Q-MedDict: Quantum Dictionary Multimodality for Lung Tissue and Lab Data

Explainable artificial intelligence (XAI) and quantum computing (QC) offer beneficial advantages in cancer data analytics.^[1] Data of disease such as cancer data can include various data types. This data can be XRAY, images, laboratory sample findings, practisioner notes and text.^[2] A pathologist can look at a slide of stained tissue. A doctor can also look at your blood and urine tests. Such combinations of data are known as multimodal data. These data don’t seem to be alike. An image can be made of millions of pixels. A laboratory table can only have a few values. Thus, a multimodal system needs to be able to make the source of each value visible.^[3] Multimodal data analytics would provide insights about insights about cancer disease.^[4] One of the key initialization is process data digitally. In such, digital pathology is growing quickly for medical data analytics. In this case, XAI and QC would be effective to handle large amount of data.^[5]

Recent lung pathology models can read many tissue patterns from images. Other work moves toward multimodal pathology. MuPD places histology, RNA, and text in a shared space.^[6] H₂O integrates Hematoxylin and Eosin (H& E) stained tissue images with spatial multi-omics data.^[7] SpatialFusion combines tissue, expression, and pathway information.^[8] These models use learned representations and large training sets. There is also growing interest in quantum computing and its applications in medical data analysis.^[9] Quantum image representation methods, such as Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR), encode image information into quantum states.^[10,11] The Quantum Pixel Representation (QPIXL) framework was used to support quantum image analysis and manage circuit data.^[12] From the study, we see that our proposed approach and these approaches are not same. We find a few research gaps in the existing literature. These gaps are related to processing multimodal data using a classical model, the black-box nature of the models, and the lack of interpretability.^[13] Black-box models are those that perform their operations through a large number of iterations, making it difficult to understand and track how the operations are concluded.^[14,15] In this case, we only get the output, not an understanding of how it was obtained. However, in medical research, not all experts have an AI background. Therefore, we need interpretable AI models.^[16] Similarly, there are some other gaps related to the complexities of quantum computing interactions. To avoid quantum complexities, we introduce dictionary-based quantum computing for processing larger datasets as well as improving interpretability. The public sources are important. Cancer Moonshot Biobank–Lung Cancer Collection (CMB-LCA) is a Cancer Moonshot Biobank lung cancer collection hosted by The Cancer Imaging Archive (TCIA) and represented in Imaging Data Commons (IDC).^[17,18] The National Health and Nutrition Examination Survey (NHANES) is a separate public survey. Its Complete Blood Count (CBC) file includes WBC, haemoglobin, and platelet measures.^[19] Its biochemistry file includes albumin, BUN, creatinine, and glucose.^[20] Its urine file includes urine albumin, urine creatinine, and albumin-tocreatinine ratio.^[21] In this research we have the following contributions:

1) A classical quantum-centric dictionary with explicit bitstring keys and amplitudes.

2) A direct numerical demonstration of all five stated dictionary rules: H, S, T, CX, and CCX.

3) A lung H&E block experiment with Hadamard, DCT, and PCA/KLT references. To prove the hypothesis, we consider a research question, which is: Can a classical quantum-based dictionary form design lung cancer image and pathological metadata in a reliable way, while considering sparse representation to be calculated separately?

Cancer image may contain small cell details and large tissue regions (Fig. 1). A workflow is to cut the slide into tiles. Each tile is translated into features. CLAM used attention-based multiple instance learning for weakly supervised image analysis.^[22] Current foundation models are trained on larger collections of pathology. PulmoFoundation focuses on lung pathology.^[23] Foundation models for pathology also suffer from issues like stain variation, site variation, data size, and clinical Validation.^[24] Here these problems are critical because two demonstration images cannot show the entire range of lung pathology. MuPD integrates histology, RNA and text.^[25] H₂O and SpatialFusion bridge tissue with molecular data.^[26,27] OmiCLIP connects histology and spatial transcriptomics.^[7] These methods utilize funcitons centric data and find hidden imag spaces. Q-MedDict is dictionary-based approach. In this method, combines a specific image pixel with respect to a desired location which is a key. Each key can show a modality and a feature position. So, our proposed method is a lightweight model that performs well on multimodal data within quantum scopes. In particular, the quantum features with superposition make it a strong candidate for handling multimodal data in cancer data analysis. FRQI stores image colour information in probability amplitudes and image position in basis states.^[28] NEQR stores grayscale values in computational basis states.^[29] QPIXL provides a common circuit framework for several quantum pixel representations.^[30] These approaches are regular quantum-state representations or circuit foundations. One the other hand, our proposed Q-MedDict is different as this is dictionary-based data mapping. It is a classical dictionary-based data structure using quantum notation. In this approach, we do not need a quantum processor. The data orientations are dictionary keys and values pair. The quantum gate functions rules are general deterministic update functions. According to the a newly proposed method, image color values data are Image color information is stored in probability amplitudes.^[31] Similarly, a grayscale values are stored in computational basis states.^[32] Another research find out a generic circuit structure for many quantum pixel representations is provided by QPIXL.^[12] Our proposed method QMedDict is not the same. It is a traditional data format that draws inspiration from quantum notation. The bit strings are standard dictionary keys.

Fig. 1: Lung adenocarcinoma image.

Table 1 presents the descriptions of existing approaches and our proposed approach. DCT works on image transform. Other methods such as PCA/KLT is a data-centric linear transform. On the other hand, FRQI and NEQR are quantum image representations. Our proposed, Q-MedDict offer key and value combinaitons to trace each data with their locations.

In this research, we used publicly available data. One of the data is CMB-LCA is a public lung cancer collection from the Cancer Moonshot Biobank. All these data.^[17] IDC lists slide microscopy as one of its modalities.^[18]

We have collected the laboratory data from public NHANES documentation for the August 2021 to August 2023 release. Table 2 presents the summaries of the metadata we used in this research from laboratory data.

These are:

• CBC_L: WBC, haemoglobin, platelet count and other blood-cell measures.
• BIOPRO_L: albumin, BUN, serum creatinine, glucose and other chemistry measures.
• ALB_CR_L: urine albumin, urine creatinine, and albumin/ creatinine ratio.

Our proposed method is an integrated approach of multiple processes. The proposed framework shown in Fig. 2. In this figure we see that, first step is about data collections and then normalizations and so on until the last state which is re-building the image. A state is stored as

The key $b_i$ is a bit sequence. The amplitude $a_i$ present the amount connected to that key. For an image patch, a key can show a pixel location. For a table, a key can mark a feature slot. In Table 3, we present quantum dictionary based gates and rules which account for quantum data processing.

The amplitudes are presented by

$a_i^{\text{'}}=\frac{a_i}{\sqrt{\left(\sum _j{\left|a_j\right|}^2\right)}}$, $$

which gives

Table 1: Descriptions of various methods along with our proposed method

Fig. 2: Q-MedDict framework.

Table 2: NHANES release metadata used in the laboratory branch. these are codebook ranges and counts, not patient measurements

Each lung H&E image is presented to grayscale for the present value. The image is represented as a 256× 256 array and split into 16×16 blocks. A block contains 256 values.

For compact notation, the orthonormal Hadamard gate is

$C=HB{H}^T$, (4)

where $B$ is one image location and $H$ is a normalised Hadamard table. The largest $K$ are kept:

The block is supported by

We test $K$ = 128, 64, and 32. These values keep 50%, 25%, and 12.5% of block coefficients.

Our proposed key and dictionary quantum approach support pairwise $H$ gate update to key and value combinations. The matrix structure is used because it is easy to execute and get output. We verified dictionary values and the reference matrix output in Table 4. We also report the fraction of squared transform coefficients kept:

Table 3: Dictionary rules used for Q-MedDict

Table 4: Numerical verification of the dictionary rules.

Here we see that due to Hadamad gate H is orthonormal, the full energy before and after the transform is the same. Therefore, RE is not supporting that the transform “preserves energy.” It measures how reserved the coefficients are after top-K selection.

We define the experiments as follows:

and a release completeness value

The reserved descriptor used $r_i{q}_i$ before min and max scaling and amplitude normalization.

Our interpretation as follows: where $r_i$ and $q_i$ are descriptors. We also do not recommend multiplying a future patient measurement by qi. We define a record is$q_i$. We define a record is

where $a_i$ is a scaled value, $m_i$ is a missing value, and $q_i$ is a metadata.

Q-MedDict uses classical update rules inspired from quantum computing rules.

In these experiments we used two public lung adenocarcinoma images. Each image was divided into 256 groups of 16 × 16 pixels. Hadamard values were managed by true size. These are 128, 64, or 32. For a base line outcome, we used same arrays and the same top-K rule with a two-dimensional orthonormal DCT image. A PCA/KLT values was also used. For PCA/KLT, one image was used to the 512 blocks from the two demonstration images. The storage cost is not measured.

Table 5: Lung H&E image results for the Hadamard-gate

Table 6: Image baselines at 64 of 256 coefficients per block (25%)

The NHANES instructions were utilized to record the minimum, maximum, valid count, and total count. Seven blood descriptors and three urine descriptors were also used. We also used “release-metadata framework.” Moreover, We also added a numerical sensitivity check. It checks the initial $r_i{q}_i$ descriptor with: (i) weighting, (ii) no log transform, and (iii) identity top-K keeping.

We define the image and other metadata for our experimental analysis. We consider these data to investigate our hypothesis weather quantum dictionary-based model can have better utilization of superposition.

Table 5 presents the original Hadamard-gate centric image outcomes. Most values are representing the image data analysis with various combinations. Table 6 presents further outcomes of 25% baseline comparative analysis. The DCT is perform better outcomes in comparison with the Hadamard for PSNR and SSIM images. Similarly, the PCA/KLT is shows in between outcomes. QMedDict offers better scopes for dictionary representation and rule tracing. Fig. 3 shows grayscale image and its 25% Hadamard framework. The largest framework remains usable. Fig. 4 shows that PSNR falls when fewer coefficients are kept. The dictionary values are irregular. Fig. 5 shows the 20 largest values from one tissue patch.

Fig. 3: Lung image which is rebuilt after keeping 64 of 256 Hadamard coefficients in each 16 × 16 block.

Fig. 4: PSNR against the share of kept Hadamard coefficients.

Fig. 5: Top 20 normalised dictionary amplitudes from one lung H&E patch.

Fig. 6 shows the comparative outcomes for completeness values. Blood variables are around 87 to 88% complete in the selected files. Urine variables are around 96%. Table 7 presents descriptor reconstruction numbers which are shows the exact coefficient counts. It also shows the error as RMSE because min and max scaling values. These numbers describe an eight-element blood metadata vector and a four element urine metadata vector. Fig. 7 shows reconstruction of the seven-value release descriptor.

Fig. 6: Share of available records reported in the selected NHANES codebooks.

Table 7: Original release-metadata dictionary reduction results

Fig. 7: Blood release-metadata descriptor before and after 50% Hadamard coefficient keeping.

The urine data analysis shows 8,154 creatinine results, and 8,153 creatinine ratio results. Fig. 8 shows a metadata-vector framework.

Fig. 8: Urine release-metadata descriptor.

Fig. 9 shows comparative outcomes of original and re-build lab data with respect to our proposed method. From the figure we see that, using quantum dictionary-based analysis produces better formations.

Fig. 9: top-K squared-coefficient.

Our analysis shows that the answer lies at the data-structure level. A classical key–value schema can store both the retained image coefficients and the laboratory release values, and the dictionary combinations built on it ran successfully in all experiments.

Fig. 10 shows the original SSIM change for the two lung images. At 50% coefficient keeping, both images were above 0.97 SSIM. At 25%, both were above 0.90. At 12.5%, both were close to 0.81. Fig. 11 shows the public range widths after a log display. It is useful for seeing scale differences. It does not describe within-patient variation.

A new analysis could use separate key value combinations. Image keys may start with 00, blood keys with 01, and urine keys with 10. For example,

Fig. 10: SSIM against the share of kept Hadamard image coefficients.

Fig. 11: Selected blood and urine variables.

Table 8: Numerical sensitivity of the 50% release-metadata descriptors

The prefix identifies the modality. The remaining bits identify a feature. A separate mask bit or mask field can record whether a value was observed.

Table 8 shows the qualitative values for validations. The outcomes indicate the metadata should not be overestimated. For urine, identity top-K keeping reconstructs the small padded descriptor. This indicates that the better retention number is a property of the positive vector and its padding.

This analysis shows that Hadamard variations framework have useful outcomes for the two demonstration images with small values to high similarity values. On the other hand, DCT baseline provides higher PSNR and SSIM on both images. H&E-1 has 30.85 dB PSNR at 25% keeping. The high ratio of framework is providing small non-negative vectors. The image and the laboratory values shows in the table are showing different values for different experiments. We basically using the similar dictionary-based analysis. Both can use a feature key, a value, an optional mask, a logged update rule, and a sparse output. It is not biological coherence. FRQI, NEQR, and QPIXL provide quantum image representations. Q-MedDict is a classical dictionary simulation inspired by gate actions.

The main limitations are substantial.

1) the data about image and lab-based data are not from

the same patients due to lack of patients data.

2) The lab-based data utilizes the metadata.

3) The image sources only two web-sourced examples.

In our next research, we will focus on demographic lung cancer data from known sources. All the experiments, lab data, and public data will be verified before going to the experiments. Moreover, we will compare with classical machine leaning outcomes with proposed quantum-based outcomes.

Our proposed method Q-MedDict is a classical quantum-based dictionary approach. It presents data with respect to bit-string keys and applies gate-like values. It is a simple method to utilize quantum concept without using quantum hardware. With this approach, we can achieve real quantum level outcomes using classical computer. We have used multiple data such DCT and PCA/KLT images. DCT outperforms the Hadamard gate on both demonstration images more than 25%. However, quantum-based dictionary model provides reliable outcomes and framework.

Sazia Parvin: Conceptualization, Formal analysis, Methodology, Software, Validation. Md Sarwar Kamal: Data curation, Visualization, Writing - Original draft, Supervision, Writing - Reviewing and editing. All authors have read and agreed to the published version of the manuscript.

This work uses public, de-identified data documentation and public web images. No new participant recruitment, intervention, or private health record access was performed.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Lung images data are used from the publicly available sources. The link is given bellow: https://portal.imaging.datacommons.cancer.gov/collections/cmb_lca/.
Laboratory metadata are available from the following sources: https://wwwn.cdc.gov/Nchs/Data/Nhanes/Public/2021/DataFiles/CBC_L.htm, https://wwwn.cdc.gov/Nchs/Data/Nhanes/Public/2021/DataFiles/BIOPRO_L.htm and https://wwwn.cdc.gov/Nchs/Data/Nhanes/Public/2021/DataFiles/ALB_CR_L.htm.

The authors received no specific financial support for the research, authorship, or publication of this work.

The authors declare that Generative AI tools were used for language editing and manuscript revision support. The authors reviewed the scientific content and checked the numerical results.

Not applicable.

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