Related papers: An improved Quantum Max Cut approximation via matc…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
Quantum Max Cut (QMC), also known as the quantum anti-ferromagnetic Heisenberg model, is a QMA-complete problem relevant to quantum many-body physics and computer science. Semidefinite programming relaxations have been fruitful in designing…
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary $k$-local Hamiltonian acting on $n$ qubits. We first consider the setting where a good ``guiding state'' is available, which is the main…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
Maximum cut (Max-Cut) problem is one of the most important combinatorial optimization problems because of its various applications in real life, and recently Quantum Approximate Optimization Algorithm (QAOA) has been widely employed to…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
In this note, we describe a $\alpha_{GW} + \tilde{\Omega}(1/d^2)$-factor approximation algorithm for Max-Cut on weighted graphs of degree $\leq d$. Here, $\alpha_{GW}\approx 0.878$ is the worst-case approximation ratio of the…
We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary…
In this work, we develop a framework aiming at designing quantum algorithms for combinatorial optimization problems while providing theoretical guarantees on their approximation ratios. The principal innovative aspect of our work is the…
The EPR Hamiltonian is a family of 2-local quantum Hamiltonians introduced by King (arXiv:2209.02589). We introduce a polynomial time $\frac{1+\sqrt{5}}{4}\approx 0.809$-approximation algorithm for the problem of computing the ground energy…
We investigate the space complexity of two graph streaming problems: Max-Cut and its quantum analogue, Quantum Max-Cut. Previous work by Kapralov and Krachun [STOC `19] resolved the classical complexity of the \emph{classical} problem,…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
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…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
The Quantum approximate optimization algorithm (QAOA) is a leading hybrid classical-quantum algorithm for solving complex combinatorial optimization problems. QAOA-in-QAOA (QAOA^2) uses a divide-and-conquer heuristic to solve large-scale…
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…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We present herein a new approach based on the simultaneous application of the deep learning and statistical physics methods to solve the combinatorial optimization problems. The recent modern advanced techniques, such as an artificial…