Quantum complexity and localization in random quantum circuits

• URL: http://arxiv.org/abs/2409.03656v1
• Date: Thu, 5 Sep 2024 16:10:54 GMT
• Title: Quantum complexity and localization in random quantum circuits
• Authors: Himanshu Sahu, Aranya Bhattacharya, Pingal Pratyush Nath,
• Abstract summary: We study complexity in random quantum circuits with and without measurements. For $N$ qubits without measurements, the saturation value scales as $2N-1$, and the saturation time scales as $2N$. We observe that complexity acts as a novel probe of Anderson localization and many-body localization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum complexity has emerged as a central concept in diverse areas of physics, ranging from quantum computing to the theory of black holes. We perform a systematic study of complexity in random quantum circuits with and without measurements. We observe that complexity grows linearly before saturating to a constant value. For $N$ qubits without measurements, the saturation value scales as $2^{N-1}$, and the saturation time scales as $2^N$. This behaviour remains identical in the presence of random measurements with different probabilities, indicating that this notion of complexity is insensitive to the rate of measurement. We also study the behaviour of complexity in two variants of the random unitary floquet circuit, where we observe that complexity acts as a novel probe of Anderson localization and many-body localization.

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