Circuit Complexity in Topological Quantum Field Theory
- URL: http://arxiv.org/abs/2108.13427v3
- Date: Tue, 11 Oct 2022 15:58:00 GMT
- Title: Circuit Complexity in Topological Quantum Field Theory
- Authors: Josiah Couch, Yale Fan, Sanjit Shashi
- Abstract summary: Quantum circuit complexity has played a central role in advances in holography and many-body physics.
In a departure from standard treatments, we aim to quantify the complexity of the Euclidean path integral.
We argue that the pants decomposition provides a natural notion of circuit complexity within the category of 2-dimensional bordisms.
We use it to formulate the circuit complexity of states and operators in 2-dimensional topological quantum field theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum circuit complexity has played a central role in recent advances in
holography and many-body physics. Within quantum field theory, it has typically
been studied in a Lorentzian (real-time) framework. In a departure from
standard treatments, we aim to quantify the complexity of the Euclidean path
integral. In this setting, there is no clear separation between space and time,
and the notion of unitary evolution on a fixed Hilbert space no longer applies.
As a proof of concept, we argue that the pants decomposition provides a natural
notion of circuit complexity within the category of 2-dimensional bordisms and
use it to formulate the circuit complexity of states and operators in
2-dimensional topological quantum field theory. We comment on analogies between
our formalism and others in quantum mechanics, such as tensor networks and
second quantization.
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