Magic state distillation is a key subroutine in many leading schemes for achieving a fault tolerant quantum computer. However, despite significant recent progress, the overhead of state-of-the-art protocols for magic distillation is still eyewatering. This poses the natural question: can we do better, even in principle?
In this talk I’ll introduce the basics of majorization theory – an abstract mathematical toolset with a wide range of applications spanning economics [*] and quantum theory alike. I’ll discuss some recent work where we apply the machinery of majorization to quasiprobability representations of magic states to obtain entropic constraints on the achievable overhead of magic distillation. These constraints give rise to fundamental trade-off relations on the code parameters appearing in practical distillation protocols. From a more foundational perspective, in this picture the processing of magic states under stabilizer circuits (a universal model for quantum computing) can be viewed as akin to classical statistical mechanics with the appearance of negative entropies. In this context, we find that negative entropy is equivalent to Wigner negativity, and thus constitutes a necessary ingredient for quantum computational speed-up.
[*] https://en.wikipedia.org/wiki/Gini_coefficient
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