Deterministic Grover search with a restricted oracle

• URL: http://arxiv.org/abs/2201.00091v3
• Date: Mon, 14 Nov 2022 16:02:51 GMT
• Title: Deterministic Grover search with a restricted oracle
• Authors: Tanay Roy, Liang Jiang, David I. Schuster
• Abstract summary: Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms. We present a modified version to return the correct result with certainty without having user control over the quantum search oracle.
• Score: 2.976027966501599
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 oracle query. The D2p protocol achieves a 100% success rate in no more than one additional iteration compared to the optimal number of steps in the original Grover's search enabling the same quadratic speed up. We also provide a visualization using the Bloch sphere for enhanced geometric intuition.

Related papers

• Near-deterministic quantum search algorithm without phase control [10.754825115553086]
  Grover's algorithm can find the target item with certainty only if searching one out of four. We propose a near-deterministic quantum search algorithm without the phase control.
  arXiv  Detail & Related papers  (2024-07-15T14:20:47Z)
• Efficient Implementation of a Quantum Search Algorithm for Arbitrary N [0.0]
  This paper presents an enhancement to Grover's search algorithm for instances where $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, we demonstrate that a considerable reduction in the number of oracle calls (and Grover's iterations) can be achieved in many cases.
  arXiv  Detail & Related papers  (2024-06-19T19:16:40Z)
• Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations [49.1574468325115]
  Sponge hashing is a widely used class of cryptographic hash algorithms. Intrepid permutations have so far remained a fundamental open problem. We show that finding zero-pairs in a random $2n$-bit permutation requires at least $Omega (2n/2)$ many queries.
  arXiv  Detail & Related papers  (2024-03-07T18:46:58Z)
• Generalized Hybrid Search and Applications to Blockchain and Hash Function Security [50.16790546184646]
  We first examine the hardness of solving various search problems by hybrid quantum-classical strategies. We then construct a hybrid quantum-classical search algorithm and analyze its success probability.
  arXiv  Detail & Related papers  (2023-11-07T04:59:02Z)
• Quantum Search Approaches to Sampling-Based Motion Planning [0.0]
  We present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections.
  arXiv  Detail & Related papers  (2023-04-10T19:12:25Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• 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 Search with Prior Knowledge [15.384459603233978]
  We propose a new generalization of Grover's search algorithm which performs better than the standard Grover algorithm in average under this setting. We prove that our new algorithm achieves the optimal expected success probability of finding the solution if the number of queries is fixed.
  arXiv  Detail & Related papers  (2020-09-18T09:50:33Z)
• Learning to Accelerate Heuristic Searching for Large-Scale Maximum Weighted b-Matching Problems in Online Advertising [51.97494906131859]
  Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. Existing exact and approximate algorithms usually fail in such settings due to either requiring intolerable running time or too much computation resource. We propose textttNeuSearcher which leverages the knowledge learned from previously instances to solve new problem instances.
  arXiv  Detail & Related papers  (2020-05-09T02:48:23Z)
• Multi-layer quantum search and inclusion of NP into BQP [6.362434591714693]
  We present a multi-layer quantum search method that generates an exponential speedup of the standard Grover's algorithm. Our results show that the speedup of quantum circuits is ubiquitous, and Grover's search is much more powerful than that has been demonstrated.
  arXiv  Detail & Related papers  (2020-04-23T17:44:51Z)

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.