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

Area of Science:

• Quantum Computing
• Quantum Simulation
• Computational Physics

Background:

• Quantum computers offer potential advantages for complex problems intractable for classical computers.
• Quantum many-body systems require advanced simulation techniques.
• Optimization and satisfiability problems are key areas for quantum advantage.

Purpose of the Study:

• To implement a low-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.
• To optimize combinatorial classical problems by sampling QAOA outputs.

Main Methods:

• Utilized an analog quantum simulator with up to 40 trapped-ion qubits.
• Employed high-fidelity, single-shot, individual qubit measurements for QAOA output sampling.
• Executed the algorithm using both exhaustive search and closed-loop optimization of variational parameters.
• Benchmarked experimental results against bootstrapping heuristic methods.

Main Results:

• Successfully estimated ground-state energy for the Transverse Field Ising Model.
• Demonstrated that QAOA performance does not degrade significantly with increasing system size.
• Observed that QAOA runtime is largely independent of the number of qubits.
• Achieved results consistent with numerical simulations.

Conclusions:

• The implemented low-depth QAOA is effective for estimating ground-state energies and optimizing combinatorial problems.
• Scalability of the QAOA approach appears robust, with performance and runtime showing favorable characteristics.
• A comprehensive error analysis was performed, crucial for future advancements in QAOA applications.