title: Quantum algorithm for universal implementation of the projective measurement of energy.
abstract: A projective measurement of energy (PME) on a quantum system is a quantum measurement determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by quantum tomography, but the time cost to achieve a given accuracy increases exponentially with the size of the quantum system. In this Letter, we improve the time cost by adapting quantum phase estimation, an algorithm designed for computational problems, to measurements on physical systems. We present a PME protocol without quantum tomography for Hamiltonians whose dimension and energy scale are given but which are otherwise unknown. Our protocol implements a PME to arbitrary accuracy without any dimension dependence on its time cost. We also show that another computational quantum algorithm may be used for efficient estimation of the energy scale. These algorithms show that computational quantum algorithms, with suitable modifications, have applications beyond their original context.
authors.affiliation: Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan.|Institute for Interdisciplinary Information Sciences, FIT Building 1-208, Tsinghua University, Beijing 100084, China.
authors.forename: Shojun
authors.initials: S
authors.lastname: Nakayama
authors.affiliation: Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan.|Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
authors.forename: Akihito
authors.initials: A
authors.lastname: Soeda
authors.affiliation: Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan.|Institute for Nano Quantum Information Electronics, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan.
authors.forename: Mio
authors.initials: M
authors.lastname: Murao