Exponentially More Precise Algorithms for Quantum Simulation of Quantum Chemistry
Annie Y. Wei · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · 2016
In quantum chemistry, the "electronic structure problem" refers to the process of numerically solving Schrodinger's equation for a given molecular system. These calculations rank among the most CPU-intensive computations that are performed nowadays, yet they are also crucial to the design of new drugs and materials. The idea behind quantum simulation of quantum chemistry is that a quantum computer could perform such calculations in a manner that is exponentially more efficient than what a classical computer could accomplish. In fact, quantum simulation is quite possibly the application most naturally suited to a quantum computer. In this work we introduce novel algorithms for the simulation of quantum chemistry, algorithms that are exponentially more precise than previous algorithms in the literature. Previous algorithms are based on the Trotter-Suzuki decomposition and scale like the inverse of the desired precision, while our algorithms represent the first practical application of the recently developed truncated Taylor series approach, and they achieve scaling that is logarithmic in the inverse of the precision. We explore algorithms for both second-quantized and first-quantized encodings of the chemistry Hamiltonian, where the second-quantized encoding requires $\\mathcal{O}(N)$ qubits for an $N$ spin-orbital system, and the highly compressed first-quantized encoding requires $\\mathcal{O}(\\eta)$ qubits, where $\\eta<