Spin-projection for quantum computation: A low-depth approach to strong correlation

Abstract

Although spin is a core property in fermionic systems, its symmetry can be easily violated in a variational simulation, especially when strong correlation plays a vital role therein. In this study, we will demonstrate that the broken spin-symmetry can be restored exactly in a quantum computer, with little overhead in circuits, while delivering additional strong correlation energy with the desired spin quantum number. The proposed scheme permits drastic reduction of a potentially large number of measurements required to ensure spin-symmetry by employing a superposition of only a few rotated quantum states. Our implementation is universal, simple, and, most importantly, straightforwardly applicable to any ansatz proposed to date.

arXiv comment9 pages, 7 figures, 2 tables

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• Challenges in the use of quantum computing hardware-efficient Ansatze in electronic structure theory
• Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective
• Filtering states with total spin on a quantum computer
• AGP-based unitary coupled cluster theory for quantum computers
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer
• Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing
• Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz
• Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems
• Simplified projection on total spin zero for state preparation on quantum computers