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: http://creativecommons.org/licenses/by/4.0/
• 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

• Error-mitigated Geometric Quantum Control over an Oscillator [2.7382619198694886]
  Quantum information is fragile to environmentally and operationally induced imperfections. We propose a robust scheme based on quantum optimal control via functional theory. Our scheme provides a promising alternative for fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2025-01-24T09:13:24Z)
• Quantum Subroutines in Branch-Price-and-Cut for Vehicle Routing [0.0]
  We demonstrate in this work how quantums with limited resources can be integrated in large-scale exact optimization algorithms for NP-hard problems. A key feature of our algorithm is it not only from the best solution returned by the quantum but from all solutions below a certain cost threshold.
  arXiv  Detail & Related papers  (2024-12-20T08:27:23Z)
• 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)
• State-Averaged Orbital-Optimized VQE: A quantum algorithm for the democratic description of ground and excited electronic states [0.0]
  The SA-OO-VQE package aims to answer both problems with its hybrid quantum-classical conception based on a typical Variational Quantum Eigensolver approach. The SA-OO-VQE has the ability to treat degenerate (or quasi-degenerate) states on the same footing, thus avoiding known numerical optimization problems around avoided crossings or conical intersections.
  arXiv  Detail & Related papers  (2024-01-22T12:16:37Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• 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)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• 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)
• 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)
• Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization [0.0]
  Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. Here, we introduce the fast-and-slow algorithm, which uses gradients to identify a promising region in Bayesian space. Our results move variational quantum algorithms closer to their envisioned applications in quantum chemistry, optimization, and quantum simulation problems.
  arXiv  Detail & Related papers  (2022-03-04T17:48:57Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• 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)
• Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms [55.41644538483948]
  We provide the first complete characterization of sources of error in a neutral-atom quantum computer. We develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace. Our protocols can be implemented in the near-term using state-of-the-art neutral atom platforms with qubits encoded in both alkali and alkaline-earth atoms.
  arXiv  Detail & Related papers  (2021-05-27T23:29:53Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

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.