A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.
Complexity in One- and Two-Qubit Systems
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abstract
We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution operators grow linearly with time, at least initially, for both the one- and two-qubit cases. The precursor operators display switchback-effect-like behavior provided we choose our cost factors so that the resulting complexity geometry is negatively curved.
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CFT Complexity and Penalty Factors
A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.