A Critique of Topos Logic in Measurement-Based Quantum Computation
S. Diephuis (TU Delft - Electrical Engineering, Mathematics and Computer Science)
K.P. Hart – Mentor (TU Delft - Analysis)
D. Elkouss Coronas – Graduation committee member (TU Delft - Quantum Information and Software)
E. Coplakova – Graduation committee member (TU Delft - Mathematical Physics)
Miriam Blaauboer – Graduation committee member (TU Delft - QN/Blaauboer Group)
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Abstract
Topos theory and quantum mechanics are both known for having a logic that is different from ordinary logic. With this in mind, much work has been done on unifying these two fields. Loveridge, Dridi and Raussendorf apply this unification to measurement-based quantum computation [14], revealing links between computation, contextuality and the failure of the law of excluded middle in the topoi associated with each computation. We review their work, fill in gaps, follow their research suggestion and have some criticism. Our main original finding is a formula, in the formal language of the topos associated with a computation, that expresses that the computation is deterministic.