Related papers: Towards An Implementation of the Subset-sum Proble…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Today, people are looking forward to get an awesome computational power. This kind of desire can be answered by quantum computing. By adopting quantum mechanics theory, it can generate a very fast computation result. As known, quantum…
We show that the algorithmic complexity of any classical algorithm written in a Turing-complete programming language polynomially bounds the number of quantum bits that are required to run and even symbolically execute the algorithm on a…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
This letter presents a novel \textit{quantum algorithm} for signal denoising, which performs a thresholding in the frequency domain through amplitude amplification and using an adaptive threshold determined by local mean values. The…
In the classical Subset Sum problem we are given a set $X$ and a target $t$, and the task is to decide whether there exists a subset of $X$ which sums to $t$. A recent line of research has resulted in $\tilde{O}(t)$-time algorithms, which…
Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the…
We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…
We present an efficient quantum algorithm for estimating Gauss sums over finite fields and finite rings. This is a natural problem as the description of a Gauss sum can be done without reference to a black box function. With a reduction…
Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that…
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
Given a multiset $S$ of $n$ positive integers and a target integer $t$, the Subset Sum problem asks to determine whether there exists a subset of $S$ that sums up to $t$. The current best deterministic algorithm, by Koiliaris and Xu…