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Quadratic speedup for spatial search by continuous-time quantum walk
Continuous-time quantum walks provide a natural framework to tackle the fundamental
problem of finding a node among a set of marked nodes in a graph, known as spatial …
problem of finding a node among a set of marked nodes in a graph, known as spatial …
Quantum walk speedup of backtracking algorithms
We describe a general method to obtain quantum speedups of classical algorithms which
are based on the technique of backtracking, a standard approach for solving constraint …
are based on the technique of backtracking, a standard approach for solving constraint …
Deterministic search on star graphs via quantum walks
We propose a novel algorithm for quantum spatial search on a star graph using interleaved
continuous-time quantum walks and marking oracle queries. Initializing the system in the …
continuous-time quantum walks and marking oracle queries. Initializing the system in the …
Implementing any linear combination of unitaries on intermediate-term quantum computers
We develop three new methods to implement any Linear Combination of Unitaries (LCU), a
powerful quantum algorithmic tool with diverse applications. While the standard LCU …
powerful quantum algorithmic tool with diverse applications. While the standard LCU …
Quadratic speedup for finding marked vertices by quantum walks
A quantum walk algorithm can detect the presence of a marked vertex on a graph
quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004) …
quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004) …
Quantum algorithm design: techniques and applications
In recent years, rapid developments of quantum computer are witnessed in both the
hardware and the algorithm domains, making it necessary to have an updated review of …
hardware and the algorithm domains, making it necessary to have an updated review of …
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 …
frameworks, most notably the hitting time framework, originally by Szegedy, the electric …
Quantum singular value transformation & its algorithmic applications
A Gilyén - 2019 - eprints.illc.uva.nl
In this dissertation we study how efficiently quantum computers can solve various problems,
and how large speedups can be achieved compared to classical computers. In particular we …
and how large speedups can be achieved compared to classical computers. In particular we …
Efficient constructions for simulating multi controlled quantum gates
Abstract Multi Controlled Gates, with Multi Controlled Toffoli as primary example are a
building block for a lot of complex quantum algorithms in the domains of discrete arithmetic …
building block for a lot of complex quantum algorithms in the domains of discrete arithmetic …
Small quantum computers and large classical data sets
We introduce hybrid classical-quantum algorithms for problems involving a large classical
data set X and a space of models Y such that a quantum computer has superposition access …
data set X and a space of models Y such that a quantum computer has superposition access …