Description of the Grover algorithm based on geometric considerations
- URL: http://arxiv.org/abs/2210.16809v2
- Date: Sat, 5 Nov 2022 17:47:13 GMT
- Title: Description of the Grover algorithm based on geometric considerations
- Authors: G\'erard Fleury, Philippe Lacomme
- Abstract summary: Grover algorithm allows amplification of quantum states previously tagged by an Oracle.
This article provides a description of the amplitude amplification quantum algorithm mechanism in a very short computational way.
- Score: 2.680349265843603
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper concerns the Grover algorithm that permits to make amplification
of quantum states previously tagged by an Oracle. Grover's algorithm allows
searches in an unstructure database of n entries finding a marked element with
a quadratic speedup. The algorithm requires a predefined number of runs to
succeed with probability close to one.This article provides a description of
the amplitude amplification quantum algorithm mechanism in a very short
computational way, based on tensor products and provides a geometric
presentation of the successive system states. All the basis changes are fully
described to provide an alternative to the wide spread Grover description based
only on matrices and complex tensor computation. Our experiments encompass
numerical evaluations of circuit using the Qiskit library of IBM that meet the
theoretical considerations
Related papers
- Generalized quantum Arimoto-Blahut algorithm and its application to
quantum information bottleneck [55.22418739014892]
We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al.
We apply our algorithm to the quantum information bottleneck with three quantum systems.
Our numerical analysis shows that our algorithm is better than their algorithm.
arXiv Detail & Related papers (2023-11-19T00:06:11Z) - Opening the Black Box Inside Grover's Algorithm [0.0]
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers.
We construct a quantum-inspired algorithm, executable on a classical computer, that performs Grover's task in a linear number of calls to (simulations of) the oracle.
arXiv Detail & Related papers (2023-03-20T17:56:20Z) - Exploring the role of parameters in variational quantum algorithms [59.20947681019466]
We introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra.
A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture.
arXiv Detail & Related papers (2022-09-28T20:24:53Z) - Compilation of algorithm-specific graph states for quantum circuits [55.90903601048249]
We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages.
The computation can then be implemented using a series of non-Pauli measurements on this graph state.
arXiv Detail & Related papers (2022-09-15T14:52:31Z) - An adiabatic oracle for Grover's algorithm [3.800391908440439]
Grover's search algorithm was originally proposed for circuit-based quantum computers.
We propose a realization of Grover's oracle for a large class of searching problems.
arXiv Detail & Related papers (2022-07-12T16:49:07Z) - The CLRS Algorithmic Reasoning Benchmark [28.789225199559834]
Learning representations of algorithms is an emerging area of machine learning, seeking to bridge concepts from neural networks with classical algorithms.
We propose the CLRS Algorithmic Reasoning Benchmark, covering classical algorithms from the Introduction to Algorithms textbook.
Our benchmark spans a variety of algorithmic reasoning procedures, including sorting, searching, dynamic programming, graph algorithms, string algorithms and geometric algorithms.
arXiv Detail & Related papers (2022-05-31T09:56:44Z) - Grover search revisited; application to image pattern matching [0.8367938108534343]
We propose a quantum algorithm that approximately executes the entire Grover database search or pattern matching algorithm.
The key idea is to use the recently proposed approximate amplitude encoding method on a shallow quantum circuit.
arXiv Detail & Related papers (2021-08-24T17:30:41Z) - Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task.
Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate.
The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
arXiv Detail & Related papers (2021-06-06T13:15:25Z) - Efficient Algorithms for Causal Order Discovery in Quantum Networks [44.356294905844834]
Given black-box access to the input and output systems, we develop the first efficient quantum causal order discovery algorithm.
We model the causal order with quantum combs, and our algorithms output the order of inputs and outputs that the given process is compatible with.
Our algorithms will provide efficient ways to detect and optimize available transmission paths in quantum communication networks.
arXiv Detail & Related papers (2020-12-03T07:12:08Z) - ACSS-q: Algorithmic complexity for short strings via quantum accelerated
approach [1.4873907857806357]
We present a quantum circuit for estimating algorithmic complexity using the coding theorem method.
As a use-case, an application framework for protein-protein interaction based on algorithmic complexity is proposed.
arXiv Detail & Related papers (2020-09-18T14:41:41Z) - Number Partitioning with Grover's Algorithm in Central Spin Systems [0.0]
We propose a Grover search for solutions to a class of NP-complete decision problems known as subset sum problems.
Each problem instance is encoded in the couplings of a set of qubits to a central spin or boson, which enables a realization of the oracle without knowledge of the solution.
arXiv Detail & Related papers (2020-09-11T17:31:39Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.