Related papers: Quantum Speedup for Some Geometric 3SUM-Hard Probl…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…
In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains…
In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
We consider the Exact-Weight-H problem of finding a (not necessarily induced) subgraph H of weight 0 in an edge-weighted graph G. We show that for every H, the complexity of this problem is strongly related to that of the infamous k-Sum…
Simon's problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the…
Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
A recent work of Schmidhuber et al (QIP, SODA, & Phys. Rev. X 2025) exhibited a quantum algorithm for the noisy planted $k$XOR problem running quartically faster than all known classical algorithms. In this work, we design a new classical…
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced…
The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…