Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization

Understand

We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition.

• We present the first application of a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision, an exponential improvement over all prior methods.
• The two algorithms developed in this work rely on a second quantized encoding of the wavefunction in which the state of an $N$ spin-orbital system is encoded in ${\cal O}(N)$ qubits.
• Our first algorithm requires at most $\widetilde{\cal O}(N^8 t)$ gates.