Transitions in Entanglement Complexity in Random Circuits

Abstract

Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The complexity of entanglement is at the root of the onset of quantum chaos, universal distribution of entanglement spectrum statistics, hardness of a disentangling algorithm and of the quantum machine learning of an unknown random circuit, and universal temporal entanglement fluctuations. In this paper, we numerically show how a crossover from a simple pattern of entanglement to a universal, complex pattern can be driven by doping a random Clifford circuit with $T$ gates. This work shows that quantum complexity and complex entanglement stem from the conjunction of entanglement and non-stabilizer resources, also known as magic.

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Cited by in corpus (29)

• Scalable measures of magic resource for quantum computers
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Complexity of frustration: a new source of non-local non-stabilizerness
• Stabilizer entropy dynamics after a quantum quench
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Unscrambling Quantum Information with Clifford decoders
• Stabilizer entropy in non-integrable quantum evolutions
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• Magic of quantum hypergraph states
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• Non-stabilizerness and entanglement from cat-state injection
• Optimal quantum reservoir learning in proximity to universality
• Limits of Clifford Disentangling in Tensor Network States
• High-expressibility Quantum Neural Networks using only classical resources