Construction of Antisymmetric Variational Quantum States with Real-Space Representation

• URL: http://arxiv.org/abs/2306.08434v1
• Date: Wed, 14 Jun 2023 11:11:31 GMT
• Title: Construction of Antisymmetric Variational Quantum States with Real-Space Representation
• Authors: Takahiro Horiba, Soichi Shirai, Hirotoshi Hirai
• Abstract summary: A major difficulty in first quantization with a real-space basis is state preparation for many-body electronic systems. We provide a design principle for constructing a variational quantum circuit to prepare an antisymmetric quantum state. We implement the variational quantum eigensolver to obtain the ground state of a one-dimensional hydrogen molecular system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Electronic state calculations using quantum computers are mostly based on second quantization, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is first quantization, which is expected to achieve smaller scaling with respect to the number of basis functions than second quantization. Among basis functions, a real-space basis is an attractive option for quantum dynamics simulations in the fault-tolerant quantum computation (FTQC) era. A major difficulty in first quantization with a real-space basis is state preparation for many-body electronic systems. This difficulty stems from of the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit. In the present paper, we provide a design principle for constructing a variational quantum circuit to prepare an antisymmetric quantum state. The proposed circuit generates the superposition of exponentially many Slater determinants, that is, a multi-configuration state, which provides a systematic approach to approximating the exact ground state. We implemented the variational quantum eigensolver (VQE) to obtain the ground state of a one-dimensional hydrogen molecular system. As a result, the proposed circuit well reproduced the exact antisymmetric ground state and its energy, whereas the conventional variational circuit yielded neither an antisymmetric nor a symmetric state. Furthermore, we analyzed the many-body wave functions based on quantum information theory, which illustrated the relation between the electron correlation and the quantum entanglement.

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