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Randomized benchmarking is a useful scheme for evaluation the averagefidelity of a noisy quantum circuit. However, it is insensitive to the unitaryerror. Here, we propose a method of randomized benchmarking in which a unitaryt-design is applied and by which the unitary error estimation can be convertedto analysis of pseudo-randomness on a set of unitary operators. We give a boundon the number of randomized benchmarking sequences, when performing a unitaryt-design on n-qubit d-dimensional system. By applying local random unitaryoperators, a decomposition of a unitary t-design, the bound is more practicalthan the previous bound for multi-qubit circuit. We also give a rigorous boundof a diamond norm between arbitrary and uniform distributions of a set ofunitary operators to form an \epsilon-approximate unitary t-design. It can beused to quantitatively analyze the corresponding average fidelity and errors ina large-scale quantum circuit.

Randomized Benchmarking Using Unitary t-Design for Average Fidelity Estimation of Practical Quantum Circuit