Built on

A. Bernamonti, F. Galli, J. Hernandez, R. C. Myers, S.-M. Ruan and J. Simón, The First Law of Complexity , 1903.04511
Original
1903
Earlier work this paper cites.
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory , Nucl. Phys. B424
1994
Earlier work this paper cites.
J. von Delft and H. Schoeller, Bosonization for beginners - refermionization for experts , Annalen der Physik 510
1998
Earlier work this paper cites.
Oxford University Press, Oxford, UK, 2003
T. Giamarchi, Quantum Physics in One Dimension · 2003
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
M. R. Dowling and M. A. Nielsen, The geometry of quantum computation , arXiv e-prints (Dec, 2006) quant–ph/0701004, [ quant-ph/0701004 ]
2006
Earlier work this paper cites.
Cambridge University Press, New York, NY, USA, 2006
I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement · 2006
Earlier work this paper cites.
F. M. Paula, T. R. de Oliveira and M. S. Sarandy, Geometric quantum discord through the schatten 1-norm , Phys. Rev. A 87
2013
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.
L. Susskind, Computational Complexity and Black Hole Horizons , Fortsch. Phys. 64
Original
2016
Earlier work this paper cites.

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2019

Circuit Complexity and 2D Bosonisation

Ge, Dongsheng, Policastro, Giuseppe

Understand

We consider the circuit complexity of free bosons, or equivalently free fermions, in 1+1 dimensions.

Motivated by the results of [1] and [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, we can consider the same state from both the bosonic and the fermionic perspectives.
In this way the discrepancy can be attributed to a different choice of the set of gates allowed in the circuit.
We study the effect in two classes of states: i) bosonic-coherent / fermionic-gaussian states; ii) states that are both bosonic- and fermionic-gaussian.

Built on

A. Bernamonti, F. Galli, J. Hernandez, R. C. Myers, S.-M. Ruan and J. Simón, The First Law of Complexity , 1903.04511
Original
1903
Earlier work this paper cites.
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory , Nucl. Phys. B424
1994
Earlier work this paper cites.
J. von Delft and H. Schoeller, Bosonization for beginners - refermionization for experts , Annalen der Physik 510
1998
Earlier work this paper cites.
Oxford University Press, Oxford, UK, 2003
T. Giamarchi, Quantum Physics in One Dimension · 2003
Earlier work this paper cites.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
M. R. Dowling and M. A. Nielsen, The geometry of quantum computation , arXiv e-prints (Dec, 2006) quant–ph/0701004, [ quant-ph/0701004 ]
2006
Earlier work this paper cites.
Cambridge University Press, New York, NY, USA, 2006
I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement · 2006
Earlier work this paper cites.
F. M. Paula, T. R. de Oliveira and M. S. Sarandy, Geometric quantum discord through the schatten 1-norm , Phys. Rev. A 87
2013
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.
L. Susskind, Computational Complexity and Black Hole Horizons , Fortsch. Phys. 64
Original
2016
Earlier work this paper cites.