State complexity and phase identification in adaptive quantum circuits
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914049723203584 |
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| author | Liu, Guoding Chen, Junjie Ma, Xiongfeng |
| author_facet | Liu, Guoding Chen, Junjie Ma, Xiongfeng |
| contents | Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states and topological phases at constant depths. However, the ancilla overhead for preparing arbitrary states can be prohibitive, raising a fundamental question: which states can be efficiently realized with limited ancilla and low depth? Addressing this question requires a rigorous quantitative characterization of state complexity, or the minimum depth and ancillas, to realize a state in adaptive circuits. In this work, we tackle this problem by introducing two properties of quantum states: state weight and anti-shallowness, connected to the correlation range and correlation strength within a state, respectively. We prove that these quantities are bounded under limited circuit resources, thereby providing rigorous bounds on the approximate complexity of state preparation and gate implementation. Illustrative examples include the GHZ state, W state, QLDPC code states, and the Toffoli gate. Besides complexity, we show that states within the same quantum phase, defined by a set of quantum states connected with constant-depth circuits, must share the same scaling of weight or anti-shallowness. This establishes these quantities as indicators of quantum phases and their essential roles in many-body physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | State complexity and phase identification in adaptive quantum circuits Liu, Guoding Chen, Junjie Ma, Xiongfeng Quantum Physics Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states and topological phases at constant depths. However, the ancilla overhead for preparing arbitrary states can be prohibitive, raising a fundamental question: which states can be efficiently realized with limited ancilla and low depth? Addressing this question requires a rigorous quantitative characterization of state complexity, or the minimum depth and ancillas, to realize a state in adaptive circuits. In this work, we tackle this problem by introducing two properties of quantum states: state weight and anti-shallowness, connected to the correlation range and correlation strength within a state, respectively. We prove that these quantities are bounded under limited circuit resources, thereby providing rigorous bounds on the approximate complexity of state preparation and gate implementation. Illustrative examples include the GHZ state, W state, QLDPC code states, and the Toffoli gate. Besides complexity, we show that states within the same quantum phase, defined by a set of quantum states connected with constant-depth circuits, must share the same scaling of weight or anti-shallowness. This establishes these quantities as indicators of quantum phases and their essential roles in many-body physics. |
| title | State complexity and phase identification in adaptive quantum circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.17014 |