论文标题
正交-Ansatz VQE：在不修改成本功能的情况下找到激发态
Orthogonal-ansatz VQE: Locating excited states without modifying a cost-function
论文作者
论文摘要
通过最小化量子计算的成本功能，大多数文献中的大多数文献都集中在寻找物理系统的基态。当需要激发状态时，通常对成本功能进行修改，以包括其他术语，以确保与基态正交性。这通常需要额外的量子电路执行和测量，从而增加算法复杂性。在这里，我们提出了一个差异ANSATZ的设计策略，该策略在候选人激发状态下执行正交性，同时仍充分探索Hilbert Space的剩余子集。结果是一个激发的VQE求解器，该求解器的测量复杂度增加，以提高电路复杂性。随着量子误差缓解和校正变得更加精致，预计后者会变得更加优选。我们用三个不同的Ansatze展示了我们的方法，从一个简单的单体示例开始，然后再概括以适应所有量子位跨越的Hilbert空间，并限制了Hilbert Space遵守粒子数量保存。
Most literature in the Variational Quantum Eigensolver (VQE) algorithm focuses on finding the ground state of a physical system, by minimizing a quantum-computed cost-function. When excited states are required, the cost-function is usually modified to include additional terms ensuring orthogonality with the ground state. This generally requires additional quantum circuit executions and measurements, increasing algorithmic complexity. Here we present a design strategy for the variational ansatz which enforces orthogonality in candidate excited states while still fully exploring the remaining subset of Hilbert space. The result is an excited-state VQE solver which trades increasing measurement complexity for increasing circuit complexity. The latter is anticipated to become preferable as quantum error mitigation and correction become more refined. We demonstrate our approach with three distinct ansatze, beginning with a simple single-body example, before generalizing to accommodate the full Hilbert space spanned by all qubits, and a constrained Hilbert space obeying particle number conservation.
