Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets

• URL: http://arxiv.org/abs/2502.08962v1
• Date: Thu, 13 Feb 2025 04:55:51 GMT
• Title: Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets
• Authors: Guorui Zhu, Joel Bierman, Jianfeng Lu, Yingzhou Li,
• Abstract summary: This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of $O(n)$ with about $n$ ancilla qubits. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry.
• Score: 4.289769713465494
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• Abstract: 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.

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