SNR value when one increases the number (L) of selected 2D QFT components in the QFT compression process?
    1. The SNR Increases
    2. The SNR Decreases
    3. The SNR Remains the same
    4. None of the above
  1. Which method provides better reconstructed image quality (higher SNR) in peak picking?
    1. Highest L frequency magnitude components
    2. First L frequency magnitude components
    3. Both methods provide the same reconstructed image quality
    4. None of the above
  1. What is the primary purpose of using the Inverse 2D QFT (IQFT)?
    1. To enhance image details
    2. To perform edge detection
    3. To convert the frequency domain data back to the spatial domain
    4. To apply image filters
    5. All of the above
    6. None of the above
  1. How does Google Collab facilitate the execution of the provided code for 2D FFT and 2D Hybrid QFT?
    1. By providing a pre-configured environment with the necessary libraries
    2. By requiring manual installation of all dependencies
    3. By running the code offline
    4. By limiting the use of GPU resources
    5. All of the above
    6. None of the above