
Exponentialtime quantum algorithms for graph coloring problems
The fastest known classical algorithm deciding the kcolorability of nv...
read it

Lower Bounds on the Running Time of TwoWay Quantum Finite Automata and SublogarithmicSpace Quantum Turing Machines
The twoway finite automaton with quantum and classical states (2QCFA), ...
read it

Quantum Radon Transform and Its Application
This paper extends the Radon transform, a classical image processing too...
read it

qmeans: A quantum algorithm for unsupervised machine learning
Quantum machine learning is one of the most promising applications of a ...
read it

Quantum classification of the MNIST dataset via Slow Feature Analysis
Quantum machine learning carries the promise to revolutionize informatio...
read it

An efficient high dimensional quantum Schur transform
The Schur transform is a unitary operator that block diagonalizes the ac...
read it

Revisiting Shor's quantum algorithm for computing general discrete logarithms
We heuristically demonstrate that Shor's algorithm for computing general...
read it
Quantum LegendreFenchel Transform
We present a quantum algorithm to compute the discrete LegendreFenchel transform. Given access to a convex function evaluated at N points, the algorithm outputs a quantummechanical representation of its corresponding discrete LegendreFenchel transform evaluated at K points in the transformed space. For a fixed regular discretizaton of the dual space the expected running time scales as O(√(κ) polylog(N,K)), where κ is the condition number of the function. If the discretization of the dual space is chosen adaptively with K equal to N, the running time reduces to O(polylog(N)). We explain how to extend the presented algorithm to the multivariate setting and prove lower bounds for the query complexity, showing that our quantum algorithm is optimal up to polylogarithmic factors. For certain scenarios, such as computing an expectation value of an efficientlycomputable observable associated with a LegendreFencheltransformed convex function, the quantum algorithm provides an exponential speedup compared to any classical algorithm.
READ FULL TEXT
Comments
There are no comments yet.