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 circui...
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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 a tth-order generalization of randomized benchmarking (t-RB) as an application of exact 2t-designs. We particularly study the 2-RB in detail and show that it reveals self-adjointness of quantum noise, a metric related to the feasibility of quantum error correction (QEC). We numerically demonstrate that the 2-RB in one- and two-qubit systems is feasible, and experimentally characterize background noise of a superconducting qubit by the 2-RB. It is shown from the experiment that interactions with adjacent qubits induce the noise that may result in an obstacle toward a realization of QEC.
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 ...
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To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a f...
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Quantum simulation is one of the key applications of quantum computing, which accelerates research and development in the fields such as chemistry and material science. The recent development of noisy intermediate-sca...
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