arXiv subjects

Alok Shukla

Publications and source records attributed to Alok Shukla.

At least 37 records · Page 2Linked to original sources

arXiv2025

Computational study of geometry, electronic structure and low-lying excited states of linear T-graphene quantum dots

A few years ago, by means of first-principles calculations, Enyashin et al.(2011) proposed several novel monolayers of carbon containing rings other than hexagons. One of those monolayers containing tetragons and octagons was investigated later in detail by Liu et al.(2012) who called it T-graphene, and found that it exists both in strictly planar and buckled forms, with the planar structure being metallic in nature. Given the fact that Kotakoski et al.(2011) had already found experimental evidence of 1D carbon structures containing tetragons and octagons, we decided to investigate finite linear fragments of T-graphene, with the strictly planar structures, referred to as T-graphene quantum dots (TQDs). In order to avoid the dangling bonds in the finite T-graphene fragments, we considered the edges to be saturated by hydrogen atoms. We first optimized the geometries of the considered TQDs using a first-principles density-functional theory (DFT) methodology, followed by calculations of their linear optical absorption spectra using the time-dependent DFT (TDDFT) approach. Given the fact that strictly planar T-graphene structures will have $σ$-$π$ separation with the $π$ electrons near the Fermi level, we also parameterized an effective $π$-electron Hamiltonian for TQDs, similar to the Pariser-Parr-Pople model for $π$-conjugated molecules. We further used the effective Hamiltonian to perform high-order electron-correlated calculations using the configuration interaction (CI) approach to compute the optical absorption spectra of TQDs, and also their singlet-triplet gaps. The symmetry analysis reveals that TQDs are photoluminescent materials. Moreover, in all the TQDs HOMO-LUMO transition is optically forbidden, the optical gaps of these molecules are quite large, suggesting the intriguing possibility of the fission of a singlet optical exciton into several triplet excitons.

cond-mat.mtrl-sci↗

arXiv2025

Enhanced UV Photodetector Efficiency with a ZnO/Ga$_2$O$_3$ Heterojunction

Heterostructures comprising uncoated ZnO and coated with thin layers of Ga$_2$O$_3$ were produced using spin-coating and subsequent hydrothermal processing. X-ray diffraction examination verifies the structural integrity of the synthesized heterostructures (HTs). Optical and photoluminescence spectra were recorded to assess the variation in absorption and emission of the Ga$_2$O$_3$-coated HTs in comparison to the pristine ZnO. We conducted comparative density-functional theory (DFT) computations to corroborate the measured band gaps of both categories of HTs. To assess the stability of our devices, the transient response to on/off light switching under zero bias has been studied. The rise time $τ_{r1}$ ($τ_{r2}$) is 2300 (500) ms and the decay time $τ_{d1}$ ($τ_{d2}$) is 2700 (5000) ms have been observed for bare ZnO and ZnO/Ga$_2$O$_3$ HTs, respectively. A significant amount of change was also observed in the electrical transport properties from bare ZnO to ZnO/Ga$_2$O$_3$. To see the performance of device, responsivity (R) and detectivity (D = 1/NEP$_B$) have been measured. It is evident from observation that responsivity of a device shows maximum value in UV region while it is reducing with visible region for HTs. In case of detectivity, the maximum value reached was $145 \times 10^{14}$ Hz$^{1/2}$/W (at ~ 200 nm) and $38 \times 10^{14}$ Hz$^{1/2}$/W (at 300 nm) for Ga$_2$O$_3$ coated ZnO, and bare ZnO HTs, respectively. The maximum responsivity measured for the bare ZnO HTs is 7 (A/W) while that of Ga$_2$O$_3$ coated ZnO HTs is 38 (A/W). It suggests a simple way of designing materials for fabricating broad-range cost-effective photodetectors.

cond-mat.mtrl-sci↗

arXiv2025

A generalization of Bernstein-Vazirani algorithm with multiple secret keys and a probabilistic oracle

A probabilistic version of the Bernstein-Vazirani problem (which is a generalization of the original Bernstein-Vazirani problem) and a quantum algorithm to solve it are proposed. The problem involves finding one or more secret keys from a set of multiple secret keys (encoded in binary form) using a quantum oracle. From a set of multiple unknown keys, the proposed quantum algorithm is capable of (a) obtaining any key (with certainty) using a single query to the probabilistic oracle and (b) finding all keys with a high probability (approaching 1 in the limiting case). In contrast, a classical algorithm will be unable to find even a single bit of a secret key with certainty (in the general case). Owing to the probabilistic nature of the oracle, a classical algorithm can only be useful in obtaining limiting probability distributions of $ 0 $ and $ 1 $ for each bit-position of secret keys (based on multiple oracle calls) and this information can further be used to infer some estimates on the distribution of secret keys based on combinatorial considerations. For comparison, it is worth noting that a classical algorithm can be used to exactly solve the original Bernstein-Vazirani problem (involving a deterministic oracle and a single hidden key containing $n$ bits) with a query complexity of $\mathcal{O}(n)$. An interesting class of problems similar to the probabilistic version of the Bernstein-Vazirani problem can be construed, where quantum algorithms can provide efficient solutions with certainty or with a high degree of confidence and classical algorithms would fail to do so.

quant-ph↗

arXiv2025

Efficient Implementation of a Quantum Search Algorithm for Arbitrary N

This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, we demonstrate that a considerable reduction in the number of oracle calls (and Grover's iterations) can be achieved in many cases. For special cases (i.e., when $N$ is of the form such that it is slightly greater than an integer power of 2), the reduction in the number of oracle calls (and Grover's iterations) asymptotically approaches 29.33\%. This improvement is significant compared to the traditional Grover's algorithm, which handles such cases by rounding $N$ up to the nearest power of 2. The key to this improvement is our algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, which requires gate complexity and circuit depth of only $ O (\log_2 (N)) $, without using any ancilla qubits.

quant-ph↗

arXiv2025

A quantum approach for optimal control

In this work, we propose a novel variational quantum approach for solving a class of nonlinear optimal control problems. Our approach integrates Dirac's canonical quantization of dynamical systems with the solution of the ground state of the resulting non-Hermitian Hamiltonian via a variational quantum eigensolver (VQE). We introduce a new perspective on the Dirac bracket formulation for generalized Hamiltonian dynamics in the presence of constraints, providing a clear motivation and illustrative examples. Additionally, we explore the structural properties of Dirac brackets within the context of multidimensional constrained optimization problems. Our approach for solving a class of nonlinear optimal control problems employs a VQE-based approach to determine the eigenstate and corresponding eigenvalue associated with the ground state energy of a non-Hermitian Hamiltonian. Assuming access to an ideal VQE, our formulation demonstrates excellent results, as evidenced by selected computational examples. Furthermore, our method performs well when combined with a VQE-based approach for non-Hermitian Hamiltonian systems. Our VQE-based formulation effectively addresses challenges associated with a wide range of optimal control problems, particularly in high-dimensional scenarios. Compared to standard classical approaches, our quantum-based method shows significant promise and offers a compelling alternative for tackling complex, high-dimensional optimization challenges.

quant-ph↗

arXiv2025

Exciton Basis Description of Ultrafast Triplet Separation in Pentacene-(Tetracene)2-Pentacene Intramolecular Singlet Fission Chromophore

Precise understanding of the electronic structures of optically dark triplet-triplet multiexcitons that are the intermediate states in singlet fission (SF) continues to be a challenge. This is particularly true for intramolecular singlet fission (iSF) chromophores, that are oligomers of large monomer molecules. We have performed quantum many-body calculations of the complete set of excited states relevant to iSF in Pentacene-(Tetracene)2-Pentacene oligomers, consisting of two terminal pentacene monomers linked by two tetracene monomers. Our computations use an exciton basis that gives physical pictorial descriptions of all eigenstates, and are performed over an active space of twenty-eight monomer molecular orbitals, including configuration interaction with all relevant quadruple excitations within the active space, thereby ensuring very high precision. We discuss the many-electron structures of the optical predominantly intramonomer spin-singlets, intermonomer charge-transfer excitations, and most importantly, the complete set of low energy covalent triplet-triplet multiexcitons. We are able to explain the weak binding energy of the pentacene-tetracene triplet-triplet eigenstate that is generated following photoexcitation. We explain the increase in lifetime with increasing numbers of tetracene monomers of the transient absorption associated with contiguous pentacene-tetracene triplet-triplet in this family of oligomers. We are consequently able to give a pictorial description of the triplet separation following generation of the initial triplet-triplet, leading to a state with individual triplets occupying only the two pentacene monomers. We expect many applications of our theoretical approach to triplet separation.

cond-mat.mtrl-sci↗

arXiv2025

PromptArtisan: Multi-instruction Image Editing in Single Pass with Complete Attention Control

We present PromptArtisan, a groundbreaking approach to multi-instruction image editing that achieves remarkable results in a single pass, eliminating the need for time-consuming iterative refinement. Our method empowers users to provide multiple editing instructions, each associated with a specific mask within the image. This flexibility allows for complex edits involving mask intersections or overlaps, enabling the realization of intricate and nuanced image transformations. PromptArtisan leverages a pre-trained InstructPix2Pix model in conjunction with a novel Complete Attention Control Mechanism (CACM). This mechanism ensures precise adherence to user instructions, granting fine-grained control over the editing process. Furthermore, our approach is zero-shot, requiring no additional training, and boasts improved processing complexity compared to traditional iterative methods. By seamlessly integrating multi-instruction capabilities, single-pass efficiency, and complete attention control, PromptArtisan unlocks new possibilities for creative and efficient image editing workflows, catering to both novice and expert users alike.

cs.CV↗

arXiv2025

Two dimensional transition metal dichalcogenide based bilayer heterojunctions for efficient solar cells and photocatalytic applications

This work presents a first-principles study of the optoelectronic properties of vertically-stacked bilayer heterostructures composed of 2D transition-metal dichalcogenides (TMDs). The calculations are performed using the density-functional theory (DFT) and many-body perturbation theory within $G_0W_0$-BSE methodology. We aim to propose these TMD heterostructures for solar cell applications. The TMD monolayers comprising the heterojunctions considered in this work are $MoS_2$, $WS_2$, $MoSe_2$, and $WSe_2$ due to their favorable band gaps, high carrier mobility, robust absorption in the visible region, and excellent stability. These four TMD monolayers provide the basis for six heterostructures. Consequently, we have examined the structural, electronic, and optical properties of six heterostructures ($WS_2/MoS_2$, $MoSe_2/MoS_2$, $MoSe_2/WS_2$, $WSe_2/MoS_2$, $WSe_2/MoSe_2$, and $WSe_2/WS_2$). At the DFT level, all the six considered TMD heterostructures meet the essential criterion of type II band alignment, a critical factor in extending carrier lifetime. However, according to $G_0W_0$ results, $MoSe_2/WS_2$ does not exhibit the type II band alignment, instead it shows type I band alignment. The large quasiparticle gaps obtained from $G_0W_0$ approximation suggest the presence of strong electron-correlation effects. The quality of these heterojunction solar cells is estimated by computing their power conversion efficiencies (PCE). The PCEs are calculated at both the HSE06 and $G_0W_0$ levels, and the maximum PCE predicted by HSE06 calculations on our designed solar cells can reach up to 19.25% for the $WSe_2/WS_2$ heterojunction. In addition, all six TMD heterostructures are examined for their potential applications in photocatalysis for hydrogen evolution reaction, and the three of them, namely, $WS_2/MoS_2$, $MoSe_2/MoS_2$, and $WSe_2/MoS_2$ heterostructures qualify for the same.

cond-mat.mtrl-sci↗

arXiv2025

Theoretical prediction of a novel Pt3Sn2S2 as a Nonmagnetic Weyl Semimetal in Kagome System

We present a detailed theoretical study of Pt3Sn2S2 a layered kagome type material inspired by recent investigation of Co3Sn2S2 reported in [Nature Communication 11, 3985 (2020) whose physical properties remain largely unexplored. Thermodynamic stability was confirmed via formation energy calculations while mechanical stability was evaluated using Voigt Reuss Hill approximation and elastic stability condition. Dynamical and thermal stability were validated through Phonon dispersion and Ab Initio Molecular Dynamics simulations with Pughs criterion classifying the material as ductile. Spin orbit coupling induced band splitting, giving rise to Weyl points and a Weyl semimetal phase accompanied by a SOC driven transition from non relativistic band touching to relativistic band touching making a topological phase shift. Under applied pressure, the coupling of spin and valley degrees of freedom generates spin valley intertwined Dirac cones enabling tunable electronic properties for spintronic and valleytronic applications. Boltzman transport calculations using AMSET reveal a high Seebeck coefficient with SOC and low thermal conductivity highlighting its potential for high performance thermoelectric devices.

cond-mat.str-el↗

arXiv2025

Defect engineering in two-dimensional pentagonal PdTe$_2$: Tuning electronic, optical, and magnetic properties

Recently, the successful synthesis of the pentagonal form of PdTe$_{2}$ monolayer (\emph{p}-PdTe$_{2}$) was reported [Liu~\emph{et al.}, Nature Materials \textbf{23}, 1339 (2024)]. In this work, we present an extensive first-principles density-functional theory (DFT) based computational study of vacancies in this material. Our study covers the evolution of the electronic, optical, and magnetic properties of various defect configurations and compares those to the pristine monolayer (\emph{p}-PdTe$_{2}$). We find that V$_{Pd}$ (V$_{Te}$) is the most stable defect in the~\emph{p}-PdTe$_{2}$ monolayer in the Te-rich (Pd-rich) limit. The defects alter the electronic properties of the monolayer significantly, leading to changes in their magnetic and optical properties due to the emergence of midgap impurity states. The defect complex V$_{Pd+4Te}$ is found to induce spin-polarization in the system with a total magnetic moment of 1.87 $μ_{B}$. The obtained low diffusion energy barriers of 1.13 eV (in-plane) and 0.063 eV (top-bottom) corresponding to V$_{Te}$ indicates its facile migration probability is higher in the top-bottom direction at room temperature, as revealed by AIMD simulations as well. In order to guide the experimentalists, we also simulated the scanning-tunneling microscope (STM) images corresponding to all the defect configurations. Moreover, we also computed the electron-beam energies required for creating mono-vacancies. In the optical absorption spectra of the defective configurations, finite peaks appear below the band edge that are unique to the respective defective configuration. We have also computed the excess polarizability of the defective configurations with respect to the pristine one and found that maximum changes occur in the infrared and visible regions, providing insights into the change in their optical response as compared to the pristine monolayer.

cond-mat.mtrl-sci↗

arXiv2024

DFT and Model Hamiltonian Study of Optoelectronic Properties of Some Low-Symmetry Graphene Quantum Dots

We have studied the electronic and optical properties of three low-symmetry graphene quantum dots (GQDs), with the point-group symmetries $C_{2v}$, and $C_{2h}$. For the calculations of linear optical absorption spectra, we employed both the first-principles time-dependent density-functional theory (TDDFT), and the electron-correlated Pariser-Parr-Pople (PPP) model coupled with the configuration-interaction (CI) approach. In the PPP-CI approach, calculations were performed using both screened and standard parameters, along with efficiently incorporating electron correlation effects using multi-reference singles-doubles configuration-interaction for both ground and excited states. We assume that the GQDs are saturated by hydrogen atoms at the edges, making them effectively polycyclic aromatic hydrocarbons (PAHs) dibenzo[bc,ef]coronene (also known as benzo(1,14)bisanthene, C$_{30}$H$_{14}$), and two isomeric compounds, dinaphtho[8,1,2abc;2,1,8klm]coronene and dinaphtho[8,1,2abc;2,1,8jkl]coronene with the chemical formula C$_{36}$H$_{16}$. The two isomers have different point group symmetries, therefore, this study will also help us understand the influence of symmetry on optical properties. A common feature of the absorption spectra of the three GQDs is that the first peak representing the optical gap is of low to moderate intensity, while the intense peaks appear at higher energies. For each GQD, PPP model calculations performed with the screened parameters agree well with the experimental results of the corresponding PAH, and also with the TDDFT calculations. To further quantify the influence of electron-correlation effects, we also computed the singlet-triplet gap (spin gap) of the three GQDs, and we found them to be significant.

physics.chem-ph↗

arXiv2024

Characterization of Silicon Carbide Biphenylene Network through G0W0-BSE Calculations

Two-dimensional silicon carbide stands out among 2D materials, primarily due to its notable band gap, unlike its carbon-based counterparts. However, the binary nature and non-layered structure of bulk SiC present challenges in fabricating its 2D counterpart. Recent advancements in technology have led to the successful synthesis of atomically thin, large-scale epitaxial monolayers of hexagonal-SiC and Si9C15 , marking a significant milestone in semiconductor research. Inspired by these advancements, we have computationally designed another stable phase of 2D-SiC in the popular biphenylene network, termed SiC-biphenylene. This structure is characterized by interconnected polygons of octagons, hexagons, and tetragons arranged periodically. The dynamical and thermal stability has been confirmed through ab initio phonon dispersion and molecular dynamics simulations. The structure demonstrates a high melting point of approximately 3475 K and a direct band gap of 2.16 eV using the HSE06 functional. Upon considering many-body effects, the quasiparticle band gap widens to 2.89 eV at the G0W0 level, indicating pronounced electron correlation effects within the material. The optical spectrum obtained from solving the Bethe-Salpeter equation (G0W0+BSE) identifies the first optically active exciton peak at 2.07 eV, corresponding to a strongly bound exciton with a binding energy of 0.82 eV. Furthermore, the investigation into stable bilayer structures across various stacking configurations highlights the impact of stacking patterns on excitonic binding energies. Our investigation extends to identifying the stable bulk phase of SiC-biphenylene, revealing lower self-energy corrections compared to monolayer and bilayer structures, attributed to increased electron delocalization in bulk structures.

cond-mat.mtrl-sci↗

arXiv2024

Efficient quantum algorithm for weighted partial sums and numerical integration

This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration, cumulative probability distributions, and probabilistic modeling. The proposed quantum algorithm uses a custom unitary construction to achieve the desired partial sums with gate complexity and circuit depth of $O(\log_2 M)$, where $M$ represents the number of terms in the partial sum. For cases where $M$ is a power of two, the unitary construction is straightforward; however, for arbitrary $M$, we develop an efficient quantum algorithm to create the required unitary matrix. Computational examples for evaluation certain partial sums and numerical integration based on our proposed algorithm are provided. We also extend the algorithm to evaluate partial sums of even or odd components and more complex weighted sums over specified intervals.

quant-ph↗

arXiv2024

An efficient quantum algorithm for preparation of uniform quantum superposition states

Quantum state preparation involving a uniform superposition over a non-empty subset of $n$-qubit computational basis states is an important and challenging step in many quantum computation algorithms and applications. In this work, we address the problem of preparation of a uniform superposition state of the form $\ketΨ = \frac{1}{\sqrt{M}}\sum_{j = 0}^{M - 1} \ket{j}$, where $M$ denotes the number of distinct states in the superposition state and $2 \leq M \leq 2^n$. We show that the superposition state $\ketΨ$ can be efficiently prepared with a gate complexity and circuit depth of only $O(\log_2~M)$ for all $M$. This demonstrates an exponential reduction in gate complexity in comparison to other existing approaches in the literature for the general case of this problem. Another advantage of the proposed approach is that it requires only $n=\ceil{\log_2~M}$ qubits. Furthermore, neither ancilla qubits nor any quantum gates with multiple controls are needed in our approach for creating the uniform superposition state $\ketΨ$. It is also shown that a broad class of nonuniform superposition states that involve a mixture of uniform superposition states can also be efficiently created with the same circuit configuration that is used for creating the uniform superposition state $\ketΨ$ described earlier, but with modified parameters.

quant-ph↗

arXiv2024

Enhanced hydrogen evolution reaction activity of nitrogen deficient $hg-C_{3}N_{4}$ quantum dot

The present study investigates the catalytic performance of a $hg-C_{3}N_{4}$ quantum dot aimed at enhancing electrochemical water splitting, using the first-principles density functional theory. The size of the considered quantum dot lies within the range reported experimentally (2nm - 4nm) [Zhou et al. ACS Nano 9, 12480 (2015)]. The nitrogen vacancies are created in the considered $hg-C_{3}N_{4}$ structure to simulate the realistic scenario, as the presence of nitrogen and carbon defects are reported in the synthesized $hg-C_{3}N_{4}$ quantum dots. First, the structural and vibrational properties are computed to ensure the stability of the nitrogen deficient $hg-C_{3}N_{4}$ quantum dots, and subsequently, their electronic and hydrogen evolution reaction (HER) properties are investigated. The calculate HER parameters, i.e., adsorption energies, Gibbs free energies, and overpotentials demonstrate that the considered $hg-C_{3}N_{4}$ quantum dot with nitrogen vacancies can be used as a moderately effective electrocatalyst for HER performance. We also considered the quantum dot to be dissolved in water and ethanol, and find that the overpotential gets drastically reduced to 16 mV for the alcohol dissolved quantum dot, while some significant reduction is seen for the aqueous solution also. As a result, this study suggests that the nitrogen-deficient $hg-C_{3}N_{4}$ quantum dots dissolved in ethanol are excellent candidates for catalysis aimed at sustainable hydrogen production via electrochemical water splitting.

cond-mat.mtrl-sci↗

arXiv2024

Influence of strain and point defects on the electronic structure and related properties of (111)NiO epitaxial films

(111)NiO epitaxial films are grown on c-sapphire substrates at various growth temperatures ranging from room-temperature to 600C using pulsed laser deposition (PLD) technique. Two series of samples, where different laser fluences are used to ablate the target, are studied here. Films grown with higher laser fluence, are found to be embedded with Ni-clusters crystallographically aligned with the (111)NiO matrix. While the layers grown with lower laser energy density exhibit p-type conductivity specially at low growth temperatures. X-ray diffraction study shows the coexistence of biaxial compressive and tensile hydrostatic strains in these samples, which results in an expansion of the lattice primarily along the growth direction. This effective uniaxial expansion {epsilon}_perpendicular increases with the reduction of the growth temperature. Band gap of these samples is found to decrease linearly with {epsilon}_perpendicular. This result is validated by density functional theory (DFT) calculations. Experimental findings and the theoretical study further indicate that V_Ni + O_I and V_O + Ni_I complexes exist as the dominant native defects in samples grown with Ni-deficient (low laser fluence) and Ni-rich (high laser fluence) conditions, respectively. P-type conductivity observed in the samples grown in Ni-deficient condition is more likely to be resulting from V_Ni + O_I defects than Ni-vacancies (V_Ni).

cond-mat.mtrl-sci↗

arXiv2024

First-Principles Study of Penta-CN2 Quantum Dots for Efficient Hydrogen Evolution Reaction

The objective of our research is to investigate the electrocatalytic properties of novel metal-free quantum dots (QDs) composed of the recently discovered 2D material penta-CN2, with the aim of replacing costly and scarce catalysts such as Pt and Pd. Employing a first-principles density functional theory (DFT) based approach, the geometries of the three penta-CN2 quantum dots (QDs) of increasing sizes, 3 x 3, 3 x 4, 4 x 4 are optimized. Through comprehensive analysis, our research extensively explored the structural stability of penta-CN2 QDs, delved into their electronic properties, and assessed their catalytic performance concerning the Hydrogen Evolution Reaction (HER). Notably, the H-adsorbed penta-CN2 QDs exhibit a significant reduction in the HOMO-LUMO gap (E_{g}) ranging from 35% to 49% compared to the pristine QD. Next, we investigated their catalytic performance relevant to HER, using well-known descriptors: (i) adsorption energy, (ii) over-potential, (iii) Gibbs free energy and (iv) exchange current density along with the volcano curve. As far as size dependence of the catalytic performance is concerned, the value of Delta G^{(av)} is minimum for 3 x 3 penta-CN2 QD, with those of 3 x 4 and 4 x 4 QDs being slightly larger. Our calculations predict a high value of exchange current density 2.24 x 10^{-3} A-cm^{-2} for one of the sites (N11 for 3 x 3 QD), which we believe will lead to significantly enhanced HER properties. Our research outcomes hold great promise in advancing the discovery of abundant, non-toxic, and cost-effective catalysts for HER, playing a vital role in facilitating large-scale hydrogen production.

cond-mat.mtrl-sci↗

arXiv2024

Hybrid classical-quantum image processing via polar Walsh basis functions

We propose a novel hybrid classical-quantum approach for image processing based on polar Walsh basis functions. Using this approach, we present an algorithm for the removal of the circular banding noise (including Airy pattern noise) and the azimuthal banding noise. This approach is based on a formulation of Walsh basis functions in polar coordinates for image representations. This approach also builds upon an earlier work on a hybrid classical-quantum algorithm for Walsh-Hadamard transforms. We provide two kinds of polar representations using uniform area measure and uniform radial measure. Effective smoothening and interpolating techniques are devised relevant to the transformations between Cartesian and polar coordinates, mitigating the challenges posed by the non-injectivity of the transformation in the context of digital images. The hybrid classical-quantum approach presented here involves an algorithm for Walsh-Hadamard transforms, which has a lower computational complexity of $\mathcal{O}(N)$ compared to the well-known classical Fast Walsh-Hadamard Transform, which has a computational complexity of $\mathcal{O}(N \log_2 N)$. We demonstrated the applicability of our approach through computational examples involving the removal of the circular banding noise (including Airy pattern noise) and the azimuthal banding noise.

quant-ph↗