Citation: Aharonov, Dorit, Alexei Kitaev, and Noam Nisan. "Quantum circuits with mixed states." Proceedings of the thirtieth annual ACM symposium on Theory of computing. 1998.
Web: https://arxiv.org/abs/quant-ph/9806029
Tags: Foundational, Universal-scheme
In this paper, Aharonov, Kitaev, and Nisan introduce a model for quantum computation based on mixed states. This allows for mid-circuit measurements, and for the analysis of noise and decoherence. Both of these special topics had been analyzed in the literature before, but it had been in an awkward way which didn't mesh well with the literal formalism. This paper fixed the problem with the right formalism.
Another key aspect of this paper is that it introduced the correct norms which allow for the effective bounding of noise throughout computations. This norm is known as the diamond norm. They give two definitions for this norm, and they show it satisfies nice properties.
One more application of this generalized model is that it allows for "subroutines", when you can apply one computation and then another. Previously this was not allowed because the output of subroutines is probabilistic and hence necessarily requires mixed states. The authors shown that subroutines do not give any extra computational power, as expected.