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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.18440 |
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| _version_ | 1866929513164701696 |
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| author | Richelli, Pietro Schoutens, Kareljan Zorzato, Alberto |
| author_facet | Richelli, Pietro Schoutens, Kareljan Zorzato, Alberto |
| contents | We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, hamiltonian limit $H_γ$ in closed form. We find that the fermionic symmetry pins $H_γ$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brick Wall Quantum Circuits with Global Fermionic Symmetry Richelli, Pietro Schoutens, Kareljan Zorzato, Alberto Quantum Physics We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, hamiltonian limit $H_γ$ in closed form. We find that the fermionic symmetry pins $H_γ$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits. |
| title | Brick Wall Quantum Circuits with Global Fermionic Symmetry |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.18440 |