Rydberg Quantum Wires for Maximum Independent Set Problems with Nonplanar and High-Degree Graphs

• URL: http://arxiv.org/abs/2109.03517v1
• Date: Wed, 8 Sep 2021 09:37:18 GMT
• Title: Rydberg Quantum Wires for Maximum Independent Set Problems with Nonplanar and High-Degree Graphs
• Authors: Minhyuk Kim, Kangheun Kim, Jaeyong Hwang, Eun-Gook Moon, and Jaewook Ahn
• Abstract summary: We present experiments with Rydberg atoms to solve non-deterministic-time hard (NP-hard) problems. We introduce the Rydberg quantum wire scheme with auxiliary atoms to engineer long-ranged networks of qubit atoms. Three-dimensional (3D) Rydberg-atom arrays are constructed, overcoming the intrinsic limitations of two-dimensional arrays.
• Score: 0.7046417074932257
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One prominent application of near-term quantum computing devices is to solve combinatorial optimization such as non-deterministic polynomial-time hard (NP-hard) problems. Here we present experiments with Rydberg atoms to solve one of the NP-hard problems, the maximum independent set (MIS) of graphs. We introduce the Rydberg quantum wire scheme with auxiliary atoms to engineer long-ranged networks of qubit atoms. Three-dimensional (3D) Rydberg-atom arrays are constructed, overcoming the intrinsic limitations of two-dimensional arrays. We demonstrate Kuratowski subgraphs and a six-degree graph, which are the essentials of non-planar and high-degree graphs. Their MIS solutions are obtained by realizing a programmable quantum simulator with the quantum-wired 3D arrays. Our construction provides a way to engineer many-body entanglement, taking a step toward quantum advantages in combinatorial optimization.

Related papers

• 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)
• 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)
• Embedding the MIS problem for non-local graphs with bounded degree using 3D arrays of atoms [0.0]
  The Maximum Independent Set (MIS) is a known NP-hard problem that can be naturally encoded in Rydberg atom arrays. We present a deterministic and efficient construction to embed a large family of non-local graphs in 3D atomic arrays. This construction is a first crucial step towards tackling tasks on quantum computers for which no classical efficient epsilon-approximation scheme exists.
  arXiv  Detail & Related papers  (2022-09-12T11:46:10Z)
• Quantum optimization with arbitrary connectivity using Rydberg atom arrays [0.0]
  We extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from the original problems. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization.
  arXiv  Detail & Related papers  (2022-09-08T18:00:00Z)
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays [39.76254807200083]
  We experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We find the problem hardness is controlled by the solution degeneracy and number of local minima. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions.
  arXiv  Detail & Related papers  (2022-02-18T19:00:01Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)

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.