Grover's search algorithm for $n$ qubits with optimal number of iterations

• URL: http://arxiv.org/abs/2011.04051v2
• Date: Sun, 22 Nov 2020 07:59:09 GMT
• Title: Grover's search algorithm for $n$ qubits with optimal number of iterations
• Authors: Simanraj Sadana
• Abstract summary: Grover's search algorithm depends on the number of iterations of the composite operation of the oracle followed by Grover's diffusion operation. General scheme for the construction of $n$-qubit Grover's search algorithm with $1 leq M leq N$ target states is presented.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 operation. Although the required number of iterations scales as $\mathcal{O}(\sqrt{N})$ for large $N$, the asymptote is not a good indicator of the optimal number of iterations when $\sqrt{M/N}$ is not small. A scheme for the determination of the exact number of iterations, subject to a threshold set for the success probability of the search (probability of detecting the target state(s)), is crucial for the efficacy of the algorithm. In this work, a general scheme for the construction of $n$-qubit Grover's search algorithm with $1 \leq M \leq N$ target states is presented, along with the procedure to find the optimal number of iterations for a successful search. It is also shown that for given $N$ and $M$, there is an upper-bound on the success probability of the algorithm.

Related papers

• A Bi-directional Quantum Search Algorithm [30.62704006898929]
  This paper combines Partial Grover's search algorithm and Bi-directional Search to create a fast Grover's quantum search algorithm. We incorporated a bi-directional search tactic with a partial Grover search, starting from an initial state and a single marked state in parallel. The proposed BDGS algorithm is benchmarked against the state-of-the-art Depth-First Grover's Search (DFGS) and generic Grover's Search (GS) implementations for $2$ to $20$ qubits.
  arXiv  Detail & Related papers  (2024-04-24T03:11:10Z)
• Accelerated quantum search using partial oracles and Grover's algorithm [0.0]
  Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. We explore the idea of associating a separate oracle with each bit of the matching condition, obtaining multiple partial oracle functions which can be tested independently. The algorithm is validated against the simplest kind of search scenario, where the incoming index bits are scrambled using a permutation operation.
  arXiv  Detail & Related papers  (2024-03-19T11:32:02Z)
• A Scalable Algorithm for Individually Fair K-means Clustering [77.93955971520549]
  We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. A clustering is then called individually fair if it has centers within distance $delta(x)$ of $x$ for each $xin P$. We show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.
  arXiv  Detail & Related papers  (2024-02-09T19:01:48Z)
• Algoritmo de Contagem Qu\^antico Aplicado ao Grafo Bipartido Completo [0.0]
  Grover's algorithm is capable of finding $k$ elements in an unordered database with $N$ elements using $O(sqrtN/k)$ steps. This work tackles the problem of using the quantum counting algorithm for estimating the value $k$ of marked elements in other graphs.
  arXiv  Detail & Related papers  (2023-12-05T21:15:09Z)
• Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end [114.3957763744719]
  We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems. We show that the algorithm finds the optimal solution in time $O*(2(0.5-c)n)$ for an $n$-independent constant $c$. We also show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case.
  arXiv  Detail & Related papers  (2022-12-03T02:45:23Z)
• On the Sample Complexity of Representation Learning in Multi-task Bandits with Global and Local structure [77.60508571062958]
  We investigate the sample complexity of learning the optimal arm for multi-task bandit problems. Arms consist of two components: one that is shared across tasks (that we call representation) and one that is task-specific (that we call predictor) We devise an algorithm OSRL-SC whose sample complexity approaches the lower bound, and scales at most as $H(Glog(delta_G)+ Xlog(delta_H))$, with $X,G,H$ being, respectively, the number of tasks, representations and predictors.
  arXiv  Detail & Related papers  (2022-11-28T08:40:12Z)
• Depth-First Grover Search Algorithm on Hybrid Quantum-Classical Computer [2.487445341407889]
  Combination of Depth-First Search and Grover's algorithm to generate Depth-First Grover Search(DFGS) DFGS handles multi-solution searching problems on unstructured databases with an unknown number of solutions. New algorithm attains an average complexity of $mathcalO(msqrtN)$ which performs as efficient as a normal Grover Search.
  arXiv  Detail & Related papers  (2022-10-10T13:10:28Z)
• Bayesian Optimistic Optimisation with Exponentially Decaying Regret [58.02542541410322]
  The current practical BO algorithms have regret bounds ranging from $mathcalO(fraclogNsqrtN)$ to $mathcal O(e-sqrtN)$, where $N$ is the number of evaluations. This paper explores the possibility of improving the regret bound in the noiseless setting by intertwining concepts from BO and tree-based optimistic optimisation. We propose the BOO algorithm, a first practical approach which can achieve an exponential regret bound with order $mathcal O(N-sqrt
  arXiv  Detail & Related papers  (2021-05-10T13:07:44Z)
• Towards Optimally Efficient Tree Search with Deep Learning [76.64632985696237]
  This paper investigates the classical integer least-squares problem which estimates signals integer from linear models. The problem is NP-hard and often arises in diverse applications such as signal processing, bioinformatics, communications and machine learning. We propose a general hyper-accelerated tree search (HATS) algorithm by employing a deep neural network to estimate the optimal estimation for the underlying simplified memory-bounded A* algorithm.
  arXiv  Detail & Related papers  (2021-01-07T08:00:02Z)
• Quantum Approximate Counting with Nonadaptive Grover Iterations [1.14219428942199]
  In the quantum setting, Approximate Counting can be done with $Oleft(sqrtN/epsilon, sqrtN/K/epsilonright)$ queries. We show that algorithms using only nonadaptive Grover iterations can achieve $Oleft(sqrtN/epsilonright)$ query complexity, which is tight.
  arXiv  Detail & Related papers  (2020-10-09T04:48:14Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)

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.