An evolving objective function for improved variational quantum optimisation

• URL: http://arxiv.org/abs/2105.11766v3
• Date: Fri, 24 Jun 2022 12:56:22 GMT
• Title: An evolving objective function for improved variational quantum optimisation
• Authors: Ioannis Kolotouros and Petros Wallden
• Abstract summary: We introduce an evolving objective function, which we call Ascending-CVaR and that can be used for any optimisation problem. We show that Ascending-CVaR in all cases performs better than standard objective functions or the "constant" CVaR of Barkoutsos et al (Quantum 2020) Our proposal achieves higher overlap with the ideal state in all problems, whether we consider easy or hard instances.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A promising approach to useful computational quantum advantage is to use variational quantum algorithms for optimisation problems. Crucial for the performance of these algorithms is to ensure that the algorithm converges with high probability to a near-optimal solution in a small time. In Barkoutsos et al (Quantum 2020) an alternative class of objective functions, called Conditional Value-at-Risk (CVaR), was introduced and it was shown that they perform better than standard objective functions. Here we extend that work by introducing an evolving objective function, which we call Ascending-CVaR and that can be used for any optimisation problem. We test our proposed objective function, in an emulation environment, using as case-studies three different optimisation problems: Max-Cut, Number Partitioning and Portfolio Optimisation. We examine multiple instances of different sizes and analyse the performance using the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz and the Quantum Approximate Optimization Algorithm (QAOA). We show that Ascending-CVaR in all cases performs better than standard objective functions or the "constant" CVaR of Barkoutsos et al (Quantum 2020) and that it can be used as a heuristic for avoiding sub-optimal minima. Our proposal achieves higher overlap with the ideal state in all problems, whether we consider easy or hard instances -- on average it gives up to ten times greater overlap at Portfolio Optimisation and Number Partitioning, while it gives an 80% improvement at Max-Cut. In the hard instances we consider, for the number partitioning problem, standard objective functions fail to find the correct solution in almost all cases, CVaR finds the correct solution at 60% of the cases, while Ascending-CVaR finds the correct solution in 95% of the cases.

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)
• Variational Quantum Multi-Objective Optimization [5.381539115778766]
  We present a variational quantum optimization algorithm to solve discrete multi-objective optimization problems on quantum computers. We show the effectiveness of the proposed algorithm on several benchmark problems with up to five objectives.
  arXiv  Detail & Related papers  (2023-12-21T18:59:21Z)
• Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees [56.848265937921354]
  Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy. Many algorithms for IRL have an inherently nested structure. We develop a novel single-loop algorithm for IRL that does not compromise reward estimation accuracy.
  arXiv  Detail & Related papers  (2022-10-04T17:13:45Z)
• Iteration Complexity of Variational Quantum Algorithms [5.203200173190989]
  We argue that noise makes evaluations of the objective function via quantum circuits biased. We derive the missing guarantees and find that the rate of convergence is unaffected.
  arXiv  Detail & Related papers  (2022-09-21T19:18:41Z)
• Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm [3.508346077709686]
  We study unsupervised Machine Learning approaches for setting parameters without optimization. We showcase them within Recursive-QAOA up to depth $3$ where the number of QAOA parameters used per iteration is limited to $3$. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.
  arXiv  Detail & Related papers  (2022-02-18T19:55:42Z)
• Unified Convergence Analysis for Adaptive Optimization with Moving Average Estimator [75.05106948314956]
  We show that an increasing large momentum parameter for the first-order moment is sufficient for adaptive scaling. We also give insights for increasing the momentum in a stagewise manner in accordance with stagewise decreasing step size.
  arXiv  Detail & Related papers  (2021-04-30T08:50:24Z)
• Improving the Quantum Approximate Optimization Algorithm with postselection [0.0]
  Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. We consider a well-studied quantum algorithm for optimization: the Quantum Approximate Optimization Algorithm (QAOA) applied to the MaxCut problem on 3-regular graphs. We derive theoretical upper and lower bounds showing that a constant (though small) increase of the fraction of satisfied edges is indeed achievable.
  arXiv  Detail & Related papers  (2020-11-10T22:17:50Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic [142.1492359556374]
  Bilevel optimization is a class of problems which exhibit a two-level structure. We propose a two-timescale approximation (TTSA) algorithm for tackling such a bilevel problem. We show that a two-timescale natural actor-critic policy optimization algorithm can be viewed as a special case of our TTSA framework.
  arXiv  Detail & Related papers  (2020-07-10T05:20:02Z)
• 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)
• 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.