Exponentially more precise quantum simulation of fermions in second quantization

By Ryan Babbush, Dominic W. Berry, I. Kivlichan, Annie Y. Wei, Peter J. Love, Alán Aspuru-Guzik. 2015

137 citations recorded by the source corpus.

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  ˜ ( 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/032cd30d9c4c2907b3f8e2c4ba13fab6b3336517

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum optimization using variational algorithms on near-term quantum devices (2017, background): “e challenge of eciently mapping the fermionic problem to the available qubit hardware is overcome. In fact, on a quantum device the natural way is to solve the chemical system in second quantization [3,4,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 26,27,28,29,30,31,32,33] formulated in terms ”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, methodology): “Importantly, our scheme does not increase the value of L or λ, which would usually be the case for most “on-the-fly” strategies for implementing PREPARE [23,42,59].”
Potential of quantum computing for drug discovery (2018, methodology): “The ﬁrst methods used the dynamical evolution under the target Hamiltonian, which was implemented using techniques such as Trotterization [8, 90, 92, 98–100, 103, 104] and approximate decomposition into a sum of unitaries using a Taylor expansion ( Taylorization ) [91, 174].”