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Quantum Information Processing

Faster search by lackadaisical quantum walk

  • 01-03-2018
Published in:
Author
Thomas G. Wong
Published in
Quantum Information Processing | Issue 3/2018

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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 \(O(\sqrt{N \log N})\) steps, which with amplitude amplification yields an overall runtime of \(O(\sqrt{N} \log N)\). 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 \(O(\sqrt{N \log N})\) steps, thus yielding an \(O(\sqrt{\log N})\) 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.

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previous article Quantum pattern recognition with multi-neuron interactions
next article Open quantum random walk in terms of quantum Bernoulli noise
Title
Faster search by lackadaisical quantum walk
Author
Thomas G. Wong
Publication date
01-03-2018
Publisher
Springer US
Published in
Quantum Information Processing / Issue 3/2018
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-018-1840-y
This content is only visible if you are logged in and have the appropriate permissions.

Other articles of this Issue 3/2018

Multi-dimensional quantum state sharing based on quantum Fourier transform

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

Quantum metrology of phase for accelerated two-level atom coupled with electromagnetic field with and without boundary

Quantum pattern recognition with multi-neuron interactions

Open quantum random walk in terms of quantum Bernoulli noise

Security of BB84 with weak randomness and imperfect qubit encoding