Exact and approximate unitary 2-designs and their application to fidelity estimation
- 6 July 2009
- journal article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 80 (1)
- https://doi.org/10.1103/physreva.80.012304
Abstract
We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an O(n)-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on n qubits with quantum circuits of size O(n) without requiring any ancilla qubits, thereby improving upon previous approaches.Comment: 7 pages, updating to version published in 200Keywords
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