Faster search by lackadaisical quantum walk

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of O(1 / log N) in O(NlogN) steps, which with amplitude amplification yields an overall runtime of O(NlogN). We show that making the quantum walk lackadaisical or lazy by adding a self-loop of weight 4 / N to each vertex speeds up the search, causing the success probability to reach a constant near 1 in O(NlogN) steps, thus yielding an O(logN) improvement over the typical, loopless algorithm. This improved runtime matches the best known quantum algorithms for this search problem. Our results are based on numerical simulations since the algorithm is not an instance of the abstract search algorithm.

Original languageEnglish (US)
Article number68
JournalQuantum Information Processing
Volume17
Issue number3
DOIs
StatePublished - Mar 1 2018

Fingerprint

Quantum Walk
Quantum Algorithms
Search Problems
Vertex of a graph
Amplification
Search Algorithm
apexes
Discrete-time
Speedup
Grid
Numerical Simulation
grids
Computer simulation
Model
simulation

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modeling and Simulation
  • Electrical and Electronic Engineering

Cite this

Faster search by lackadaisical quantum walk. / Wong, Thomas.

In: Quantum Information Processing, Vol. 17, No. 3, 68, 01.03.2018.

Research output: Contribution to journalArticle

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