论文标题
大型$ n $矩阵量子力学作为量子记忆
Large $N$ Matrix Quantum Mechanics as a Quantum Memory
论文作者
论文摘要
在本文中，我们探讨了使用大型$ N $矩阵量子力学模型来构建量子内存的可能性。首先，我们研究了测量的$ su（n）$矩阵谐波振荡器，并在其中编码量子信息。通过计算系统之间的共同信息和净化编码信息的参考，我们确定了过渡温度$ t_c $，在该温度下，在该温度下，在该温度下，在该温度下，在该温度下，将编码的量子信息免受热噪声的保护，以将内存时间缩放为$ n^2 $。相反，对于高于$ t_c $的温度，信息噪声很快就会破坏。其次，我们放宽了量规不变性的需求，并研究了仅具有全局对称性的矩阵谐波振荡器模型。最后，我们进一步放松了对称要求，并提出了一个由大量$ n^2 $ Qubits组成的模型，其交互源自大约$ su（n）$对称性。在这两个Ungaig模型中，我们发现可以使用能量惩罚模仿测量的效果，从而在记忆时间中产生相似的结果。最终的Qubit模型还有可能在实验室中实现。
In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large $N$ matrix quantum mechanics models. First, we investigate the gauged $SU(N)$ matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify a transition temperature, $T_c$, below which the encoded quantum information is protected from thermal noise for a memory time scaling as $N^2$. Conversely, for temperatures higher than $T_c$, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number $N^2$ of qubits, with interactions derived from an approximate $SU(N)$ symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.
