Abstract
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient: it requires a number of experiments that is independent of the number of qubits and classical computational resources that scale only polynomially in . Here, we identify the requirements for efficient Monte Carlo estimation and the corresponding properties of the measurement operator basis when replacing two-level qubits by -level qudits. Our analysis illuminates the intimate connection between mutually unbiased measurements and the existence of unitaries that can be characterized efficiently. It allows us to propose a “hierarchy” of generalizations of the standard Pauli basis from qubits to qudits according to the associated scaling of resources required in Monte Carlo estimation of the average fidelity.
- Received 6 April 2014
- Revised 25 July 2014
DOI:https://doi.org/10.1103/PhysRevA.90.032317
©2014 American Physical Society