Quantum Information Theory promises to speed up computation so is observed in real quantum computers as proved to its classical counterpart. This revolutionizes every field linked directly or indirectly with computation. Grover algorithm in quantum information gives quadratic speed up in unstructured database search. With the availability of public online resources for quantum computers like IBM, quantum image processing came into the picture for making use of quantum computers in the image processing field. Our research interest is to find all darker pixels in a 2x2 grayscale image using Grover's algorithm. We studied it in two different ways. In the first method, I ran Grover's algorithm on the python generated classical image. In the second method, I converted a python-generated 2x2 image into a quantum image and then ran Grover's algorithm to locate the darker pixels. As has been observed in complexity analysis, Grover's unstructured search has the O(2^{n}) while as for classical schemes O(2^{2n+2m}), where m and n denote the dimensions of the image.
Quantum Computing offers an entirely new way of doing computation governed by the rules of quantum mechanics like Superposition and Entanglement. These rules allow us to do computation over all the possible states simultaneously. Hence, offering exponentially higher computation power than the present classical computers. Quantum computing algorithms are entirely different from classical algorithms due to quantum parallel computing derived from quantum state superposition and entanglement, which has natural advantages over classical image processing. Grover algorithm is a quantum-based search a…
Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant probability on each query, but in general, requiring several iterations of the algorithm. We present a modified version to return the correct result with certainty without having user control over the quantum search oracle. Our deterministic, two-parameter "D2p" protocol utilizes generalized phase rotations replacing the phase inversions after a standard orac…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept of well-known Grover's quantum search algorithm. The algorithm finds the solution by rotating the initial state vector in the Hilbert space to get the target solution state. It mainly involves finding particular matrices that solve the set of equations and constructing corresponding quantum circuits using the basic quantum gates. We explicitly illustrate the…
We confirmed the annealing time of Grover's search which is required to obtain desired success probability for quantum annealing by the imaginary-time and the real-time Schrödinger equation with two kinds of schedulings; one linearly decreases the quantum fluctuation and the other tunes the evolution rate of the Hamiltonian based on the adiabatic condition. With linear scheduling, the required annealing time for quantum annealing by the imaginary-time Schrödinger equation is of order $\log N$, which is very different from $O(N)$ required for the quantum annealing by the real-time Schrödinger e…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In this situation, we find that quantum signal processing lets us estimate the amplitude in a more flexible way. We leverage this technique to give improved and simplified algorithms for many amplitude estimation tasks: we perform non-destructive estimation without any assumptions on the amplitude, develop an algorithm with improved performance in practice, presen…
The nature of discrete-time quantum walk in the presence of multiple marked states has been studied by Nahimovs and Rivosh. They introduced an exceptional configuration of clustered marked states $i.e.,$ if the marked states are arranged in a $\sqrt{k} \times \sqrt{k}$ cluster within a $\sqrt{N} \times \sqrt{N}$ grid, where $k=n^{2}$ and $n$ an odd integer. They showed that finding a single marked state among the multiple ones using quantum walk with AKR (Ambainis, Kempe and Rivosh) coin requires $Ω(\sqrt{N} - \sqrt{k})$ time. Furthermore, Nahimov and Rivosh also showed that the Grover's coin …
End-to-End QGAN-Based Image Synthesis via Neural Noise Encoding and Intensity Calibration
Shanghai Maritime University（上海海洋大学）；Agency for Science, Technology and Research（科技研究局）；Singapore University of Technology and Design（新加坡科技设计大学）；Institute of High Performance Computing（高性能计算研究院）
