Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

• URL: http://arxiv.org/abs/2108.02175v3
• Date: Fri, 23 Dec 2022 14:06:10 GMT
• Title: Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Authors: Joris Kattem\"olle and Jasper van Wezel
• Abstract summary: We give a detailed proposal for a Vari Quantum Eigensolver (VQE) intending to solve a quantum problem on a quantum computer. We emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a Variational Quantum Eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise-resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.

Related papers

• Quantum subspace expansion in the presence of hardware noise [0.0]
  Finding ground state energies on current quantum processing units (QPUs) continues to pose challenges. Hardware noise severely affects both the expressivity and trainability of parametrized quantum circuits. We show how to integrate VQE with a quantum subspace expansion, allowing for an optimal balance between quantum and classical computing capabilities and costs.
  arXiv  Detail & Related papers  (2024-04-14T02:48:42Z)
• GQHAN: A Grover-inspired Quantum Hard Attention Network [53.96779043113156]
  Grover-inspired Quantum Hard Attention Mechanism (GQHAM) is proposed. GQHAN adeptly surmounts the non-differentiability hurdle, surpassing the efficacy of extant quantum soft self-attention mechanisms. The proposal of GQHAN lays the foundation for future quantum computers to process large-scale data, and promotes the development of quantum computer vision.
  arXiv  Detail & Related papers  (2024-01-25T11:11:16Z)
• Quantum error mitigation for Fourier moment computation [49.1574468325115]
  This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude.
  arXiv  Detail & Related papers  (2024-01-23T19:10:24Z)
• Go-No go criteria for performing quantum chemistry calculations on quantum computers [0.0]
  We propose two criteria for evaluating the two leading quantum approaches for this class of problems. We find a crippling effect of noise with an overall scaling of the precision that is generically it less favourable than in the corresponding classical algorithms. The second criterion applies to the Quantum Phase Estimation (QPE) algorithm that is often presented as the go-to replacement of VQE upon availability of (noiseless) fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2023-06-05T06:41:22Z)
• Variational Denoising for Variational Quantum Eigensolver [0.28675177318965045]
  The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems. VQE faces challenges in task-specific design and machine-specific architecture, particularly when running on noisy quantum devices. We propose variational denoising, an unsupervised learning method that employs a parameterized quantum neural network to improve the solution of VQE.
  arXiv  Detail & Related papers  (2023-04-02T14:56:15Z)
• Noise-robust ground state energy estimates from deep quantum circuits [0.0]
  We show how the underlying energy estimate explicitly filters out incoherent noise in quantum algorithms. We implement QCM for a model of quantum magnetism on IBM Quantum hardware. We find that QCM maintains a remarkably high degree of error robustness where VQE completely fails.
  arXiv  Detail & Related papers  (2022-11-16T09:12:55Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Simulating noisy variational quantum eigensolver with local noise models [4.581041382009666]
  Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic quantum computers. We study systematically the effect of noise for the VQE algorithm, by performing numerical simulations with various local noise models.
  arXiv  Detail & Related papers  (2020-10-28T08:51:59Z)
• 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)

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.