Hamiltonian Simulation by Qubitization
Name
q-2019-07-12-163.pdf
Description
Published version
Size
947.63 KB
Format
Adobe PDF
Checksum (MD5)
c152945a17e3b5c165d4e0b05295b106
Author(s)
Low, Guang Hao
Chuang, Isaac L.
Date Issued
July 2019
Journal
Quantum
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Citation
Low, Guang Hao and Isaac L. Chuang. "Hamiltonian Simulation by Qubitization." Quantum 3 (July 2019): 163 © Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Version
Final published version
Abstract
We present the problem of approximating the time-evolution operator e-iHt to error ϵ, where the Hamiltonian H = ((G|⊗I)U (|Gi⊗I) is the projection of a unitary oracle U onto the state |Gi created by another unitary oracle. Our algorithm solves this with a query complexity O ( t + log(1/ϵ) ) to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are d-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where H is a density matrix. A key technical result is 'qubitization', which uses the controlled version of these oracles to embed any H in an invariant SU(2) subspace. A large class of operator functions of H can then be computed with optimal query complexity, of which e-iHt is a special case.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.22331/q-2019-07-12-163
