[Paper Review] Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator

Guido Pagano, Aniruddha Bapat+14 more|arXiv (Cornell University)|Jun 6, 2019

Quantum Computing Algorithms and Architecture13 citations

TL;DR

This paper demonstrates the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) on a trapped-ion quantum simulator, using up to 40 qubits to approximate the ground state energy of a transverse field Ising model with tunable long-range interactions. By combining variational parameter search with classical optimization and efficient single-shot measurements, the study achieves high-fidelity sampling of the full QAOA output distribution.

ABSTRACT

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.

Motivation & Objective

• To implement a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) on a trapped-ion quantum simulator.
• To estimate the ground state energy of the transverse field Ising model with tunable long-range interactions using up to 40 trapped-ion qubits.
• To combine quantum simulation with classical optimization to efficiently find optimal variational parameters.
• To enable high-fidelity, single-shot measurement of the full QAOA output probability distribution across all qubits.

Proposed method

• Employ a trapped-ion quantum simulator to realize a transverse field Ising Hamiltonian with tunable long-range interactions.
• Implement a shallow-depth QAOA circuit using dynamically generated spin-spin interactions via laser-driven Raman transitions.
• Perform an exhaustive search over variational control parameters to approximate the ground state energy across 40 qubits.
• Integrate the quantum simulator with a classical optimization algorithm to efficiently converge on the optimal parameter set.
• Use single-shot, high-fidelity measurements to sample the full output probability distribution of the QAOA state.

Experimental results

Research questions

• RQ1 Can a shallow-depth QAOA be successfully implemented on a trapped-ion quantum simulator with up to 40 qubits?
• RQ2 How effectively can variational parameters be optimized to approximate the ground state energy of a long-range interacting Ising model?
• RQ3 To what extent can classical optimization accelerate convergence to the optimal QAOA parameters in a quantum simulation setting?
• RQ4 What is the fidelity and efficiency of single-shot measurement in sampling the full QAOA output distribution across all qubits?

Key findings

• The QAOA was successfully implemented on a trapped-ion quantum simulator with up to 40 qubits, demonstrating scalability of the approach.
• The variational parameter search achieved accurate approximation of the ground state energy for the transverse field Ising model with long-range interactions.
• Classical optimization significantly improved the efficiency of finding optimal parameters, reducing the search space required.
• High-fidelity single-shot measurements enabled efficient and complete sampling of the full QAOA output probability distribution across all qubits.