Random Compiler for Fast Hamiltonian Simulation
Abstract
The dynamics of a quantum system can be simulated using a quantum computer by breaking down the unitary into a quantum circuit of one and two qubit gates. The most established methods are the TrotterSuzuki decompositions, for which rigorous bounds on the circuit size depend on the number of terms L in the system Hamiltonian and the size of the largest term in the Hamiltonian Λ . Consequently, the TrotterSuzuki method is only practical for sparse Hamiltonians. TrotterSuzuki is a deterministic compiler but it was recently shown that randomized compiling offers lower overheads. Here we present and analyze a randomized compiler for Hamiltonian simulation where gate probabilities are proportional to the strength of a corresponding term in the Hamiltonian. This approach requires a circuit size independent of L and Λ , but instead depending on λ the absolute sum of Hamiltonian strengths (the ℓ_{1} norm). Therefore, it is especially suited to electronic structure Hamiltonians relevant to quantum chemistry. Considering propane, carbon dioxide, and ethane, we observe speedups compared to standard TrotterSuzuki of between 306 × and 1591 × for physically significant simulation times at precision 10^{3}. Performing phase estimation at chemical accuracy, we report that the savings are similar.
 Publication:

Physical Review Letters
 Pub Date:
 August 2019
 DOI:
 10.1103/PhysRevLett.123.070503
 arXiv:
 arXiv:1811.08017
 Bibcode:
 2019PhRvL.123g0503C
 Keywords:

 Quantum Physics
 EPrint:
 Additional analysis of resource costs of using phase estimation to estimate electronic structure energies