Related papers: Low-depth Clifford circuits approximately solve Ma…
Quantum Approximate Optimization Algorithm (QAOA) is studied primarily to find approximate solutions to combinatorial optimization problems. For a graph with $n$ vertices and $m$ edges, a depth $p$ QAOA for the Max-cut problem requires…
We present an algorithm for building a circuit that approximates single qubit unitaries with precision {\epsilon} using O(log(1/{\epsilon})) Clifford and T gates and employing up to two ancillary qubits. The algorithm for computing our…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
We show a linear-size reduction from gap Max-2-Lin(2) (a generalization of the gap $\mathrm{Max}$-$\mathrm{Cut}$ problem) to $\gamma\text{-}\mathrm{CVP}_p$ for $\gamma = \mathrm{O}(1)$ and finite $p\geq 1$, as well as a no-go theorem…
The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical…
We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations…
Clifford group lies at the core of quantum computation -- it underlies quantum error correction, its elements can be used to perform magic state distillation and they form randomized benchmarking protocols, Clifford group is used to study…
In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs.…
We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
A promising approach to the practical application of the Quantum Approximate Optimization Algorithm (QAOA) is finding QAOA parameters classically in simulation and sampling the solutions from QAOA with optimized parameters on a quantum…
The Sparsest Cut is a fundamental optimization problem that has been extensively studied. For planar inputs the problem is in $P$ and can be solved in $\tilde{O}(n^3)$ time if all vertex weights are $1$. Despite a significant amount of…
Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…
Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that the approximation ratio of the Goemans-Williamson algorithm is optimal assuming…
We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most $\smash{\phi n^{O(\sqrt{\log n})}}$, where $n$ is the number of nodes in the graph and $\phi$ is a parameter that measures the magnitude of…
We describe a new approximation algorithm for Max Cut. Our algorithm runs in $\tilde O(n^2)$ time, where $n$ is the number of vertices, and achieves an approximation ratio of $.531$. On instances in which an optimal solution cuts a…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…
We consider the maximum cut and maximum independent set problems on random regular graphs in the infinite-size limit, and calculate the energy densities achieved by QAOA for high degrees up to $d=100$. Such an analysis is possible because…