Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem

• URL: http://arxiv.org/abs/2308.02342v2
• Date: Sun, 2 Jun 2024 13:49:44 GMT
• Title: Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem
• Authors: Ruslan Shaydulin, Changhao Li, Shouvanik Chakrabarti, Matthew DeCross, Dylan Herman, Niraj Kumar, Jeffrey Larson, Danylo Lykov, Pierre Minssen, Yue Sun, Yuri Alexeev, Joan M. Dreiling, John P. Gaebler, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Nathan Hewitt, Chandler V. Horst, Shaohan Hu, Jacob Johansen, Mitchell Matheny, Tanner Mengle, Michael Mills, Steven A. Moses, Brian Neyenhuis, Peter Siegfried, Romina Yalovetzky, Marco Pistoia,
• Abstract summary: The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem. We observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers.
• Score: 8.738180371389097
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

Related papers

• Hybrid Classical-Quantum Simulation of MaxCut using QAOA-in-QAOA [0.0]
  In this work, an implementation of the QAOA2 method for the scalable solution of the MaxCut problem is presented. The limits of the Goemans-Williamson (GW) algorithm as a purely classical alternative to QAOA are investigated. Results from large-scale simulations of up to 33 qubits are presented, showing the advantage of QAOA in certain cases and the efficiency of the implementation.
  arXiv  Detail & Related papers  (2024-06-25T09:02:31Z)
• Multiscale Quantum Approximate Optimization Algorithm [0.0]
  The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to optimization problems. We propose a new version of QAOA that incorporates the capabilities of QAOA and the real-space renormalization group transformation.
  arXiv  Detail & Related papers  (2023-12-11T07:47:16Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• How Much Entanglement Do Quantum Optimization Algorithms Require? [0.0]
  We study the entanglement generated during the execution of ADAPT-QAOA. By incrementally restricting this flexibility, we find that a larger amount of entanglement entropy at earlier stages coincides with faster convergence at later stages.
  arXiv  Detail & Related papers  (2022-05-24T18:00:02Z)
• 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)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• 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)
• Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits [15.279642278652654]
  We present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
  arXiv  Detail & Related papers  (2021-12-21T12:41:31Z)
• Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection [80.28858481461418]
  Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices. Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
  arXiv  Detail & Related papers  (2021-07-11T10:56:24Z)
• Quantum constraint learning for quantum approximate optimization algorithm [0.0]
  This paper introduces a quantum machine learning approach to learn the mixer Hamiltonian required to hard constrain the search subspace. One can directly plug the learnt unitary into the QAOA framework using an adaptable ansatz. We also develop an intuitive metric that uses Wasserstein distance to assess the performance of general approximate optimization algorithms with/without constraints.
  arXiv  Detail & Related papers  (2021-05-14T11:31:14Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

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.