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Quantum Circuits for Exact Unitary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>t</mml:mi></mml:math> -Designs and Applications to Higher-Order Randomized Benchmarking
A unitary $t$-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general $t$. In this paper, we provide for the first time quantum circuits that generate exact unitary $t$-designs for any $t$ on an arbitrary number of qubits. …