## Abstract

We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random access memory (qRAM) which allows for the efficient preparation of states that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to achieve poly-logarithmic dependence on precision.√ The time complexity of our algorithm, measured in terms of the circuit depth, is O(t N||H|| polylog(N, t||H||, 1/ɛ)), where t is the evolution time, N is the dimension of the system, and ɛ is the error in the final state, which we call precision. Our algorithm can be directly applied as a subroutine for unitary implementation and quantum linear systems solvers, achieving Õ(√N) dependence for both applications.

Original language | English (US) |
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Pages (from-to) | 597-615 |

Number of pages | 19 |

Journal | Quantum Information and Computation |

Volume | 20 |

Issue number | 7-8 |

State | Published - 2020 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- General Physics and Astronomy
- Computational Theory and Mathematics