Quantum Circuits for Exact Unitary -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 quantum circuits that generate exact unitary t-designs for any t on
an arbitrary number of qubits. Our construction is inductive and is of practical use in small
systems. We then introduce at th-order generalization of randomized benchmarking (t-RB)
as an application of exact 2 t-designs. We particularly study the 2-RB in detail and show that …
physics. Despite its usefulness, only approximate implementations were known for general t.
In this paper, we provide quantum circuits that generate exact unitary t-designs for any t on
an arbitrary number of qubits. Our construction is inductive and is of practical use in small
systems. We then introduce at th-order generalization of randomized benchmarking (t-RB)
as an application of exact 2 t-designs. We particularly study the 2-RB in detail and show that …
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