Higher-order quantum transformations of Hamiltonian dynamics
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of an...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.L012063 |
| _version_ | 1797210269543301120 |
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| author | Tatsuki Odake Hlér Kristjánsson Akihito Soeda Mio Murao |
| author_facet | Tatsuki Odake Hlér Kristjánsson Akihito Soeda Mio Murao |
| author_sort | Tatsuki Odake |
| collection | DOAJ |
| description | We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of any seed Hamiltonian with a bounded energy range consisting of a polynomial number of terms in system size, making use of only controlled-Pauli gates and time-correlated randomness. This algorithm is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. By way of example, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task. |
| first_indexed | 2024-04-24T10:07:55Z |
| format | Article |
| id | doaj.art-e19f730c08af4b37bc23c29b47d48b68 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:55Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-e19f730c08af4b37bc23c29b47d48b682024-04-12T17:40:47ZengAmerican Physical SocietyPhysical Review Research2643-15642024-03-0161L01206310.1103/PhysRevResearch.6.L012063Higher-order quantum transformations of Hamiltonian dynamicsTatsuki OdakeHlér KristjánssonAkihito SoedaMio MuraoWe present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of any seed Hamiltonian with a bounded energy range consisting of a polynomial number of terms in system size, making use of only controlled-Pauli gates and time-correlated randomness. This algorithm is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. By way of example, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task.http://doi.org/10.1103/PhysRevResearch.6.L012063 |
| spellingShingle | Tatsuki Odake Hlér Kristjánsson Akihito Soeda Mio Murao Higher-order quantum transformations of Hamiltonian dynamics Physical Review Research |
| title | Higher-order quantum transformations of Hamiltonian dynamics |
| title_full | Higher-order quantum transformations of Hamiltonian dynamics |
| title_fullStr | Higher-order quantum transformations of Hamiltonian dynamics |
| title_full_unstemmed | Higher-order quantum transformations of Hamiltonian dynamics |
| title_short | Higher-order quantum transformations of Hamiltonian dynamics |
| title_sort | higher order quantum transformations of hamiltonian dynamics |
| url | http://doi.org/10.1103/PhysRevResearch.6.L012063 |
| work_keys_str_mv | AT tatsukiodake higherorderquantumtransformationsofhamiltoniandynamics AT hlerkristjansson higherorderquantumtransformationsofhamiltoniandynamics AT akihitosoeda higherorderquantumtransformationsofhamiltoniandynamics AT miomurao higherorderquantumtransformationsofhamiltoniandynamics |