Circuit Complexity through phase transitions: consequences in quantum
state preparation
- URL: http://arxiv.org/abs/2301.04671v3
- Date: Mon, 9 Oct 2023 19:34:26 GMT
- Title: Circuit Complexity through phase transitions: consequences in quantum
state preparation
- Authors: Sebasti\'an Roca-Jerat, Teresa Sancho-Lorente, Juan Rom\'an-Roche and
David Zueco
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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