Hamiltonian simulation algorithms for near-term quantum hardware

Area of Science:

• Quantum Computing
• Quantum Simulation
• Condensed Matter Physics

Background:

• The quantum circuit model is standard for quantum algorithms but incurs overhead.
• Abstraction from hardware limits the efficiency of quantum simulations.

Purpose of the Study:

• To develop quantum algorithms for Hamiltonian simulation operating below the standard circuit model.
• To reduce overhead and improve feasibility for quantum simulations on current hardware.

Main Methods:

• Developed quantum algorithms exploiting direct qubit interaction control.
• Derived analytic circuit identities for synthesizing multi-qubit evolutions from two-qubit interactions.
• Analyzed algorithm performance under per-gate and per-unit-time error models.

Main Results:

• Reduced circuit depth for simulating a 5x5 Fermi-Hubbard lattice from 1,243,586 to 3,209 (per-gate error model).
• Achieved a circuit-depth-equivalent of 259 under a per-time error model.
• Demonstrated significant reductions in circuit depth for Hamiltonian simulation.

Conclusions:

• The developed techniques bring Hamiltonian simulation closer to feasibility in the NISQ era.
• Operating "one level below" the circuit model offers substantial efficiency gains.
• New error bounds and analysis tailored for non-asymptotic regimes improve simulation accuracy.