Circuit complexity and 2D bosonisation
- 9 Downloads
We consider the circuit complexity of free bosons and free fermions in 1+1 dimensions. Motivated by the results of [1, 2, 3] who found different behavior in the complexity of free bosons and fermions, in any dimension, we consider the 1+1 dimensional case where, thanks to the bosonisation equivalence of the Hilbert spaces, we can consider the same state from both the bosonic and the fermionic perspectives. This allows us to study the dependence of the complexity on the choice of the set of gates, which explains the discrepancy. We study the effect in two classes of states: i) bosonic-coherent / fermionic- gaussian states; ii) states that are both bosonic- and fermionic-gaussian. We consider the complexity relative to the ground state. In the first class, the different complexities can be related to each other by introducing a mode-dependent cost function in one of the descriptions. The differences in the second class are more important, in terms of the structure of UV divergencies and the overall behavior of the complexity.
KeywordsAdS-CFT Correspondence Effective Field Theories Field Theories in Lower Dimensions
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
- M.R. Dowling and M.A. Nielsen, The geometry of quantum computation, quant-ph/0701004.
- J. Watrous, Quantum computational complexity, arXiv:0804.3401.
- R. Cleve, An introduction to quantum complexity theory, quant-ph/9906111.