Jansen Nathan D, Loucks Matthew, Gilbert Scott, Fleming-Dittenber Corbin, Egbert Julia, Hunt Katharine L C
Department of Chemistry, Michigan State University, East Lansing, Michigan, 48824, USA.
Phys Chem Chem Phys. 2022 Mar 30;24(13):7666-7681. doi: 10.1039/d1cp05255a.
Using IBM's publicly accessible quantum computers, we have analyzed the entropies of Schrödinger's cat states, which have the form = (1/2) [|0 0 0⋯0〉 + |1 1 1⋯1〉]. We have obtained the average Shannon entropy of the distribution over measurement outcomes from 75 runs of 8192 shots, for each of the numbers of entangled qubits, on each of the quantum computers tested. For the distribution over N fault-free measurements on pure cat states, would approach one as N → ∞, independent of the number of qubits; but we have found that varies nearly linearly with the number of qubits . The slope of the number of qubits differs among computers with the same quantum volumes. We have developed a two-parameter model that reproduces the near-linear dependence of the entropy on the number of qubits, based on the probabilities of observing the output 0 when a qubit is set to |0〉 and 1 when it is set to |1〉. The slope increases as the error rate increases. The slope provides a sensitive measure of the accuracy of a quantum computer, so it serves as a quickly determinable index of performance. We have used tomographic methods with error mitigation as described in the qiskit documentation to find the density matrix and evaluate the von Neumann entropies of the cat states. From the reduced density matrices for individual qubits, we have calculated the entanglement entropies. The reduced density matrices represent mixed states with approximately 50/50 probabilities for states |0〉 and |1〉. The entanglement entropies are very close to one.
利用IBM的可公开访问的量子计算机，我们分析了薛定谔猫态的熵，其形式为 = (1/2) [|0 0 0⋯0〉 + |1 1 1⋯1〉]。对于测试的每台量子计算机上的每个纠缠量子比特数，我们从75次运行、每次8192次测量的测量结果分布中获得了平均香农熵 。对于纯猫态上N次无故障测量的分布，当N → ∞时， 会趋近于1，与量子比特数无关；但我们发现 几乎与量子比特数 呈线性变化。在具有相同量子体积的计算机中， 与量子比特数的斜率有所不同。我们基于当一个量子比特设置为|0〉时观察到输出0的概率以及当它设置为|1〉时观察到输出1的概率，开发了一个双参数模型，该模型再现了熵对量子比特数的近似线性依赖关系。斜率随着错误率的增加而增大。该斜率提供了对量子计算机精度的灵敏度量，因此它可作为一个可快速确定的性能指标。我们使用了qiskit文档中描述的带有误差缓解的断层扫描方法来找到密度矩阵 并评估猫态的冯·诺依曼熵。从单个量子比特的约化密度矩阵中，我们计算了纠缠熵。约化密度矩阵表示状态|0〉和|1〉概率近似为50/50的混合态。纠缠熵非常接近1。
