Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators
arxiv(2024)
摘要
Hamiltonian simulation is arguably the most fundamental application of
quantum computers. The Magnus operator is a popular method for time-dependent
Hamiltonian simulation in computational mathematics, yet its usage requires the
implementation of exponentials of commutators, which has previously made it
unappealing for quantum computing. The development of commutator-free
quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a
lack of provable global numeric error bounds. In this work, we establish one
such error bound for CFQM-based time-dependent quantum Hamiltonian simulation
by carefully estimating the error of each step involved in their definition.
This allows us to compare its cost with the alternatives, and show that CFQMs
are often the most efficient product-formula technique available by more than
an order of magnitude. As a result, we find that CFQMs may be particularly
useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum
computers.
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