Modern adiabatic quantum computers (AQC) are already used to solve difficult
combinatorial optimisation problems in various domains of science. Currently,
only a few applications of AQC in computer vision have been demonstrated. We
review AQC and derive a new algorithm for correspondence problems on point sets
suitable for execution on AQC. Our algorithm has a subquadratic computational
complexity of the state preparation. Examples of successful transformation
estimation and point set alignment by simulated sampling are shown in the
systematic experimental evaluation. Finally, we analyse the differences in the
solutions and the corresponding energy values.

研究使用 AQC 求解对应问题及点集对齐问题的新算法，并通过实验评估其解决方案及相应能量值的差异。

关于点集对应问题的量子计算方法

A Quantum Computational Approach to Correspondence Problems on Point  Sets

We show that the NP-hard quadratic unconstrained binary optimization (QUBO)
problem on a graph $G$ can be solved using an adiabatic quantum computer that
implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding
of $G$ in the quantum hardware graph $U$. There are two components to this
reduction: embedding and parameter setting. The embedding problem is to find a
minor-embedding $G^{emb}$ of a graph $G$ in $U$, which is a subgraph of $U$
such that $G$ can be obtained from $G^{emb}$ by contracting edges. The
parameter setting problem is to determine the corresponding parameters, qubit
biases and coupler strengths, of the embedded Ising Hamiltonian. In this paper,
we focus on the parameter setting problem. As an example, we demonstrate the
embedded Ising Hamiltonian for solving the maximum independent set (MIS)
problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system.
We close by discussing several related algorithmic problems that need to be
investigated in order to facilitate the design of adiabatic algorithms and AQC
architectures.

本文使用少数嵌入和参数设置，通过实现 Ising 自旋 - 1/2 哈密顿量的绝热量子计算机，证明了在量子硬件图 U 中，可以解决图 G 上的 NP-hard 二次无约束二进制优化问题。