Sublinear-Time Quantum Computation of the Diameter in CONGEST Networks

• URL: http://arxiv.org/abs/1804.02917v3
• Date: Thu, 11 Jan 2024 18:32:19 GMT
• Title: Sublinear-Time Quantum Computation of the Diameter in CONGEST Networks
• Authors: Fran\c{c}ois Le Gall and Fr\'ed\'eric Magniez
• Abstract summary: The computation of the diameter is one of the most central problems in distributed computation. We show a $tilde O(sqrtnD)$-round quantum distributed algorithm for exact diameter computation, where $D$ denotes the diameter. This shows a separation between the computational power of quantum and classical algorithms in the CONGEST model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The computation of the diameter is one of the most central problems in distributed computation. In the standard CONGEST model, in which two adjacent nodes can exchange $O(\log n)$ bits per round (here $n$ denotes the number of nodes of the network), it is known that exact computation of the diameter requires $\tilde \Omega(n)$ rounds, even in networks with constant diameter. In this paper we investigate quantum distributed algorithms for this problem in the quantum CONGEST model, where two adjacent nodes can exchange $O(\log n)$ quantum bits per round. Our main result is a $\tilde O(\sqrt{nD})$-round quantum distributed algorithm for exact diameter computation, where $D$ denotes the diameter. This shows a separation between the computational power of quantum and classical algorithms in the CONGEST model. We also show an unconditional lower bound $\tilde \Omega(\sqrt{n})$ on the round complexity of any quantum algorithm computing the diameter, and furthermore show a tight lower bound $\tilde \Omega(\sqrt{nD})$ for any distributed quantum algorithm in which each node can use only $\textrm{poly}(\log n)$ quantum bits of memory.

Related papers

• Rank Is All You Need: Estimating the Trace of Powers of Density Matrices [1.5133368155322298]
  Estimating the trace of powers of identical $k$ density matrices is a crucial subroutine for many applications. Inspired by the Newton-Girard method, we developed an algorithm that uses only $mathcalO(r)$ qubits and $mathcalO(r)$ multi-qubit gates.
  arXiv  Detail & Related papers  (2024-08-01T06:23:52Z)
• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model. We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Quantum algorithms for Hopcroft's problem [45.45456673484445]
  We study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. The classical complexity of this problem is well-studied, with the best known algorithm running in $O(n4/3)$ time. Our results are two different quantum algorithms with time complexity $widetilde O(n5/6)$.
  arXiv  Detail & Related papers  (2024-05-02T10:29:06Z)
• Mind the $\tilde{\mathcal{O}}$: Asymptotically Better, but Still Impractical, Quantum Distributed Algorithms [0.0]
  We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability. The algorithms achieve a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. An existing framework for using distributed version of Grover's search algorithm to accelerate triangle finding lies at the core of the speedup.
  arXiv  Detail & Related papers  (2023-04-06T02:18:52Z)
• Quantum Complexity of Weighted Diameter and Radius in CONGEST Networks [6.236743421605786]
  This paper studies the complexity of computing the weighted diameter and radius of a graph in the quantum CONGEST model. We present a quantum algorithm that $widetilde Oleft(minleftn9/10D3/10,nrightright)$, where $D$ denotes the unweighted diameter.
  arXiv  Detail & Related papers  (2022-06-06T17:43:27Z)
• A Framework for Distributed Quantum Queries in the CONGEST Model [0.0]
  We give a general framework for implementing quantum query algorithms in Quantum CONGEST. We generalize the protocol for the distributed Deutsch-Jozsa problem. We also give quantum speedups for the problems of cycle detection and computation.
  arXiv  Detail & Related papers  (2022-02-22T15:18:39Z)
• On quantum algorithms for the Schr\"odinger equation in the semi-classical regime [27.175719898694073]
  We consider Schr"odinger's equation in the semi-classical regime. Such a Schr"odinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics.
  arXiv  Detail & Related papers  (2021-12-25T20:01:54Z)
• Benchmarking Small-Scale Quantum Devices on Computing Graph Edit Distance [52.77024349608834]
  Graph Edit Distance (GED) measures the degree of (dis)similarity between two graphs in terms of the operations needed to make them identical. In this paper we present a comparative study of two quantum approaches to computing GED.
  arXiv  Detail & Related papers  (2021-11-19T12:35:26Z)
• Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis [24.555887999356646]
  The problem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth and size complexity remain open when ancillary qubits are available. In this paper, we study efficient constructions of quantum circuits with $m$ ancillary qubits that can prepare $psi_vrangle$ in depth. Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide range of parameter regime.
  arXiv  Detail & Related papers  (2021-08-13T09:47:11Z)
• Distributed Saddle-Point Problems Under Similarity [173.19083235638104]
  We show that a given suboptimality $epsilon0$ is achieved master/workers networks in $Omegabig. We then propose algorithms matching the lower bounds either types of networks (up to log-overs) We assess effectiveness of the proposed algorithms on a robust logistic regression problem.
  arXiv  Detail & Related papers  (2021-07-22T14:25:16Z)
• Low-depth Quantum State Preparation [3.540171881768714]
  A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=lceil logNrceil$-qubit state. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with $mathcal O(n2)$ circuit depth to encode any $N$ complex numbers.
  arXiv  Detail & Related papers  (2021-02-15T13:11:43Z)

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.