Painting with Qubits on the Quantum Canvas
Day 24 — Quantum30 Challenge 2.0
In the realm of computers and image processing, one of the fundamental aspects is image representation. Traditionally, in classical computing, digital images are encoded using matrices, where each value in the matrix corresponds to the pixel’s intensity or color value. This matrix-based representation is widely employed for various grayscale and colored image processing tasks.
However, with the rise of quantum computing, researchers are delving into the potential of harnessing the unique quantum properties of quantum computers to efficiently represent digital images. This has led to a new domain known as Quantum Image Processing (QIP).
QIP representations
Currently, there are two primary quantum image representation models that have been proposed:
Amplitude Representation
FRQI (Fast and Robust Quantum Image):
- A qubit is portrayed as a superposition or a linear combination of various eigenstates.
- In amplitude representation, also known as FRQI, the color or intensity value of each pixel is stored in the amplitude of a qubit. Essentially, the pixel value is represented by the states of a qubit.
- Furthermore, qubits are entangled with another set of qubits to store pixel positions.
- Notably, an enhanced version of FRQI (EFRQI) was introduced in 2011, which offers improved storage, reduced quantum cost (making image representation and processing more efficient with fewer quantum resources), and enhanced image manipulation capabilities, including efficient algorithms for image transformations and color adjustments.
Basis State Representation
NEQR (Negative Eigenvalue Quantum Representation):
- This representation model employs the basis state representation. Here, pixel values are stored in the basis states or eigenstates of a sequence of qubits, which include both positive and negative values.
- Positive values straightforwardly represent pixel data, with each positive value corresponding to a specific color or shade in an image.
- In contrast, negative values represent the shade or color in a complementary way. Instead of directly encoding pixel values, negative values represent pixels as the negation of the corresponding positive value.
- This allows NEQR to efficiently encode both the original pixel data and its inverse, resulting in efficient storage, image manipulation, and enhanced quantum image processing (QIP).
- Like FRQI, NEQR also employs another set of qubits to store pixel positions.
- In 2013, an enhanced version of NEQR (ENEQR) was proposed, offering enhancements in optimization, additional qubits for improved encoding and precision, reduced quantum cost, and improved image processing capabilities, including faster image transformation algorithms and enhanced image filtering.
Preparation Process
The preparation process for these quantum image representations involves applying quantum gates to encode pixel values and their positions. In EFRQI, the RX (Rotation X) operator is applied to represent pixel values, while in ENEQR, the CNOT gate is used to encode pixel values in the basis state of a qubit sequence. The number of gates applied depends on the grayscale value of each pixel.
Future Scope and Conclusion
Quantum Image Processing holds immense potential for the future. Compared to classical methods, quantum image representations can achieve significant speedup in the preparation process. When combined with quantum algorithms, they have the potential to outperform classical counterparts in various image-related applications.
As quantum computing technology continues to advance, these representations are likely to play a pivotal role in the future of image-related applications. Researchers and practitioners are continually exploring novel quantum approaches to image representation and processing, opening up exciting possibilities in the realm of computer vision and beyond.