Quantum complexity in gravity, quantum field theory, and quantum information science
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918204747546624 |
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| author | Baiguera, Stefano Balasubramanian, Vijay Caputa, Pawel Chapman, Shira Haferkamp, Jonas Heller, Michal P. Halpern, Nicole Yunger |
| author_facet | Baiguera, Stefano Balasubramanian, Vijay Caputa, Pawel Chapman, Shira Haferkamp, Jonas Heller, Michal P. Halpern, Nicole Yunger |
| contents | Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10753 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum complexity in gravity, quantum field theory, and quantum information science Baiguera, Stefano Balasubramanian, Vijay Caputa, Pawel Chapman, Shira Haferkamp, Jonas Heller, Michal P. Halpern, Nicole Yunger High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence. |
| title | Quantum complexity in gravity, quantum field theory, and quantum information science |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2503.10753 |