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arXiv · 1404.1608

Efficient Monte Carlo characterization of quantum operations for qudits

Giulia Gualdi·David Licht·Daniel M. Reich·Christiane P. Koch
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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 $n$ of qubits and classical computational resources that scale only polynomially in $n$. 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 $p$-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.

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Giulia Gualdi, David Licht, Daniel M. Reich, Christiane P. Koch. 2014-04-06. Efficient Monte Carlo characterization of quantum operations for qudits. https://doi.org/10.1103/physreva.90.032317

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