Efficient quantum circuits for diagonal unitaries without ancillas
The accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but generally require ancilla registers, which can dominate the qu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/3/033040 |
| _version_ | 1797751481927991296 |
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| author | Jonathan Welch Daniel Greenbaum Sarah Mostame Alan Aspuru-Guzik |
| author_facet | Jonathan Welch Daniel Greenbaum Sarah Mostame Alan Aspuru-Guzik |
| author_sort | Jonathan Welch |
| collection | DOAJ |
| description | The accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but generally require ancilla registers, which can dominate the qubit resources. In this paper, we give a simple way to construct efficient circuits for diagonal unitaries without ancillas, using a correspondence between Walsh functions and a basis for diagonal operators. This correspondence reduces the problem of constructing the minimal-depth circuit within a given error tolerance, for an arbitrary diagonal unitary ${{e}^{if\left( \hat{x}\, \right)}}$ in the $\left| x \right\rangle$ basis, to that of finding the minimal-length Walsh-series approximation to the function f ( x ). We apply this approach to the quantum simulation of the classical Eckart barrier problem of quantum chemistry, demonstrating that high-fidelity quantum simulations can be achieved with few qubits and low depth. |
| first_indexed | 2024-03-12T16:49:12Z |
| format | Article |
| id | doaj.art-093d0267bc8344b1af69a275af34e4b3 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:49:12Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-093d0267bc8344b1af69a275af34e4b32023-08-08T11:22:08ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116303304010.1088/1367-2630/16/3/033040Efficient quantum circuits for diagonal unitaries without ancillasJonathan Welch0Daniel Greenbaum1Sarah Mostame2Alan Aspuru-Guzik3Department of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USAMIT Lincoln Laboratory , 244 Wood Street, Lexington, MA 02420, USADepartment of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USADepartment of Chemistry and Chemical Biology, Harvard University , Cambridge, MA 02138, USAThe accurate evaluation of diagonal unitary operators is often the most resource-intensive element of quantum algorithms such as real-space quantum simulation and Grover search. Efficient circuits have been demonstrated in some cases but generally require ancilla registers, which can dominate the qubit resources. In this paper, we give a simple way to construct efficient circuits for diagonal unitaries without ancillas, using a correspondence between Walsh functions and a basis for diagonal operators. This correspondence reduces the problem of constructing the minimal-depth circuit within a given error tolerance, for an arbitrary diagonal unitary ${{e}^{if\left( \hat{x}\, \right)}}$ in the $\left| x \right\rangle$ basis, to that of finding the minimal-length Walsh-series approximation to the function f ( x ). We apply this approach to the quantum simulation of the classical Eckart barrier problem of quantum chemistry, demonstrating that high-fidelity quantum simulations can be achieved with few qubits and low depth.https://doi.org/10.1088/1367-2630/16/3/033040walsh functionquantum simulationquantum computationfourier methods |
| spellingShingle | Jonathan Welch Daniel Greenbaum Sarah Mostame Alan Aspuru-Guzik Efficient quantum circuits for diagonal unitaries without ancillas New Journal of Physics walsh function quantum simulation quantum computation fourier methods |
| title | Efficient quantum circuits for diagonal unitaries without ancillas |
| title_full | Efficient quantum circuits for diagonal unitaries without ancillas |
| title_fullStr | Efficient quantum circuits for diagonal unitaries without ancillas |
| title_full_unstemmed | Efficient quantum circuits for diagonal unitaries without ancillas |
| title_short | Efficient quantum circuits for diagonal unitaries without ancillas |
| title_sort | efficient quantum circuits for diagonal unitaries without ancillas |
| topic | walsh function quantum simulation quantum computation fourier methods |
| url | https://doi.org/10.1088/1367-2630/16/3/033040 |
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