TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.5.186
TI  - Circuit Complexity through phase transitions: Consequences in quantum state preparation
PY  - 2023/11/08
UR  - https://scipost.org/SciPostPhys.15.5.186
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 5
SP  - 186
A1  - Roca-Jerat, Sebastián
AU  - Sancho-Lorente, Teresa
AU  - Román-Roche, Juan
AU  - Zueco, David
AB  - In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.
ER  -

@Article{10.21468/SciPostPhys.15.5.186,
	title={{Circuit Complexity through phase transitions: Consequences in quantum state preparation}},
	author={Sebastián Roca-Jerat and Teresa Sancho-Lorente and Juan Román-Roche and David Zueco},
	journal={SciPost Phys.},
	volume={15},
	pages={186},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.5.186},
	url={https://scipost.org/10.21468/SciPostPhys.15.5.186},
}