Quantum adiabatic optimization with Rydberg arrays: localization phenomena and encoding strategies

• URL: http://arxiv.org/abs/2411.04645v1
• Date: Thu, 07 Nov 2024 12:10:01 GMT
• Title: Quantum adiabatic optimization with Rydberg arrays: localization phenomena and encoding strategies
• Authors: Lisa Bombieri, Zhongda Zeng, Roberto Tricarico, Rui Lin, Simone Notarnicola, Madelyn Cain, Mikhail D. Lukin, Hannes Pichler,
• Abstract summary: We study the quantum dynamics of the encoding scheme proposed in [Nguyen et al., PRX Quantum 4, 010316 (2023) We look at minimum gap scaling with system size along adiabatic protocols. We observe such localization and its effect on the success probability of finding the correct solution.
• Score: 0.9500919522633157
• License:
• Abstract: We study the quantum dynamics of the encoding scheme proposed in [Nguyen et al., PRX Quantum 4, 010316 (2023)], which encodes optimization problems on graphs with arbitrary connectivity into Rydberg atom arrays. Here, a graph vertex is represented by a wire of atoms, and the (crossing) crossing-with-edge gadget is placed at the intersection of two wires to (de)couple their degrees of freedom and reproduce the graph connectivity. We consider the fundamental geometry of two vertex-wires intersecting via a single gadget and look at minimum gap scaling with system size along adiabatic protocols. We find that both polynomial and exponential scaling are possible and, by means of perturbation theory, we relate the exponential closing of the minimum gap to an unfavorable localization of the ground-state wavefunction. Then, on the QuEra Aquila neutral atom machine, we observe such localization and its effect on the success probability of finding the correct solution to the encoded optimization problem. Finally, we propose possible strategies to avoid this quantum bottleneck, leading to an exponential improvement in the adiabatic performance.

Related papers

• Scalable Graph Compressed Convolutions [68.85227170390864]
  We propose a differentiable method that applies permutations to calibrate input graphs for Euclidean convolution. Based on the graph calibration, we propose the Compressed Convolution Network (CoCN) for hierarchical graph representation learning.
  arXiv  Detail & Related papers  (2024-07-26T03:14:13Z)
• Generation of quantum phases of matter and finding a maximum-weight independent set of unit-disk graphs using Rydberg atoms [4.619601221994331]
  We study the problem of a maximum-weight independent set of unit-disk graphs using Rydberg excitation. We consider driving the quantum system of interacting atoms to the many-body ground state using a non-linear quasi-adiabatic profile for sweeping the Rydberg detuning. We also investigate the quantum phases of matter realizing commensurate and incommensurate phases in one- and two-dimensional spatial arrangements of the atomic array.
  arXiv  Detail & Related papers  (2024-05-16T04:23:17Z)
• Demonstration of weighted graph optimization on a Rydberg atom array using local light-shifts [0.0]
  We present first demonstrations of weighted graph optimization on a Rydberg atom array. We verify the ability to prepare weighted graphs in 1D and 2D arrays.
  arXiv  Detail & Related papers  (2024-04-03T11:42:38Z)
• Solving optimization problems with local light shift encoding on Rydberg quantum annealers [0.0]
  We provide a non-unit disk framework to solve optimization problems on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits. Our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state.
  arXiv  Detail & Related papers  (2023-08-15T14:24:45Z)
• Exploring the impact of graph locality for the resolution of MIS with neutral atom devices [0.755972004983746]
  We build upon recent progress made for using 3D arrangements to embed more complex classes of graphs. We report experimental and theoretical results which represent important steps towards tackling hard problems on quantum computers.
  arXiv  Detail & Related papers  (2023-06-23T08:53:16Z)
• Quantum Gate Optimization for Rydberg Architectures in the Weak-Coupling Limit [55.05109484230879]
  We demonstrate machine learning assisted design of a two-qubit gate in a Rydberg tweezer system. We generate optimal pulse sequences that implement a CNOT gate with high fidelity. We show that local control of single qubit operations is sufficient for performing quantum computation on a large array of atoms.
  arXiv  Detail & Related papers  (2023-06-14T18:24:51Z)
• Graph Neural Network Autoencoders for Efficient Quantum Circuit Optimisation [69.43216268165402]
  We present for the first time how to use graph neural network (GNN) autoencoders for the optimisation of quantum circuits. We construct directed acyclic graphs from the quantum circuits, encode the graphs and use the encodings to represent RL states. Our method is the first realistic first step towards very large scale RL quantum circuit optimisation.
  arXiv  Detail & Related papers  (2023-03-06T16:51:30Z)
• Graph Signal Sampling for Inductive One-Bit Matrix Completion: a Closed-form Solution [112.3443939502313]
  We propose a unified graph signal sampling framework which enjoys the benefits of graph signal analysis and processing. The key idea is to transform each user's ratings on the items to a function (signal) on the vertices of an item-item graph. For the online setting, we develop a Bayesian extension, i.e., BGS-IMC which considers continuous random Gaussian noise in the graph Fourier domain.
  arXiv  Detail & Related papers  (2023-02-08T08:17:43Z)
• Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs [131.53471236405628]
  We present three methods that exploit the induced graphon representation of graphs and graph signals on partitions of [0, 1]2 in the graphon space. We prove that those low dimensional representations constitute a convergent sequence of graphs and graph signals. We observe that graphon pooling performs significantly better than other approaches proposed in the literature when dimensionality reduction ratios between layers are large.
  arXiv  Detail & Related papers  (2022-12-15T22:11:34Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Quantum optimization via four-body Rydberg gates [0.0]
  We propose and analyze a fast, high fidelity four-body Rydberg parity gate. Our gate relies on onetime-optimized adiabatic laser pulses and is fully programmable by adjusting two hold-times during operation. We demonstrate an implementation of the quantum approximate optimization algorithm (QAOA) for a small scale test problem.
  arXiv  Detail & Related papers  (2021-06-04T18:33:09Z)

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.