Reducing Entanglement with Physically Inspired Fermion-To-Qubit Mappings

Abstract

In electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step from the problem of fermions into a problem of qubits. This work introduces a physically inspired method for constructing mappings that significantly simplify entanglement requirements when one is simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground-states of small molecules and observe an enhanced performance when compared with classical and quantum variational approaches from prior research using conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <a:mi>LiH</a:mi> </a:math> , <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <d:msub> <d:mrow> <d:mi mathvariant="normal">H</d:mi> </d:mrow> <d:mn>2</d:mn> </d:msub> </d:math> , <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <h:mo stretchy="false">(</h:mo> <h:msub> <h:mrow> <h:mi mathvariant="normal">H</h:mi> </h:mrow> <h:mn>2</h:mn> </h:msub> <h:msub> <h:mo stretchy="false">)</h:mo> <h:mn>2</h:mn> </h:msub> </h:math> , <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <n:msubsup> <n:mrow> <n:mi mathvariant="normal">H</n:mi> </n:mrow> <n:mn>4</n:mn> <n:mo>≠</n:mo> </n:msubsup> </n:math> stretching, and benzene’s <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <r:mi>π</r:mi> </r:math> system using the RY hardware-efficient ansatz. In addition, our mappings also provide an enhanced ground-state simulation performance in the density matrix renormalization group algorithm for the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <u:msub> <u:mrow> <u:mi mathvariant="normal">N</u:mi> </u:mrow> <u:mn>2</u:mn> </u:msub> </u:math> molecule. Published by the American Physical Society 2024

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