This paper recasts quantum computation in terms of C*-algebras, states as functionals, and a new diagram calculus, re-deriving known results such as the Bloch sphere, Born rule, and Knill-Laflamme conditions without adding a working implementation.
Improved simulation of stabilizer circuits
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The Structure and Interpretation of Quantum Programs I: Foundations
This paper recasts quantum computation in terms of C*-algebras, states as functionals, and a new diagram calculus, re-deriving known results such as the Bloch sphere, Born rule, and Knill-Laflamme conditions without adding a working implementation.