Hamiltonian learning for 300 trapped ion qubits with long-range couplings.

Area of Science:

• Quantum Simulation
• Quantum Many-Body Physics
• Quantum Information Science

Background:

• Quantum simulators offer potential for studying complex quantum models intractable for classical computers.
• Learning the simulated Hamiltonian is crucial for quantitative applications but faces challenges in scaling and fidelity.
• Current noisy intermediate-scale quantum (NISQ) devices lack high-fidelity universal gate operations, hindering Hamiltonian learning.

Purpose of the Study:

• To demonstrate efficient Hamiltonian learning on a large-scale, two-dimensional ion trap quantum simulator.
• To overcome the time and resource scaling challenges associated with learning Hamiltonians in quantum systems.
• To enable quantitative applications of large-scale quantum simulators.

Main Methods:

• Utilized a 300-qubit two-dimensional ion trap quantum simulator.
• Employed global manipulations and single-qubit-resolved state detection for Hamiltonian learning.
• Developed a physically guided learning scheme by fitting the anharmonic trap potential.

Main Results:

• Successfully learned the all-to-all-coupled Ising model Hamiltonian.
• Achieved efficient learning with quantum resources scaling linearly with the qubit number.
• Demonstrated a quantum sample complexity independent of system size using the guided learning scheme.

Conclusions:

• The developed Hamiltonian learning method is efficient and scalable for large ion trap quantum simulators.
• This work addresses a critical bottleneck in utilizing quantum simulators for scientific discovery.
• Paves the way for wide applications of large-scale ion trap quantum simulators in exploring quantum many-body physics.