Problem-Size Independent Angles for a Grover-Driven Quantum Approximate Optimization Algorithm

• URL: http://arxiv.org/abs/2208.10453v1
• Date: Mon, 22 Aug 2022 17:18:25 GMT
• Title: Problem-Size Independent Angles for a Grover-Driven Quantum Approximate Optimization Algorithm
• Authors: David Headley, Frank K. Wilhelm
• Abstract summary: We show that the calculation of the expectation of a problem Hamiltonian under a Grover-driven, QAOA-prepared state can be performed independently of system size. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work we demonstrate that if one knows the probability density function describing how the objective function of a problem is distributed, that the calculation of the expectation of such a problem Hamiltonian under a Grover-driven, QAOA-prepared state can be performed independently of system size. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes, in particular, for the number partitioning problem.

Related papers

• 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)
• Performance Upper Bound of Grover-Mixer Quantum Alternating Operator Ansatz [3.5023108034606256]
  The Quantum Alternating Operator Ansatz (QAOA) represents a branch of quantum algorithms for solving optimization problems. A specific variant, the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA), ensures uniform amplitude across states that share equivalent objective values. We show that the GM-QAOA provides a quadratic enhancement in sampling probability and requires circuit depth that scales exponentially with problem size to maintain consistent performance.
  arXiv  Detail & Related papers  (2024-05-06T05:47:27Z)
• Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing [93.83016310295804]
  AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for computer vision tasks. In this work, we explore the potential of using this information for probabilistic balanced k-means clustering. Instead of discarding non-optimal solutions, we propose to use them to compute calibrated posterior probabilities with little additional compute cost. This allows us to identify ambiguous solutions and data points, which we demonstrate on a D-Wave AQC on synthetic tasks and real visual data.
  arXiv  Detail & Related papers  (2023-10-18T17:59:45Z)
• Fermionic Quantum Approximate Optimization Algorithm [11.00442581946026]
  We propose fermionic quantum approximate optimization algorithm (FQAOA) for solving optimization problems with constraints. FQAOA tackle the constrains issue by using fermion particle number preservation to intrinsically impose them throughout QAOA. We provide a systematic guideline for designing the driver Hamiltonian for a given problem Hamiltonian with constraints.
  arXiv  Detail & Related papers  (2023-01-25T18:36:58Z)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• 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)
• Parameters Fixing Strategy for Quantum Approximate Optimization Algorithm [0.0]
  We propose a strategy to give high approximation ratio on average, even at large circuit depths, by initializing QAOA with the optimal parameters obtained from the previous depths. We test our strategy on the Max-cut problem of certain classes of graphs such as the 3-regular graphs and the Erd"os-R'enyi graphs.
  arXiv  Detail & Related papers  (2021-08-11T15:44:16Z)
• Polynomial unconstrained binary optimisation inspired by optical simulation [52.11703556419582]
  We propose an algorithm inspired by optical coherent Ising machines to solve the problem of unconstrained binary optimization. We benchmark the proposed algorithm against existing PUBO algorithms, and observe its superior performance. The application of our algorithm to protein folding and quantum chemistry problems sheds light on the shortcomings of approxing the electronic structure problem by a PUBO problem.
  arXiv  Detail & Related papers  (2021-06-24T16:39:31Z)
• 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)
• A Hybrid Quantum-Classical Heuristic to solve large-scale Integer Linear Programs [0.4925222726301578]
  We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm. The role of the quantum algorithm is to find integer solutions to subproblems appearing in Branch-and-Price.
  arXiv  Detail & Related papers  (2021-03-29T08:59:26Z)
• 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.