Talks

Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds. In particular, we show how a k-qubit controlled-Z gate can be implemented by a transversal circuit on m-by-m^k Bacon-Shor codes and provide some estimates of its performance in terms of pseudo-thresholds and resource overhead.

The unrenormalised energy momentum tensor is both huge and fluctuating from point to point. Taking this seriously we (Qingdi Wang, Zhen Zhu, and myself) argue that the slow exponential expansion of the universe (on time scales of 10^10 years) comes from a very weak parametric resonance induced by the fluctuating energy mementum tensor on the rapidly fluctuating scale factor (on time scales much shorter than the Planck scale). We see only the slow exponential growth because we avarage over the scale factor squared.