Room 117

The resource theory of stabilizer quantum computation

Gautam Sharma

IMSc

Recent results on the non-universality of fault-tolerant
gate sets underline the
critical role of resource states, such as magic states, to power
scalable, universal
quantum computation. Here we develop a resource theory, analogous to the
theory of entanglement, that is relevant for fault-tolerant stabilizer
computa-
tion. We introduce two quantitative measures—monotones—for the amount
of non-stabilizer resource. As an application we give absolute bounds on the
efficiency of magic state distillation. One of these monotones is the
sum of the
negative entries of the discrete Wigner representation of a quantum
state, thereby
resolving a long-standing open question of whether the degree of negativity in
a quasi-probability representation is an operationally meaningful indicator of
quantum behavior.

Link to Ref- iopscience.iop.org/article/10.1088/1367-2630/16/1/013009