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Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Journal Article · · Proceedings of the National Academy of Sciences of the United States of America
 [1];  [2];  [2];  [2];  [2];  [3];  [2];  [2];  [2];  [2];  [4];  [2];  [2];  [5];  [2];  [2]
  1. Univ. of Maryland, College Park, MD (United States). National Institute of Standards and Technology. Joint Quantum Inst. Joint Center for Quantum Information and Computer Science. Physics Dept.; Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
  2. Univ. of Maryland, College Park, MD (United States). National Institute of Standards and Technology. Joint Quantum Inst. Joint Center for Quantum Information and Computer Science. Physics Dept.
  3. Univ. of Maryland, College Park, MD (United States). National Institute of Standards and Technology. Joint Quantum Inst. Joint Center for Quantum Information and Computer Science. Physics Dept.; Middlebury College, Middlebury, VT (United States). Dept. of Physics
  4. Univ. of Maryland, College Park, MD (United States). National Institute of Standards and Technology. Joint Quantum Inst. Joint Center for Quantum Information and Computer Science
  5. Univ. of Maryland, College Park, MD (United States). Univ. of Maryland Institute for Advanced Computer Studies
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Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

Research Organization:
Iowa State Univ., Ames, IA (United States); Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0019139; SC0019449
OSTI ID:
1816228
Journal Information:
Proceedings of the National Academy of Sciences of the United States of America, Vol. 117, Issue 41; ISSN 0027-8424
Publisher:
National Academy of SciencesCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (2)

Computational phase transitions: benchmarking Ising machines and quantum optimisers journal March 2021
Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design text January 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
quantum information science
quantum simulation
quantum computing
quantum algorithms
trapped ions