A Normal Form for Single-Qudit Clifford+$T$ Operators
| Autor: | Amolak Ratan Kalra, Shiroman Prakash, Akalank Jain |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Quantum Physics
Efficient algorithm Dimension (graph theory) FOS: Physical sciences Statistical and Nonlinear Physics Prime (order theory) Theoretical Computer Science Electronic Optical and Magnetic Materials Combinatorics Operator (computer programming) Computer Science::Emerging Technologies Modeling and Simulation Signal Processing A-normal form Uniqueness Electrical and Electronic Engineering Quantum Physics (quant-ph) Time complexity Mathematics Quantum computer |
| Popis: | We propose a normal form for single-qudit gates composed of Clifford and $T$-gates for qudits of odd prime dimension $p\geq 5$. We prove that any single-qudit Clifford+$T$ operator can be re-expressed in this normal form in polynomial time. We also provide strong numerical evidence that this normal form is unique. Assuming uniqueness, we are able to use this normal form to provide an algorithm for exact synthesis of any single-qudit Clifford+$T$ operator with minimal $T$-count. 20 pages |
| Databáze: | OpenAIRE |
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