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 language | English (US) |
|---|---|
| Article number | 68 |
| Journal | Quantum Information Processing |
| Volume | 17 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 1 2018 |
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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 journal › Article
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TY - JOUR
T1 - Faster search by lackadaisical quantum walk
AU - Wong, Thomas
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s11128-018-1840-y
DO - 10.1007/s11128-018-1840-y
M3 - Article
VL - 17
JO - Quantum Information Processing
JF - Quantum Information Processing
SN - 1570-0755
IS - 3
M1 - 68
ER -