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Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms…
Developing hardware-efficient implementations of quantum algorithms is crucial in the NISQ era to achieve practical quantum advantage. Here, we construct a generic quantum solver for NP problems based on Grover's search algorithm,…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using…
Quantum algorithm is a key tool for cryptanalysis. At present, people are committed to building powerful quantum algorithms and tapping the potential of quantum algorithms, so as to further analyze the security of cryptographic algorithms…
An important and usual problem is to search all states we want from a database with a large number of states. In such, recall is vital. Grover's original quantum search algorithm has been generalized to the case of multiple solutions, but…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by…
Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is…
Searching for marked items from an unsorted database is an important scientific problem and a benchmark for computing devices as well. Using a 7-qubit liquid NMR quantum computer, we have demonstrated successfully an hybrid quantum fetching…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
The steadily growing research interest in quantum computing - together with the accompanying technological advances in the realization of quantum hardware - fuels the development of meaningful real-world applications, as well as…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the…
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…
By harnessing the superposition and entanglement of physical states, quantum computers could outperform their classical counterparts in solving problems of technological impact, such as factoring large numbers and searching databases. A…