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.
Highlights
Recent advancements in quantum devices have created widespread interest in the development of efficient quantum algorithms
Among the several candidates for |ψ, the unitary coupled cluster with singles and doubles (UCCSD)[3,4,5] Ansatz has been extensively used as an entangler in the preparation of a trial state from HartreeFock (HF) |, as shown by the following equation:
We have shown that numerically exact spinprojection can be made feasible within the framework of variational quantum eigensolver (VQE)
Summary
Recent advancements in quantum devices have created widespread interest in the development of efficient quantum algorithms. More flexible Ansätze have been proposed, where, in the product of exponential operators, the same anti-Hermitian excitations may be repeated albeit with different amplitudes [11,12] To our knowledge, these recent studies on unitary coupled cluster (UCC) and its variants have vastly neglected the spin properties of the obtained solutions. HF (RHF) reference, UCC amplitudes can spontaneously violate spin symmetry, thereby variationally lowering its energy as opposed to traditional coupled cluster (CC). This often happens especially in strongly correlated systems, such as bond dissociations, as will be demonstrated below.
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