QAOA with fewer qubits: a coupling framework to solve larger-scale Max-Cut problem

• URL: http://arxiv.org/abs/2307.15260v1
• Date: Fri, 28 Jul 2023 02:06:42 GMT
• Title: QAOA with fewer qubits: a coupling framework to solve larger-scale Max-Cut problem
• Authors: Yiren Lu, Guojing Tian, Xiaoming Sun
• Abstract summary: We propose a framework for designing QAOA circuits to solve larger-scale Max-Cut problem. We derive an approximation guarantee theoretically, assuming the approximation ratio of the classical algorithm and QAOA. Our framework only consumes $18$ qubits and $0.9950$ approximation ratio on average.
• Score: 6.783232060611114
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 solve it. However, as the size of the problem increases, the number of qubits required will become larger. With the aim of saving qubits, we propose a coupling framework for designing QAOA circuits to solve larger-scale Max-Cut problem. This framework relies on a classical algorithm that approximately solves a certain variant of Max-Cut, and we derive an approximation guarantee theoretically, assuming the approximation ratio of the classical algorithm and QAOA. Furthermore we design a heuristic approach that fits in our framework and perform sufficient numerical experiments, where we solve Max-Cut on various $24$-vertex Erd\H{o}s-R\'enyi graphs. Our framework only consumes $18$ qubits and achieves $0.9950$ approximation ratio on average, which outperforms the previous methods showing $0.9778$ (quantum algorithm using the same number of qubits) and $0.9643$ (classical algorithm). The experimental results indicate our well-designed quantum-classical coupling framework gives satisfactory approximation ratio while reduces the qubit cost, which sheds light on more potential computing power of NISQ devices.

Related papers

• A Multilevel Approach For Solving Large-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization [3.3493770627144004]
  We experimentally test how existing quantum processing units (QPUs) perform as subsolvers within a multilevel strategy. We find approximate solutions to $10$ instances of fully connected $82$-qubit Sherrington-Kirkpatrick graphs. We observe that quantum optimization results are competitive regarding the quality of solutions compared to classicals.
  arXiv  Detail & Related papers  (2024-08-14T20:06:32Z)
• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• An Analysis of Quantum Annealing Algorithms for Solving the Maximum Clique Problem [49.1574468325115]
  We analyse the ability of quantum D-Wave annealers to find the maximum clique on a graph, expressed as a QUBO problem. We propose a decomposition algorithm for the complementary maximum independent set problem, and a graph generation algorithm to control the number of nodes, the number of cliques, the density, the connectivity indices and the ratio of the solution size to the number of other nodes.
  arXiv  Detail & Related papers  (2024-06-11T04:40:05Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Extending relax-and-round combinatorial optimization solvers with quantum correlations [0.0]
  We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $pgeq 1$ layers. We show for many problems, including Sherrington-Kirk glasses, that at $p=1$, it is as accurate as its classical counterpart. We pave the way for an overarching quantum relax-and-round framework with performance on par with some of the best classical algorithms.
  arXiv  Detail & Related papers  (2023-07-11T22:02:01Z)
• NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization [0.0]
  We present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms.
  arXiv  Detail & Related papers  (2023-05-23T16:17:57Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines [81.4597482536073]
  Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution. We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
  arXiv  Detail & Related papers  (2022-05-24T03:49:10Z)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• Large-scale Quantum Approximate Optimization via Divide-and-Conquer [8.733794945008562]
  We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the challenges for graph maximum cut (MaxCut) problem. DC-QAOA achieves 97.14% approximation ratio (20.32% higher than classical counterpart) It also reduces the time complexity of conventional QAOA from exponential to quadratic.
  arXiv  Detail & Related papers  (2021-02-26T03:10:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.