
Quantum Walk Sampling by Growing Seed Sets
This work describes a new algorithm for creating a superposition over th...
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Random walks on graphs: new bounds on hitting, meeting, coalescing and returning
We prove new results on lazy random walks on finite graphs. To start, we...
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Detecting quantum speedup by quantum walk with convolutional neural networks
Quantum walks are at the heart of modern quantum technologies. They allo...
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Time Dependent Biased Random Walks
We study the biased random walk where at each step of a random walk a "c...
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Improved Quantum Information Set Decoding
In this paper we present quantum information set decoding (ISD) algorith...
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Efficient Computation of Optimal Temporal Walks under WaitingTime Constraints
Node connectivity plays a central role in temporal network analysis. We ...
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Fast deterministic tourist walk for texture analysis
Deterministic tourist walk (DTW) has attracted increasing interest in co...
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A Unified Framework of Quantum Walk Search
The main results on quantum walk search are scattered over different, incomparable frameworks, most notably the hitting time framework, originally by Szegedy, the electric network framework by Belovs, and the MNRS framework by Magniez, Nayak, Roland and Santha. As a result, a number of pieces are currently missing. For instance, the electric network framework allows quantum walks to start from an arbitrary initial state, but it only detects marked elements. In recent work by Ambainis et al., this problem was resolved for the more restricted hitting time framework, in which quantum walks must start from the stationary distribution. We present a new quantum walk search framework that unifies and strengthens these frameworks. This leads to a number of new results. For instance, the new framework not only detects, but finds marked elements in the electric network setting. The new framework also allows one to interpolate between the hitting time framework, which minimizes the number of walk steps, and the MNRS framework, which minimizes the number of times elements are checked for being marked. This allows for a more natural tradeoff between resources. Whereas the original frameworks only rely on quantum walks and phase estimation, our new algorithm makes use of a technique called quantum fastforwarding, similar to the recent results by Ambainis et al. As a final result we show how in certain cases we can simplify this more involved algorithm to merely applying the quantum walk operator some number of times. This answers an open question of Ambainis et al.
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