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Growth and collapse of subsystem complexity under random unitary circuits
by Jeongwan Haah, Douglas Stanford
Submission summary
| Authors (as registered SciPost users): | Jeongwan Haah |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2510.18805v2 (pdf) |
| Date submitted: | Dec. 19, 2025, 6:27 p.m. |
| Submitted by: | Jeongwan Haah |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity is defined as the minimum number of local quantum channels to generate a given state from a product state to a good approximation. In $1+1$d, we prove that the complexity of subsystems of length $\ell$ smaller than half grows linearly in time $T$ at least up to $T = \ell / 4$ but becomes zero after time $T = \ell /2$ in the limit of a large local dimension, while the complexity of the complementary subsystem of length larger than half grows linearly in time up to exponentially late times. Using holographic correspondence, we give some evidence that the state complexity of the smaller subsystem should actually grow linearly up to time $T = \ell/2$ and then abruptly decay to zero.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
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Strengths
2-Clearly states definitions and results for brickwork random circuits, which build upon prior work for pure state and unitary circuit complexity;
3-Describes a few other interesting results and conjectures, e.g. on maximal sets of pairwise distinguishable or nearly orthogonal mixed states and potential broader implications for quantum Shannon theory
Weaknesses
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