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Related papers: A Generalization of Grover's Algorithm

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For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…

Quantum Physics · Physics 2013-04-10 Akira Shimizu , Yuichiro Matsuzaki , Akihisa Ukena

Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits…

Quantum Physics · Physics 2026-03-17 Haomu Yuan , Hanqing Wu , Kuan-Cheng Chen , Bin Cheng , Crispin H. W. Barnes

In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…

Quantum Physics · Physics 2025-12-08 Sören Wilkening , Timo Ziegler , Maximilian Hess

We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…

Quantum Physics · Physics 2008-05-12 Andris Ambainis

We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization)…

Quantum Physics · Physics 2023-02-02 Daniel Koch , Massimiliano Cutugno , Saahil Patel , Laura Wessing , Paul M. Alsing

The success probability of a search of $M$ targets from a database of size $N$, using Grover's search algorithm depends critically on the number of iterations of the composite operation of the oracle followed by Grover's diffusion…

Quantum Physics · Physics 2020-11-24 Simanraj Sadana

We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…

Quantum Physics · Physics 2020-07-20 Go Kato

The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…

Quantum Physics · Physics 2016-09-08 Eli Biham , Ofer Biham , David Biron , Markus Grassl , Daniel A. Lidar , Daniel Shapira

Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…

Quantum Physics · Physics 2007-05-23 David Collins

Vectorial Genetic Programming (Vec-GP) extends GP by allowing vectors as input features along regular, scalar features, using them by applying arithmetic operations component-wise or aggregating vectors into scalars by some aggregation…

Neural and Evolutionary Computing · Computer Science 2023-03-07 Philipp Fleck , Stephan Winkler , Michael Kommenda , Michael Affenzeller

Optimizing high-degree of freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum native framework…

Robotics · Computer Science 2025-10-30 Hassen Nigatu , Shi Gaokun , Li Jituo , Wang Jin , Lu Guodong , Howard Li

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…

Quantum Physics · Physics 2017-11-22 Yan Wang

Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…

Quantum Physics · Physics 2023-07-31 Guanzhong Li , Lvzhou Li

We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…

Quantum Physics · Physics 2009-11-06 Alberto Galindo , Miguel A. Martin-Delgado

Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The…

Grover discovered a quantum algorithm for identifying a target element in an unstructured search universe of N items in approximately square-root of N queries to a quantum oracle, thus achieving a square-root speed-up over classical…

Quantum Physics · Physics 2007-05-23 Erdal Arikan

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This…

Quantum Physics · Physics 2026-02-13 Yudai Suzuki , Marek Gluza , Jeongrak Son , Bi Hong Tiang , Nelly H. Y. Ng , Zoë Holmes

The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the…

Quantum Physics · Physics 2022-03-28 Hiroyuki Tezuka , Kouhei Nakaji , Takahiko Satoh , Naoki Yamamoto

Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…

Quantum Physics · Physics 2018-03-08 Anirban Narayan Chowdhury , Yigit Subasi , Rolando D. Somma

Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…

Quantum Physics · Physics 2015-03-05 Apoorva Patel