Random Compiler for Fast Hamiltonian Simulation

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Simulation

Background:

• Quantum systems dynamics are simulated using quantum computers by decomposing unitaries into quantum circuits.
• Trotter-Suzuki decompositions are standard but limited to sparse Hamiltonians due to circuit size dependencies on Hamiltonian properties.
• Randomized compiling has emerged as a lower-overhead alternative to deterministic methods.

Purpose of the Study:

• To present and analyze a novel randomized compiler for Hamiltonian simulation.
• To develop a method suitable for complex Hamiltonians, particularly in quantum chemistry.
• To demonstrate significant performance improvements over existing techniques.

Main Methods:

• A randomized compiler is proposed where gate probabilities correlate with Hamiltonian term strengths.
• Circuit size is made independent of the number of terms (L) and largest term size (Λ).
• The new method's size depends on the ℓ₁ norm (λ) of Hamiltonian strengths.

Main Results:

• The proposed method shows speed-ups of 306× to 1591× for propane, carbon dioxide, and ethane simulations.
• These speed-ups are observed at a precision of 10⁻³ for chemically relevant simulation times.
• Similar savings were found when performing phase estimation at chemical accuracy.

Conclusions:

• The novel randomized compiling approach is highly efficient for electronic structure Hamiltonians.
• This method overcomes limitations of Trotter-Suzuki, enabling simulations of complex quantum systems.
• The findings suggest a practical advancement for quantum chemistry applications on quantum computers.