Related papers: Classical algorithms for Forrelation
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
Let a classical algorithm be determined by sequential applications of a black box performing one step of this algorithm. If we consider this black box as an oracle which gives a value F(a) for any query a, we can compute T sequential…
Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum…
We design quantum algorithms for maximum matching. Working in the query model, in both adjacency matrix and adjacency list settings, we improve on the best known algorithms for general graphs, matching previously obtained results for…
Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
This research explores the integration of the Quantum Approximate Optimization Algorithm (QAOA) into Hybrid Quantum-HPC systems for solving the Max-Cut problem, comparing its performance with classical algorithms like brute-force search and…
With the rapid advancement of quantum computing, Quantum Approximate Optimization Algorithm (QAOA) is considered as a promising candidate to demonstrate quantum supremacy, which exponentially solves a class of Quadratic Unconstrained Binary…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…
In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses $O(2.616^n)$ time and…
The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into…
Simon's problem plays an important role in the history of quantum algorithms, as it inspired Shor to discover the celebrated quantum algorithm solving integer factorization in polynomial time. Besides, the quantum algorithm for Simon's…
Given the success of deep learning in classical machine learning, quantum algorithms for traditional neural network architectures may provide one of the most promising settings for quantum machine learning. Considering a fully-connected…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising algorithm for solving combinatorial optimization problems (COPs), with performance governed by variational parameters $\{\gamma_i, \beta_i\}_{i=0}^{p-1}$. While most prior…
Span program is a linear-algebraic model of computation which can be used to design quantum algorithms. For any Boolean function there exists a span program that leads to a quantum algorithm with optimal quantum query complexity. In…
We propose a surrogate-based method for optimizing parameterized quantum circuits which is designed to operate with few calls to a quantum computer. We employ a computationally inexpensive classical surrogate to approximate the cost…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…