Journal
NEW JOURNAL OF PHYSICS
Volume 18, Issue -, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/18/3/033032
Keywords
quantum algorithms; quantum simulation; electronic structure theory
Categories
Funding
- Australian Research Council [FT100100761, DP160102426]
- National Science Foundation [PHY-0955518]
- Office of Naval Research [N00014-16-1-2008]
- Air Force Office of Scientific Research [FA9550-12-1-0046]
- Australian Research Council [FT100100761] Funding Source: Australian Research Council
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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 O (N(5)t) 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.
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