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

Randomized benchmarking is a useful scheme for characterizing the noise in quantum system. However, it is insensitive to practical unitary errors. We propose a method of applying unitary t-design in quantum process tomography with local random unitary operator, which is constructed by a lot of nearest neighboring two-qubit unitary operators, to estimate average fidelity. This method converts the estimation of unitary errors to the analysis of pseudo-randomness about a set of unitary operators. We then give a upper bound of a diamond norm between arbitrary and invariant Haar distribution to form an \epsilon-approximate unitary t-design. We apply \epsilon-approximate unitary t-design to a large-scale quantum circuit to analysis the errors caused by practical implementation.