arXiv subjects

Pulak Ranjan Giri

Publications and source records attributed to Pulak Ranjan Giri.

At least 19 recordsLinked to original sources

arXiv2026

Grover's algorithm for image edge detection

Grover's algorithm is one of the most significant quantum algorithms, enabling the search for a marked element in an unsorted database quadratically faster than classical search algorithms. We utilize Groves's algorithm to detect the edges of a digital image faster than any classical edge detection methods. The high success probability of our method in detecting image edges, compared to most existing quantum edge detection methods, makes it a more suitable candidate for use in the presence of noise on current quantum devices. We implemented our model for the $2\times 2$ blocks of the image using a two-qubit Qiskit circuit with the QASM simulator and the noisy IBM Sydney(fake) device, making it suitable for most of the current NISQ devices.

quant-ph↗

arXiv2026

Quantum hash function using discrete-time quantum walk on Hanoi network

Quantum walk based hash functions have attracted a lot of attention in recent years because of its faster execution time and robust resistance against attacks compared to classical hash functions. It has been observed that the underlying graph and the way message controls the quantum walk iteration steps play a crucial role for the robustness of the hash function. We propose a quantum hash function based on the discrete-time quantum walk on a Hanoi network--a one dimensional periodic lattice with extra long-range edges of a specific form--which is highly collision resistant. The message bits of our scheme control the flow of probability amplitude through the extra long-range edges and the conditional shift operators. Our method even works for messages with small bit-lengths, contrary to most of the quantum walk based hash functions defined on a cycle, which usually work for messages with bit-lengths more than the length of the cycle.

quant-ph↗

arXiv2026

Quantum walk search for exceptional configurations on one- and two-dimensional lattice with extra long-range edges of Hanoi network of degree four

There exist several types of configurations of marked vertices, referred to as the exceptional configurations, on one- and two-dimensional periodic lattices with additional long-range edges of the Hanoi network of degree four (HN4), which are challenging to find using discrete-time quantum walk algorithms. In this article, we conduct a comparative analysis of the discrete-time quantum walk algorithm utilizing various coin operators to search for these exceptional configurations. First, we study the emergence of several new exceptional configurations/vertices due to the additional long-range edges of the HN4 on both one- and two-dimensional lattices. Second, our study shows that the diagonal configuration on a two-dimensional lattice, which is exceptional in the case without long-range edges, no longer remains an exceptional configuration. Third, it is also shown that a recently proposed modified coin can search all these configurations, including any other configurations in one- and two-dimensional lattices with very high success probability. Additionally, we construct stationary states for the exceptional configurations caused by the additional long-range edges, which explains why the standard and lackadaisical quantum walks with the Grover coin cannot search these configurations.

quant-ph↗

arXiv2025

Quantum walk search based edge detection of images

Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its range of applications further. In this article, we propose a novel application of this advanced quantum walk search algorithm for the edge detection of images\textemdash a critical task in digital image processing. Given the probabilistic nature of quantum computing, obtaining measurement result with a high success probability is essential alongside faster computation time. Our quantum walk search algorithm demonstrates a high success probability in detecting the image edges compared to the existing quantum edge detection methods and outperforms classical edge detection methods with a quadratically faster speed. A small Qiskit circuit implementation of our method using a one-dimensional quantum walk search has been executed in Qiskit's $qasm\_simulator$ and $ibm\_sydney(fake)$ device.

quant-ph↗

arXiv2025

Multi-target quantum walk search on Johnson graph

The discrete-time quantum walk on the Johnson graph $J(n,k)$ is a useful tool for performing target vertex searches with high success probability. This graph is defined by $n$ distinct elements, with vertices being all the $\binom{n}{k}$ $k$-element subsets and two vertices are connected by an edge if they differ exactly by one element. However, most works in the literature focus solely on the search for a single target vertex on the Johnson graph. In this article, we utilize lackadaisical quantum walk--a form of discrete-time coined quantum walk with a wighted self-loop at each vertex of the graph--along with our recently proposed modified coin operator, $\mathcal{C}_g$, to find multiple target vertices on the Johnson graph $J(n,k)$ for various values of $k$. Additionally, a comparison based on the numerical analysis of the performance of the $\mathcal{C}_g$ coin operator in searching for multiple target vertices on the Johnson graph, against various other frequently used coin operators by the discrete-time quantum walk search algorithms, shows that only $\mathcal{C}_g$ coin can search for multiple target vertices with a very high success probability in all the scenarios discussed in this article, outperforming other widely used coin operators in the literature.

quant-ph↗

arXiv2025

Fast variational knowledge graph embedding

Embedding of a knowledge graph(KG) entities and relations in the form of vectors is an important aspect for the manipulation of the KG database for several downstream tasks, such as link prediction, knowledge graph completion, and recommendation. Because of the growing size of the knowledge graph databases, it has become a daunting task for the classical computer to train a model efficiently. Quantum computer can help speedup the embedding process of the KGs by encoding the entities into a variational quantum circuit of polynomial depth. Usually, the time complexity for such variational circuit-dependent quantum classical algorithms for each epoch is $\mathcal{O}(N \mbox{poly}(\log M))$, where $N$ is number of elements in the knowledge graph and $M$ is the number of features of each entities of the knowledge graph. In this article we exploit additional quantum advantage by training multiple elements of KG in superpositions, thereby reducing the computing time further for the knowledge graph embedding model.

quant-ph↗

arXiv2025

Quantum walk search for exceptional configurations

There exist two types of configurations of marked vertices on a two-dimensional grid, known as the {\it exceptional configurations}, which are hard to find by the discrete-time quantum walk algorithms. In this article, we provide a comparative study of the quantum walk algorithm with different coins to search these {\it exceptional configurations} on a two-dimensional grid. We further extend the analysis to the hypercube, where only one type of {\it exceptional configurations} are present. Our observation, backed by numerical results, is that our recently proposed modified coin operator is the only coin which can search both types of {\it exceptional configurations} as well as non-{\it exceptional configurations} successfully. As a consequence, we observe that the existence of {\it exceptional configurations} are not a quantum phenomenon, rather a mere limitation of some of the coin operators.

quant-ph↗

arXiv2025

Quantum walk search on a two-dimensional grid with extra edges

Quantum walk has been successfully used to search for targets on graphs with vertices identified as the elements of a database. This spacial search on a two-dimensional periodic grid takes $\mathcal{O}\left(\sqrt{N\log N}\right)$ oracle consultations to find a target vertex from $N$ number of vertices with $\mathcal{O}(1)$ success probability, while reaching optimal speed of $\mathcal{O}(\sqrt{N})$ on $d \geq 3$ dimensional square lattice. Our numerical analysis based on lackadaisical quantum walks searches $M$ vertices on a 2-dimensional grid with optimal speed of $\mathcal{O}(\sqrt{N/M})$, provided the grid is attached with additional long range edges. Based on the numerical analysis performed with multiple sets of randomly generated targets for a wide range of $N$ and $M$ we suggest that the optimal time complexity of $\mathcal{O}(\sqrt{N/M})$ with constant success probability can be achieved for quantum search on a two-dimensional periodic grid with long-range edges.

quant-ph↗

arXiv2025

Quantum walk search by Grover search on coin space

Quantum walk followed by some amplitude amplification technique has been successfully used to search for marked vertices on various graphs. Lackadaisical quantum walk can search for target vertices on graphs without the help of any additional amplitude amplification technique. These studies either exploit AKR or SKW coin to distinguish the marked vertices from the unmarked vertices. The success of AKR coin based quantum walk search algorithms highly depend on the arrangements of the set of marked vertices on the graph. For example, it fails to find adjacent vertices, diagonal vertices and other exceptional configurations of vertices on a two-dimensional periodic square lattice and on other graphs. These coins also suffer from low success probability while searching for marked vertices on a one-dimensional periodic lattice and on other graphs for certain arrangements for marked vertices. In this article, we propose a modified coin for the lackadaisical quantum walk search. It allows us to perform quantum walk search for the marked vertices by doing Grover search on the coin space. Our model finds the marked vertices by searching the self-loops associated with the marked vertices. It can search for marked vertices irrespective of their arrangement on the graph with high success probability. For all analyzed arrangements of the marked vertices the time complexity for 1d-lattice and 2d-lattice are $\mathcal{O}(\frac{N}{M})$ and $\mathcal{O}\left(\sqrt{ \frac{N}{M}\log \frac{N}{M}}\right)$ respectively with constant and high success probability.

quant-ph↗

arXiv2025

Quantum negative sampling strategy for knowledge graph embedding with variational circuit

Knowledge graph is a collection of facts, known as triples(head, relation, tail), which are represented in form of a network, where nodes are entities and edges are relations among the respective head and tail entities. Embedding of knowledge graph for facilitating downstream tasks such as knowledge graph completion, link prediction, recommendation, has been a major area of research recently in classical machine learning. Because the size of knowledge graphs are becoming larger, one of the natural choices is to exploit quantum computing for knowledge graph embedding. Recently, a hybrid quantum classical model for knowledge graph embedding has been studied in which a variational quantum circuit is trained. One of the important aspects in knowledge graph embedding is the sampling of negative triples, which plays a crucial role in efficient training of the model. In classical machine learning various negative sampling strategies have been studied. In quantum knowledge graph embedding model, although we can use these strategies in principle, it is natural to ask if we can exploit quantum advantage in negative sampling. In this article we study such a negative sampling strategy, which exploits quantum superposition, and evaluate the model's performance with a knowledge graph database.

quant-ph↗

arXiv2020

Quantum search on Hanoi network

Hanoi network has a one-dimensional periodic lattice as its main structure with additional long-range edges, which allow having efficient quantum walk algorithm that can find a target state on the network faster than the exhaustive classical search. In this article, we use regular quantum walks and lackadaisical quantum walks respectively to search for a target state. From the curve fitting of the numerical results for Hanoi network of degree three and four we find that their running time for the regular quantum walks followed by amplitude amplification scales as $\mathcal{O}\left(N^{0.79} \sqrt{\log N}\right)$ and $\mathcal{O}\left(N^{0.65} \sqrt{\log N}\right)$ respectively. And for the search by lackadaisical quantum walks the running time scales as $\mathcal{O}\left(N^{0.57}\log N\right)$ and $\mathcal{O}\left(N^{0.50}\log N\right)$ respectively.

quant-ph↗

arXiv2019

Lackadaisical quantum walk for spatial search

Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical quantum walk on one- and two-dimensions. It is observed that specific values of the self-loop weight at each vertex of the graph is responsible for such speedup of the algorithm. Searching for a target state on one-dimensional lattice with periodic boundary conditions is possible using lackadaisical quantum walk, which can find a target state with $\mathcal{O}(1)$ success probability after $\mathcal{O} \left( N \right)$ time steps. In two-dimensions, our numerical simulation upto $M=6$ suggests that lackadaisical quantum walk can search one of the $M$ target states in $\mathcal{O}\left(\sqrt{\frac{N}{M}\log \frac{N}{M}}\right)$ time steps.

quant-ph↗

arXiv2016

A Review on Quantum Search Algorithms

The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It can be understood from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review the Grover quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin, called GRK algorithm are also discussed.

quant-ph↗

arXiv2015

Exact quantum numbers of collapsed and non-collapsed 2-string solutions in the Heisenberg spin chain

Every solution of the Bethe-ansatz equations (BAE) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length $N$. Here we obtain them both for real and complex solutions. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., 2-string solutions) in the sector: $2[ (N-1)/2 - (N/π) \tan^{-1}(\sqrt{N-1})]$ in terms of Gauss' symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.

cond-mat.stat-mech↗

arXiv2015

Power-law relaxation behavior of an initially localized state in the spin-1/2 Heisenberg chain

We present power-law relaxation behavior of the local magnetizations in the equilibration dynamics of the spin-1/2 Heisenberg spin chain as an isolated integrable quantum system. We perform the exact time evolution of the expectation values of the local spin operators by evaluating them with the determinant formula of the form factors. We construct such an initial quantum state that has a localized profile of the local magnetizations, and perform the exact time evolution over a very long period of time. We show that the local magnetization relaxes as some power of the time variable with no definite time scale, while the fidelity relaxes very fast with its relaxation time being proportional to the inverse of the energy width, i.e. the Boltzmann time.

cond-mat.stat-mech↗

arXiv2015

Singular eigenstates in the even(odd) length Heisenberg spin chain

We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \{λ_α\} are invariant under the sign changes of their rapidities {λ_α\}=\{-λ_α\} , then the Bethe ansatz equations are reduced to a system of (M-2)/2 ((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N= 3\left(2k+1\right) with k=1, 2, 3, \cdots. It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.

hep-th↗

arXiv2015

Non Self-conjugate Strings, Singular Strings and Rigged Configurations in the Heisenberg Model

We observe a different type of complex solutions in the isotropic spin-1/2 Heisenberg chain starting from N=12, where the central rapidity of some of the odd-length strings becomes complex making not all the strings self-conjugate individually. We show that there are at most (N-2)/2 singular solutions for M=4, M=5 down-spins and at most (N^2-6N+8)/8 singular solutions for M=6, M=7 down-spins in an even-length chain with N \geq 2M. Correspondence of the non self-conjugate string solutions and the singular string solutions to the rigged configurations has also been shown.

hep-th↗

arXiv2015

Heisenberg model and Rigged Configurations

We show a correspondence of all the solutions of the spin-1/2 isotropic Heisenberg model for N=12 to the rigged configurations based on the comparison of the set of Takahashi quantum numbers in lexicographical order with the set of riggings of the rigged configurations in co-lexicographical order.

hep-th↗