TY - JOUR

T1 - A quantum algorithm for simulating non-sparse hamiltonians

AU - Wang, Chunhao

AU - Wossnig, Leonard

N1 - Funding Information:
We thank Richard Cleve and Simone Severini for the discussion and comments on this project. We also thank anonymous reviewers for their valuable suggestions and comments on this paper. CW acknowledges financial support by a David R. Cheriton Graduate Scholarship. LW acknowledges financial support by the Royal Society through a Research Fellow Enhancement Award.
Publisher Copyright:
© Rinton Press.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85086333644

SN - 1533-7146

VL - 20

SP - 597

EP - 615

JO - Quantum Information and Computation

JF - Quantum Information and Computation

IS - 7-8

ER -