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Geometric constructions of generalized dual-unitary circuits from biunitarity
by Michael A. Rampp, Suhail A. Rather, Pieter W. Claeys
Submission summary
| Authors (as registered SciPost users): | Michael Alexander Rampp |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2411.07783v2 (pdf) |
| Date accepted: | May 19, 2025 |
| Date submitted: | March 19, 2025, 12:47 p.m. |
| Submitted by: | Michael Alexander Rampp |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We present a general framework for constructing solvable lattice models of chaotic many-body quantum dynamics with multiple unitary directions using biunitary connections. We show that a network of biunitary connections on the Kagome lattice naturally defines a multi-unitary circuit, where three `arrows of time' directly reflect the lattice symmetry. These models unify various constructions of hierarchical dual-unitary and triunitary gates and present new families of models with solvable correlations and entanglement dynamics. Using multilayer constructions of biunitary connections, we additionally introduce multilayer circuits with monoclinic symmetry and higher level hierarchical dual-unitary solvability and discuss their (non-)ergodicity. Our work demonstrates how different classes of solvable models can be understood as arising from different geometric structures in spacetime.
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
Author comments upon resubmission
please find attached our resubmission of "Geometric constructions of generalized dual-unitary circuits from biunitarity" by Michael Rampp, Suhail Rather, and Pieter Claeys.
We are grateful to the referees for their constructive and helpful suggestions. We have incorporated these suggestions into the revised manuscript.
Regards,
Michael Rampp (on behalf of all authors)
List of changes
- changed wording of introduction and added examples of pathological behavior of dual-unitary circuits
- Sec. 2.2: added references to literature
- Sec. 2.2: added an expanded introduction to the Schmidt rank
- Sec. 2.3: added explicit discussion of vertical and horizontal unitarity of several biunitary connections with graphical and algebraic equations, including explanation of the necessity of shaded regions
- Sec. 3.4: added a motivating paragraph contextualizing the various constructions
- Sec. 3.4.5: included graphical indication of bipartition in Eq. (75)
- Sec. 4: improved motivation of tensor product constructions
- Sec. 4.1: added explicit examples of multilayer complex Hadamard matrices that can be used to construct multilayer circuits
- Sec. 4.2: added Fig. 2 depicting the circuit diagram of a multilayer circuit
- Sec. 4.2 and 4.3: added algebraic expressions for multilayer gates
Published as SciPost Phys. 18, 182 (2025)
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