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When considering a sequent-style proof system for quantum programs, there arecertain elements of quantum mechanics that we may wish to capture, such asphase, dynamics of unitary transformations, and measurement probabilities.Traditional quantum logics which focus primarily on the abstract orthomodularlattice theory and structures of Hilbert spaces have not satisfactorilycaptured some of these elements. We can start from 'scratch' in an attempt toconceptually characterize the types of proof rules which should be in a systemthat represents elements necessary for quantum algorithms. This present workattempts to do this from the perspective of the quantum circuit model ofquantum computation. A sequent calculus based on single quantum circuits issuggested, and its ability to incorporate important conceptual and dynamicaspects of quantum computing is discussed. In particular, preserving therepresentation of phase helps illustrate the role of interference as a resourcein quantum computation. Interference also provides an intuitive basis for anon-monotonic calculus.

Sequent Calculus Representations for Quantum Circuits