IBM Q 53 量子位元量子電腦的Mermin不等式實驗

Abstract

量子電腦與古典電腦的差別，古典電腦位元有0態與1態，n位元的狀態僅有2^n種，而量子電腦有糾纏態的性質與相位，因此量子電腦擁有更多的變化，能有近乎無限的可能性。因此本論文主要在研究的兩大主軸便是觀察IBM Q 53量子位元量子電腦上多組量子位元(N=2 至 N=7)的糾纏態特性及相位對糾纏態性質的影響。第一部分已在Quantum Engineering發表，是IBM Rochester 上多組量子位元（N = 2 至 N = 7）的類 GHZ狀態，彼此之間對Mermin正交多項式的最大違反值與解析結果進行比較。另個實驗是利用不同相位角的兩個量子位元對相位軌跡分析，研究了在類GHZ狀態下對改良 Mermin 的多項式的影響。 我們第一部分的結果表明，當 N ≤ 4 時，IBM Rochester 的糾纏性質是相當好的，而對於更長的糾纏鏈，糾纏只對某些特殊的連接有效。另個實驗相位軌跡分析，大部分軌跡皆為穩定的圓形軌跡，而在特定情況下類GHZ狀態會與其激發態會產生死灰復燃的演變。

The difference between a quantum computer and a classical computer is that the classical computer one bit has zero and one states with only 2^n states for n bits, while the quantum computer has the nature that phase and entanglement, so the quantum computer has more variations and can have nearly infinite possibilities. Therefore, the two principal axes of this paper are to observe the entangled state characteristics of multiple qubits (N=2 to N=7) on the IBM Q 53 qubit quantum computer and the influence of phase on the entangled state properties. The first part, which has been published in Quantum Engineering, is the GHZ-like states of multiple qubits (N = 2 to N = 7) in IBM Rochester, and compares the maximum violation values of Mermin orthogonal polynomials with the analytic results among each other. In another experiment, two qubits with different phase angles were used to analyze the phase trajectory, and the effect on the improved Mermin polynomial in the GHZ-like states was studied. Our results in the first part show that the entanglement nature of IBM Rochester is fairly good when N ≤ 4, while for longer chains, entanglement is only valid for certain special connections. In the other experimental phase trajectory analysis, most of the trajectories are stable circular trajectories, and under certain circumstances the GHZ-like state and its excited state will produce the evolution of resurgence and reignition.