The Questionable Influence of Entanglement in Quantum Optimisation Algorithms

• URL: http://arxiv.org/abs/2407.17204v1
• Date: Wed, 24 Jul 2024 12:04:00 GMT
• Title: The Questionable Influence of Entanglement in Quantum Optimisation Algorithms
• Authors: Tobias Rohe, Daniëlle Schuman, Jonas Nüßlein, Leo Sünkel, Jonas Stein, Claudia Linnhoff-Popien,
• Abstract summary: Variational Quantum Eigensolver (VQE) is promising compared to other quantum algorithms. Recent research raises questions about the effectiveness of entanglement in circuits for quantum machine learning algorithms.
• Score: 4.118849293881126
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The performance of the Variational Quantum Eigensolver (VQE) is promising compared to other quantum algorithms, but also depends significantly on the appropriate design of the underlying quantum circuit. Recent research by Bowles, Ahmend \& Schuld, 2024 [1] raises questions about the effectiveness of entanglement in circuits for quantum machine learning algorithms. In our paper we want to address questions about the effectiveness of state preparation via Hadamard gates and entanglement via CNOT gates in the realm of quantum optimisation. We have constructed a total of eight different circuits, varying in implementation details, solving a total of 100 randomly generated MaxCut problems. Our results show no improvement with Hadamard gates applied at the beginning of the circuits. Furthermore, also entanglement shows no positive effect on the solution quality in our small scale experiments. In contrast, the investigated circuits that used entanglement generally showed lower, as well as deteriorating results when the number of circuit layers is increased. Based on our results, we hypothesise that entanglement can play a coordinating role, such that changes in individual parameters are distributed across multiple qubits in quantum circuits, but that this positive effect can quickly be overdosed and turned negative. The verification of this hypothesis represents a challenge for future research and can have a considerable influence on the development of new hybrid algorithms.

Related papers

• Benchmarking Variational Quantum Eigensolvers for Entanglement Detection in Many-Body Hamiltonian Ground States [37.69303106863453]
  Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. We use a specific class of VQA named variational quantum eigensolvers (VQEs) to benchmark them at entanglement witnessing and entangled ground state detection. Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
  arXiv  Detail & Related papers  (2024-07-05T12:06:40Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Parallel circuit implementation of variational quantum algorithms [0.0]
  We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution. We apply this specifically to optimization problems, where inherent structures from the problem can be identified. We show that not only can our method address larger problems, but that it is also possible to run full VQA models while training parameters using only one slice.
  arXiv  Detail & Related papers  (2023-04-06T12:52:29Z)
• 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)
• Limitations of variational quantum algorithms: a quantum optimal transport approach [11.202435939275675]
  We obtain extremely tight bounds for standard NISQ proposals in both the noisy and noiseless regimes. The bounds limit the performance of both circuit model algorithms, such as QAOA, and also continuous-time algorithms, such as quantum annealing.
  arXiv  Detail & Related papers  (2022-04-07T13:58:44Z)
• Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits [63.83649593474856]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Efficiently Solve the Max-cut Problem via a Quantum Qubit Rotation Algorithm [7.581898299650999]
  We introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA) The approximate solution of the max-cut problem can be obtained with probability close to 1. We compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.
  arXiv  Detail & Related papers  (2021-10-15T11:19:48Z)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)
• Robustly decorrelating errors with mixed quantum gates [0.0]
  Coherent errors in quantum operations are ubiquitous. We show that by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, on can dramatically suppress coherent errors.
  arXiv  Detail & Related papers  (2020-01-08T23:09:42Z)

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.