Empirical performance bounds for quantum approximate optimization
- URL: http://arxiv.org/abs/2102.06813v1
- Date: Fri, 12 Feb 2021 23:12:09 GMT
- Title: Empirical performance bounds for quantum approximate optimization
- Authors: Phillip C. Lotshaw, Travis S. Humble, Rebekah Herrman, James
Ostrowski, George Siopsis
- Abstract summary: Quantifying performance bounds provides insight into when QAOA may be viable for solving real-world applications.
We find QAOA exceeds the Goemans-Williamson approximation ratio bound for most graphs.
The resulting data set is presented as a benchmark for establishing empirical bounds on QAOA performance.
- Score: 0.27998963147546135
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The quantum approximate optimization algorithm (QAOA) is a variational method
for noisy, intermediate-scale quantum computers to solve combinatorial
optimization problems. Quantifying performance bounds with respect to specific
problem instances provides insight into when QAOA may be viable for solving
real-world applications. Here, we solve every instance of MaxCut on
non-isomorphic unweighted graphs with nine or fewer vertices by numerically
simulating the pure-state dynamics of QAOA. Testing up to three layers of QAOA
depth, we find that distributions of the approximation ratio narrow with
increasing depth while the probability of recovering the maximum cut generally
broadens. We find QAOA exceeds the Goemans-Williamson approximation ratio bound
for most graphs. We also identify consistent patterns within the ensemble of
optimized variational circuit parameters that offer highly efficient heuristics
for solving MaxCut with QAOA. The resulting data set is presented as a
benchmark for establishing empirical bounds on QAOA performance that may be
used to test on-going experimental realizations.
Related papers
- MG-Net: Learn to Customize QAOA with Circuit Depth Awareness [51.78425545377329]
Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling optimization challenges.
The requisite circuit depth for satisfactory performance is problem-specific and often exceeds the maximum capability of current quantum devices.
We introduce the Mixer Generator Network (MG-Net), a unified deep learning framework adept at dynamically formulating optimal mixer Hamiltonians.
arXiv Detail & Related papers (2024-09-27T12:28:18Z) - Improved Recursive QAOA for Solving MAX-CUT on Bipartite Graphs [4.364124102844566]
We analytically prove the performance limitations of level-1 QAOA in solving the MAX-CUT problem on bipartite graphs.
We show through numerical results that solving the same problem using level-1 Recursive QAOA (RQAOA)
We propose a modified RQAOA that reduces the parameter regime optimized in the QAOA.
arXiv Detail & Related papers (2024-08-23T16:35:47Z) - 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) - Graph Representation Learning for Parameter Transferability in Quantum Approximate Optimization Algorithm [1.0971022294548696]
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced optimization.
In this work, we apply five different graph embedding techniques to determine good donor candidates for parameter transferability.
Using this technique, we effectively reduce the number of iterations required for parameter optimization, obtaining an approximate solution to the target problem with an order of magnitude speedup.
arXiv Detail & Related papers (2024-01-12T16:01:53Z) - An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation [0.23999111269325263]
The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve optimisation problems.
While QAOA can be implemented on NISQ devices, physical limitations can limit circuit depth and decrease performance.
This work introduces the eXpressive QAOA (XQAOA) that assigns more classical parameters to the ansatz to improve its performance at low depths.
arXiv Detail & Related papers (2023-02-09T07:47:06Z) - Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity.
We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree.
These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
arXiv Detail & Related papers (2022-01-06T21:02:30Z) - Predicting parameters for the Quantum Approximate Optimization Algorithm
for MAX-CUT from the infinite-size limit [0.05076419064097732]
We present an explicit algorithm to evaluate the performance of QAOA on MAX-CUT applied to random Erdos-Renyi graphs of expected degree $d$.
This analysis yields an explicit mapping between QAOA parameters for MAX-CUT on Erdos-Renyi graphs, and the Sherrington-Kirkpatrick model.
arXiv Detail & Related papers (2021-10-20T17:58:53Z) - Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box
Optimization Framework [100.36569795440889]
This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information.
We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
arXiv Detail & Related papers (2020-12-21T17:29:58Z) - Convergence of adaptive algorithms for weakly convex constrained
optimization [59.36386973876765]
We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope.
Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
arXiv Detail & Related papers (2020-06-11T17:43:19Z) - Evaluation of QAOA based on the approximation ratio of individual
samples [0.0]
We simulate the performance of QAOA applied to the Max-Cut problem and compare it with some of the best classical alternatives.
Because of the evolving QAOA computational complexity-theoretic guidance, we utilize a framework for the search for quantum advantage.
arXiv Detail & Related papers (2020-06-08T18:00:18Z) - Cross Entropy Hyperparameter Optimization for Constrained Problem
Hamiltonians Applied to QAOA [68.11912614360878]
Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications.
Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem.
In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
arXiv Detail & Related papers (2020-03-11T13:52:41Z)
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.