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We propose a general-purpose quantum algorithm for preparing ground states ofquantum Hamiltonians from a given trial state. The algorithm is based ontechniques recently developed in the context of solving the quantum linearsystems problem [Childs,Kothari,Somma'15]. We show that, compared to algorithmsbased on phase estimation, the runtime of our algorithm is exponentially betteras a function of the allowed error, and at least quadratically better as afunction of the overlap with the trial state. We also show that our algorithmrequires fewer ancilla qubits than existing algorithms, making it attractivefor early applications of small quantum computers. Additionally, it can be usedto determine an unknown ground energy faster than with phase estimation if avery high precision is required.

Faster ground state preparation and high-precision ground energy estimation with fewer qubits