💻 computer science

QRISP: Qubit-Efficient and Resolution-Independent Quantum Image Representation for Scalable NISQ Processing

This paper proposes QRISP, a resource-efficient and resolution-independent quantum image representation framework that encodes images via statistical block descriptors to significantly reduce circuit complexity and qubit requirements for NISQ hardware while maintaining competitive classification performance.

Original authors: Sumitha Valsalam, Tony Thomas

Published 2026-08-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sumitha Valsalam, Tony Thomas

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the emerging field of quantum computing, researchers are trying to teach machines to see. Just as a human brain processes a photograph by recognizing shapes, textures, and patterns, a quantum computer needs a way to translate a classical image into a quantum state—a specific arrangement of information that its unique hardware can understand and manipulate. This translation is the foundation of quantum image processing, a discipline that sits at the intersection of visual data and the strange, powerful laws of quantum mechanics. The challenge, however, is that current methods for this translation are incredibly heavy. They require a vast amount of computational resources that grow rapidly as the image gets bigger, much like trying to carry a heavy backpack that gets heavier with every step you take. Because today's quantum computers are still in their early, noisy stages and cannot handle these massive loads, scientists have been struggling to find a way to process images that is both accurate and light enough to run on existing machines.

A team of researchers from the Kerala University of Digital Sciences, Innovation and Technology in India has proposed a new solution to this problem called QRISP. Instead of trying to feed the quantum computer every single pixel of an image, which is what older methods do, their approach breaks the image down into a fixed number of distinct blocks. Imagine taking a photograph and dividing it into a grid of sixteen equal squares. Rather than analyzing the millions of tiny dots that make up the whole picture, the system looks at each of those sixteen squares and calculates three simple, descriptive numbers for each one: the average brightness, the amount of texture or variation within the square, and the direction of the strongest lines or edges. These three numbers act as a summary of the visual information in that block. The researchers then encode these summaries into a quantum state using a very small, fixed number of quantum bits, or qubits. Crucially, the size of this quantum "backpack" does not change, no matter how large the original image is. Whether the image is tiny or huge, the system always uses the same sixteen blocks and the same number of qubits to represent it.

The researchers tested this method using standard datasets of handwritten digits and clothing items, running simulations on powerful computers to see how well it worked compared to the older, heavier techniques. They found that by using this block-based summary, they could drastically reduce the complexity of the quantum circuits needed to process the images. In their tests, the new method required only seven qubits to represent an image, whereas the older methods needed nine or even seventeen. More importantly, the time it took to perform the necessary calculations dropped dramatically. For one specific task, the new method finished the job in about 614 seconds, while the older method took nearly 15,000 seconds. This represents a reduction in time by a factor of twenty-four. The system also maintained a consistent speed regardless of the image size; as the images grew larger, the time to process them stayed roughly the same, whereas the older methods slowed down significantly as the images got bigger.

While the new method was incredibly efficient, the researchers noted a small trade-off. Because the system summarizes the image into blocks rather than looking at every single pixel, it lost some of the fine, detailed information that the older methods preserved. In their simulations, the older methods achieved slightly higher accuracy in identifying the images, reaching near-perfect scores in some cases, while the new method achieved a very competitive, though slightly lower, accuracy. However, the researchers argue that for the current generation of quantum computers, which are limited by noise and a lack of resources, this small loss in detail is a worthy price to pay for the massive gain in speed and feasibility. The method proved that it is possible to process high-resolution images on quantum hardware without needing a machine that is far more powerful than what currently exists.

The study suggests that this block-based approach offers a practical path forward for quantum image processing. By focusing on the most important statistical features of an image rather than every single pixel, the researchers created a representation that is independent of the image's resolution. This means that as quantum technology improves, this method can scale up to handle larger and more complex images without requiring a complete redesign of the underlying system. The work was conducted entirely through simulation on classical computers, meaning the results show what is theoretically possible and how the system behaves under ideal conditions. The authors indicate that the next step is to test this framework on actual quantum hardware to see how it performs in the real, noisy environment of a physical quantum processor. Until then, this research provides a compelling blueprint for how to make quantum machines see the world in a way that is both smart and manageable.

Technical Summary: QRISP – Qubit-Efficient and Resolution-Independent Quantum Image Representation

Problem Statement
The paper addresses a critical bottleneck in Quantum Image Processing (QIP) and Quantum Machine Learning (QML): the scalability of Quantum Image Representation (QIR) under Noisy Intermediate-Scale Quantum (NISQ) constraints. Existing pixel-level encoding schemes, such as the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR), suffer from poor scalability. In these models, the number of required qubits and the circuit depth grow linearly or exponentially with image resolution. Consequently, representing large-scale images becomes impractical on near-term hardware due to excessive resource demands and deep circuits that are highly susceptible to noise. While alternative compact representations exist, many either sacrifice spatial structure or fail to decouple quantum resource requirements from image size.

Methodology: The QRISP Framework
The authors propose QRISP (Qubit-Efficient and Resolution-Independent Quantum Image Representation), a feature-driven encoding framework that decouples quantum resource complexity from image resolution. The methodology operates through the following stages:

Adaptive Block Partitioning: Instead of encoding individual pixels, the input grayscale image is partitioned into a user-configurable, fixed number of non-overlapping blocks ( $N_B$ ). The block size ( $b$ ) is adaptively selected based on the image resolution to ensure $N_B$ remains constant regardless of the input image dimensions ( $H \times W$ ).
Feature Extraction: For each block, three complementary statistical descriptors are extracted and normalized to the interval $[0, 1]$ $[0, 1]$ :
- Mean Intensity ( $\mu_k$ ): Captures first-order photometric structure.
- Local Variance ( $\sigma^2_k$ ): Captures second-order texture and spatial variation.
- Dominant Gradient Orientation ( $\phi^{norm}_k$ ): Captures principal edge direction, computed via Sobel operators.
Quantum State Formulation: The framework utilizes two quantum registers:
- Position Register: Encodes the block indices ( $k$ ) in a uniform superposition using $\lceil \log_2(N_B) \rceil$ qubits.
- Feature Register: Encodes the three statistical features for each block using parameterized single-qubit rotation gates ( $R_Y$ ). The rotation angles map the normalized feature values to the range $[0, 2\pi]$ .
Entanglement Layer: A lightweight entanglement layer applies CNOT gates to correlate the feature qubits (mean, variance, and gradient), transforming independent descriptors into a joint quantum feature representation.
Resolution Independence: Because the number of blocks ( $N_B$ ) is fixed, the total number of qubits ( $n_{total} = n_p + n_f$ ) and the logical circuit structure remain constant across different image resolutions. For example, a configuration with $N_B=16$ requires only 7 qubits (4 for position, 3 for features) for images ranging from $4\times4$ to $512\times512$ .

Key Contributions
The paper identifies four primary contributions:

Resolution-Independent Encoding: An adaptive block partitioning strategy that enables fixed-qubit quantum circuits, making resource requirements dependent on block configuration rather than image size.
Multi-Feature Quantum Representation: A block-level scheme incorporating intensity, variance, and gradient information to enhance discriminative capability without pixel-level overhead.
NISQ-Aware Circuit Design: A shallow encoding circuit utilizing parameterized single-qubit rotations and two-qubit operations, specifically designed for compatibility with current hardware constraints.
Comprehensive Evaluation: A rigorous performance analysis using Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) on MNIST and Fashion-MNIST datasets, comparing resource usage and classification accuracy against FRQI and NEQR.

Experimental Results
The authors evaluated QRISP against FRQI and NEQR using simulated quantum circuits on high-performance computing systems.

Resource Efficiency: For a $16\times16$ image, QRISP required only 7 qubits compared to 9 (FRQI) and 17 (NEQR). The transpiled circuit depth was reduced by approximately 96.8% (from ~50,435 in FRQI to ~1,620 in QRISP), and the total gate count dropped by 95.5%.
Computational Speed: In QSVM experiments, the kernel computation time for QRISP was approximately 24 times faster than FRQI (614 seconds vs. 14,748 seconds for MNIST).
Scalability: As image resolution increased from $4\times4$ to $512\times512$ , the kernel computation time for QRISP remained nearly constant (600–800 seconds), whereas FRQI and NEQR times increased exponentially, with NEQR failing to scale beyond $8\times8$ under simulation constraints.
Classification Performance: QRISP achieved competitive classification accuracy. On MNIST (16x16), it achieved a mean accuracy of 0.90 compared to 0.97 for FRQI. On Fashion-MNIST, QRISP maintained accuracy between 0.90 and 1.00 across resolutions up to $512\times512$ . In QNN experiments, QRISP matched NEQR's accuracy (0.90) on $8\times8$ images but with drastically lower execution time (22.77s vs. 59,370s).

Significance and Claims
The paper claims that QRISP offers a "favourable balance" between classification performance and quantum resource efficiency. It positions the framework not as a replacement for all existing QIR models, but as a specific, NISQ-oriented alternative for classification tasks where approximate feature-level descriptions are sufficient.

The authors emphasize that while QRISP sacrifices fine-grained spatial details by aggregating pixels into blocks, this trade-off yields a compact representation that preserves the structural information necessary for classification while rendering the problem tractable on near-term hardware. The work suggests that feature-based, block-wise encoding is a promising pathway for scalable Quantum Image Processing, effectively addressing the "inverse relationship between representational fidelity and hardware feasibility" that currently limits the field. The authors note that the current study is limited to small-scale binary classification in simulation and acknowledge that future work will focus on noise-aware optimization, multi-class classification, and deployment on real quantum hardware.

Technical Summary: QRISP – Qubit-Efficient and Resolution-Independent Quantum Image Representation

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