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Lattice-based cryptography is one of the leading proposals for post-quantum cryptography. The Shortest Vector Problem (SVP) is arguably the most important problem for the cryptanalysis of latticebased cryptography, and many lattice-based schemes have security claims based on its hardness. The best quantum algorithm for the SVP is due to Laarhoven [Laa16] and runs in (heuristic) time 2 0.2653d+o(d) . In this article, we present an improvement over Laarhoven's result and present an algorithm that has a (heuristic) running time of 2 0.2570d+o(d) where d is the lattice dimension. We also present time-memory trade-offs where we quantify the amount of quantum memory and quantum random access memory of our algorithm. The core idea is to replace Grover's algorithm used in [Laa16] in a key part of the sieving algorithm by a quantum random walk in which we add a layer of local sensitive filtering.

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