Abstract
We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie–Trotter–Suzuki decomposition. We present the first application of a general technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The key difficulty in applying algorithms for general sparse Hamiltonian simulation to fermionic simulation is that a query, corresponding to computation of an entry of the Hamiltonian, is costly to compute. This means that the gate complexity would be much higher than quantified by the query complexity. We solve this problem with a novel quantum algorithm for on-the-fly computation of integrals that is exponentially faster than classical sampling. While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most studied application of Hamiltonian simulation. Our central result is an algorithm for simulating an N spin–orbital system that requires gates. This approach is exponentially faster in the inverse precision and at least cubically faster in N than all previous approaches to chemistry simulation in the literature.
Highlights
March 2016Ryan Babbush, Dominic W Berry, Ian D Kivlichan, Annie Y Wei, Peter J Love and Alán Aspuru-Guzik
As small, fault-tolerant quantum computers come increasingly close to viability [1,2,3,4] there has been substantial renewed interest in quantum simulating chemistry due to the low qubit requirements and industrial importance of the electronic structure problem
While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most for simulating an studied application of N spin–orbital system
Summary
Ryan Babbush, Dominic W Berry, Ian D Kivlichan, Annie Y Wei, Peter J Love and Alán Aspuru-Guzik. We introduce novel algorithms for the quantum simulation of fermionic systems which are author(s) and the title of the work, journal citation dramatically more efficient than those based on the Lie–Trotter–Suzuki decomposition. The key difficulty in applying algorithms for general sparse Hamiltonian simulation to fermionic simulation is that a query, corresponding to computation of an entry of the Hamiltonian, is costly to compute. This means that the gate complexity would be much higher than quantified by the query complexity. While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most for simulating an studied application of N spin–orbital system. Turhcisenaptrparloraecsuhlitsiesxapnoanlgeonrtiitahllmy faster in the inverse precision and at least cubically faster in N than all previous approaches to chemistry simulation in the literature
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