## John Preskill

*The cost of quantum fault tolerance*
A classical circuit can be accurately simulated with a fault-tolerant
circuit constructed from noisy classical gates. Similarly, a quantum
circuit can be accurately simulated with a fault-tolerant circuit
constructed from noisy quantum gates. But what is the cost of the
simulation? Classically, the fault-tolerant simulation of an ideal
circuit with size L and depth D can be achieved by a noisy circuit of
size O(L\log(L)) and depth O(D). I will show, using topological codes in
four or more spatial dimensions, that the fault-tolerant simulation of
an ideal quantum circuit with size L and depth D can be achieved by a
noisy quantum circuit with size O(L\polylog(L)) and depth
O(D\log\log(L)). This depth blow-up improves what had been established
previously using concatenated quantum codes.
This is joint work with Charlene Ahn.