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 Quantum Genetic Algorithm Framework for the MaxCut Problem [49.59986385400411]
The proposed method introduces a Quantum Genetic Algorithm (QGA) using a Grover-based evolutionary framework and divide-and-conquer principles.
On complete graphs, the proposed method consistently achieves the true optimal MaxCut values, outperforming the Semidefinite Programming (SDP) approach.
On ErdHos-R'enyi random graphs, the QGA demonstrates competitive performance, achieving median solutions within 92-96% of the SDP results.
arXiv Detail & Related papers (2025-01-02T05:06:16Z) - 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) - 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) - 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) - A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization [0.0]
We study the performance scaling of three quantum algorithms for optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the D"urr-Hoyer algorithm for quantum minimum finding (DH-QMF)
For each algorithm, we analyze its performance in solving two types of MaxCut problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from $-1$ to $1$; and randomly generated Sherrington-Kirkpatrick (SK) spin glass instances.
arXiv Detail & Related papers (2021-05-07T22:35:02Z) - 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.