Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits
Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant att...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/2/387 |
| _version_ | 1797621117650731008 |
|---|---|
| author | Anstasiia S. Nikolaeva Evgeniy O. Kiktenko Aleksey K. Fedorov |
| author_facet | Anstasiia S. Nikolaeva Evgeniy O. Kiktenko Aleksey K. Fedorov |
| author_sort | Anstasiia S. Nikolaeva |
| collection | DOAJ |
| description | Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed <i>N</i>-qubit Toffoli gate decomposition has <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula> asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others. |
| first_indexed | 2024-03-11T08:52:14Z |
| format | Article |
| id | doaj.art-cca7a511bab9477a8e9534474269311c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T08:52:14Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-cca7a511bab9477a8e9534474269311c2023-11-16T20:24:47ZengMDPI AGEntropy1099-43002023-02-0125238710.3390/e25020387Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with QuditsAnstasiia S. Nikolaeva0Evgeniy O. Kiktenko1Aleksey K. Fedorov2Russian Quantum Center, Skolkovo, Moscow 121205, RussiaRussian Quantum Center, Skolkovo, Moscow 121205, RussiaRussian Quantum Center, Skolkovo, Moscow 121205, RussiaQubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed <i>N</i>-qubit Toffoli gate decomposition has <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula> asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.https://www.mdpi.com/1099-4300/25/2/387quditsququintsToffoli gatequbit-to-qudit mappingGrover’s algorithm |
| spellingShingle | Anstasiia S. Nikolaeva Evgeniy O. Kiktenko Aleksey K. Fedorov Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits Entropy qudits ququints Toffoli gate qubit-to-qudit mapping Grover’s algorithm |
| title | Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits |
| title_full | Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits |
| title_fullStr | Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits |
| title_full_unstemmed | Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits |
| title_short | Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits |
| title_sort | generalized toffoli gate decomposition using ququints towards realizing grover s algorithm with qudits |
| topic | qudits ququints Toffoli gate qubit-to-qudit mapping Grover’s algorithm |
| url | https://www.mdpi.com/1099-4300/25/2/387 |
| work_keys_str_mv | AT anstasiiasnikolaeva generalizedtoffoligatedecompositionusingququintstowardsrealizinggroversalgorithmwithqudits AT evgeniyokiktenko generalizedtoffoligatedecompositionusingququintstowardsrealizinggroversalgorithmwithqudits AT alekseykfedorov generalizedtoffoligatedecompositionusingququintstowardsrealizinggroversalgorithmwithqudits |