Related papers: A quantum algorithm for the dihedral hidden subgro…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based…
We consider low-space algorithms for the classic Element Distinctness problem: given an array of $n$ input integers with $O(\log n)$ bit-length, decide whether or not all elements are pairwise distinct. Beame, Clifford, and Machmouchi [FOCS…
An $s{\operatorname{-}}t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices $s$ and $t$. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from $s$…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
We present an algorithm to find an {\it Euclidean Shortest Path} from a source vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\Re^2$. Our algorithm takes $O(T+m(\lg{m})(\lg{n}))$ time and $O(n)$ space. Here, $O(T)$ is the…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a…
We present an $\mathcal{O}^\star(2^{0.5n})$ time and $\mathcal{O}^\star(2^{0.249999n})$ space randomized algorithm for solving worst-case Subset Sum instances with $n$ integers. This is the first improvement over the long-standing…
Recent results suggest that quantum computers possess the potential to speed up nonconvex optimization problems. However, a crucial factor for the implementation of quantum optimization algorithms is their robustness against experimental…
Grover's algorithm is a well-known unstructured quantum search algorithm run on quantum computers. It constructs an oracle and calls the oracle O($\sqrt N$) times to locate specific data out of N unsorted data. This represents a quadratic…
The Single-Source Shortest Path (SSSP) problem is a cornerstone of computer science with vast applications, for which Dijkstra's algorithm has long been the classical baseline. While various quantum algorithms have been proposed, their…
The problem of space-efficient depth-first search (DFS) is reconsidered. A particularly simple and fast algorithm is presented that, on a directed or undirected input graph $G=(V,E)$ with $n$ vertices and $m$ edges, carries out a DFS in…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of…
We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that…
The computation of \(\operatorname{tr}(AB)\) is essential in quantum science and artificial intelligence, yet classical methods for \( d \)-dimensional matrices \( A \) and \( B \) require \( O(d^2) \) complexity, which becomes infeasible…
Kernel-based support vector machines (SVMs) are supervised machine learning algorithms for classification and regression problems. We introduce a method to train SVMs on a D-Wave 2000Q quantum annealer and study its performance in…
Noisy intermediate-scale quantum cryptanalysis focuses on the capability of near-term quantum devices to solve the mathematical problems underlying cryptography, and serves as a cornerstone for the design of post-quantum cryptographic…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum…