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We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending singleand multi-qubit URB to single-and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.Quantum computing and quantum communication typically focuse on quantum information encoded and processed with quantum bit (qubit) strings, but replacing qubits by higher-dimensional qudit strings [1,2] can be advantageous [3] for quantum simulation [4], quantum algorithms [5-7], quantum error correction [8-10], universal optics-based quantum computation [11], quantum communication [12, 13] and fault-tolerant quantum computation [14, 15]. Qudit quantum-information process could reduce space requirements and exploit natural properties such as orbital angular momentum for photons [16], superconductors [4] and neutral atoms [17]. Specifically, quantum computing on higher-dimensional systems can be more efficient than on qubits [7,14,18]. Ultimate success of quantum computing, both qubitand qudit-based, depends on being scalable, which, in turn, requires components meeting fault-tolerance conditions [19].Unitary-gate randomized benchmarking (URB) is the preferred technique to characterize unitary-gate performance due to its efficiency [20,21], which is robust against state-preparation-and-measurement (SPAM) errors and exponentially superior to the alternative of quantum process tomography (QPT) [22,23]. URB estimates average fidelity between real and ideal implementation of all 24 Clifford gates in C 2 , which normalizes the Pauli group

We address the teleportation of single- and two-qubit quantum states, parametrized by weight θ and phase ϕ parameters, in the presence of the Unruh effect experienced by a mode of a free Dirac field. We investigate the effects of the partial measurement (PM) and partial measurement reversal (PMR) on the quantum resources and quantum Fisher information (QFI) of the teleported states. In particular, we discuss the optimal behaviour of the QFI, quantum coherence (QC) as well as fidelity with respect to the PM and PMR strength and examine the effect of the Unruh noise on optimal estimation. It is found that, in the single-qubit scenario, the PM (PMR) strength at which the optimal estimation of the phase parameter occurs is the same as the PM (PMR) strength with which the teleportation fidelity and the QC of the teleported single-qubit state reaches its maximum value. On the other hand, generalizing the results to two-qubit teleportation, we find that the encoded information in the weight parameter is better protected against the Unruh noise in two-qubit teleportation than in the one-qubit scenario. However, extraction of information encoded in the phase parameter is more efficient in single-qubit teleportation than in the two-qubit version.