论文标题
用于核结构的量子计算机上的差异最小化
Variance minimisation on a quantum computer for nuclear structure
论文作者
论文摘要
量子计算为模拟多体核系统开辟了新的可能性。随着多体系统中粒子的数量增加，如果相关的哈密顿量呈指数增加，则空间的大小。在使用经典计算方法时，在大型系统上执行计算时，这提出了挑战。通过使用量子计算机，由于量子计算机的Hilbert空间的增长方式随量子位（Qubits）的数量增长，因此可以克服这一困难。我们的目的是开发量子计算算法，这些算法可以再现和预测核结构，例如水平方案和水平密度。作为样本汉密尔顿人，我们使用Lipkin-Meshkov-Glick型号。我们在多数量系统上使用有效的汉密尔顿编码，并开发了一种算法，允许用能够在当今的量子计算机上实现的量子算法的全部激发光谱，并确定数量有限的量子计算机。我们的算法使用Hamiltonian的方差，$ \ langle H ^2 \ rangle -\ langle H \ rangle ^2 $，作为广泛使用的变异量子eigensolver（VQE）的成本函数。在这项工作中，我们提出了一种基于方差的方法，该方法使用降低的编码方法，使用量子计算机找到小核系统的激发态光谱。
Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This presents a challenge when performing calculations on large systems when using classical computing methods. By using a quantum computer, one may be able to overcome this difficulty thanks to the exponential way the Hilbert space of a quantum computer grows with the number of quantum bits (qubits). Our aim is to develop quantum computing algorithms which can reproduce and predict nuclear structure such as level schemes and level densities. As a sample Hamiltonian, we use the Lipkin-Meshkov-Glick model. We use an efficient encoding of the Hamiltonian onto many-qubit systems, and have developed an algorithm allowing the full excitation spectrum of a nucleus to be determined with a variational algorithm capable of implementation on today's quantum computers with a limited number of qubits. Our algorithm uses the variance of the Hamiltonian, $\langle H^2\rangle - \langle H\rangle ^2$, as a cost function for the widely-used variational quantum eigensolver (VQE). In this work we present a variance based method of finding the excited state spectrum of a small nuclear system using a quantum computer, using a reduced-qubit encoding method.
