Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916611952214016 |
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| author | Zhu, Guorui Bierman, Joel Lu, Jianfeng Li, Yingzhou |
| author_facet | Zhu, Guorui Bierman, Joel Lu, Jianfeng Li, Yingzhou |
| contents | This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of $O(n)$ with about $n$ ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets Zhu, Guorui Bierman, Joel Lu, Jianfeng Li, Yingzhou Quantum Physics This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of $O(n)$ with about $n$ ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry. |
| title | Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.08962 |