Japanese abstract
今回は、量子コンピューティングで最も神秘的な原理である「量子もつれ」を、自作モバイルアプリで探究する。その特徴は、１量子ビットを１台のモバイルフォンに割り当て、２つの量子間のもつれ関係を、（リアルタイム性を持つ）クラウドデータベースを経由して作り出すことである。遠く離れた２台のモバイルフォン間でこれを実験することにより、遠隔量子間のもつれ現象を模倣し、理解を深めることができる。これこそが、このアプリを開発した理由なのである。このような高度な機能の実現を容易にしてくれるMIT App Inventorに改めて感謝したい！
English abstract
I would like to explore the most mysterious principle in quantum computing, "quantum entanglement", using a mobile app I created. Its major feature is that one qubit (quantum bit) is assigned to one mobile phone, and the entanglement relationship between two qubits is created via a cloud database (with real-time capabilities). By experimenting with this between two mobile phones far apart, it is possible to mimic and better understand the phenomenon of entanglement between remote quanta. That is the reason why I developed this app. Thanks again to MIT App Inventor for making it easy to achieve such advanced functionality!
●Manipulate a single qubit
In a previous post, I described a mobile application for a single qubit. Even when limited to a single qubit, it is possible to create any quantum state using various quantum gates. Using this app, we were able to learn the basics of quantum superposition and measurement. However, to handle the most mysterious and important principle of quantum entanglement, we need at least two qubits. So, what method should we use to handle more than two qubits in mobile apps? This will be explained below.
●Explore quantum entanglement by assigning one qubit to one mobile phone
The new app targets a two-qubit system, with one qubit assigned to one mobile phone. Perhaps this method will reduce the complexity of the app. To mimic quantum entanglement, we need to consider multiple qubits as a system, rather than looking at each one individually. To do this, I decided to use another mobile phone to calculate the tensor product of all qubits. The measurement result of one quantum bit in an entangled state automatically and instantly changes the state of the other quantum bit. The real-time Cloud DB included in MIT App Inventor was useful in achieving this.
●Experimental example of quantum entanglement
(1)IBM Quantum Composer
Let's take the most basic quantum entanglement as an example. Fig.1 shows the case using IBM Quantum Composer. Prepare two qubits q0 and q1. First, apply the Hadamard gate H to q0 to create a superposition state, and leave q1 in its initial state (|0⟩). At this stage, q0 has no relationship with q1.
Next, if we apply a CNOT(0,1) gate to two qubits (control bit is q0, target bit is q1), both become entangled. Then, for example, when q0 is measured, the states of q0 and q1 will be either 00 or 11. In other words, the measurement result of q0 is immediately reflected in q1. This is quantum entanglement.
The mathematical model for this example problem is explained in detail in reference [1].
(2) Mimic quantum entanglement with three mobile phones
What was done with IBM Quantum was achieved with three mobile phones. As shown in Fig. 2(a), quantum bits qubit_0 and qubit_1 are each assigned to one mobile phone, and the third mobile phone performs control. Hadamard Gate H has already been applied to qubit_0. Once the quantum states (probability amplitudes) of qubit_0 and qubit_1 are stored in CloudDB, the third mobile phone calculates the tensor product to treat the two qubits as one system. As a result, four disks (corresponding to the four basis vectors) are displayed, and the probabilities and phases are shown. Fig.2(b) shows the actual screens of the three mobile phones on which this was performed.
The third mobile phone then applies the CNOT(0,1) gate to these two qubits. This creates a quantum entangled state as shown in Fig. 3(a). Fig.3(b) shows the actual screens of the three mobile phones at this time.
Once entangled in this way, the two mobile phones set up their Cloud DBs so that they can sense when the other has taken a measurement. As shown in Fig. 4(a), when it senses the other party's measurement, it immediately changes its own state based on the already stored quantum entanglement information. Fig.4(b) is the actual screen at that time.
(Note) This example is an entanglement in which two qubits are in the Bell state. In entanglement cases other than the Bell state, the measurement result of one does not necessarily definitively determine the other state. It depends on the nature of Entanglement at that time. Quantum entanglement generally refers to a correlation, but its strength varies.
●Summary
By developing an application that mimics quantum entanglement, I have gained a deeper understanding of the meaning of the tensor product of multiple qubits and the phenomenon of quantum entanglement. This time, I used CNOT(0,1), but you can also use CNOT(1,0) with the control bit and target bit reversed. Additionally, other gates can be combined to create quantum entanglement.
References
[1] Chris Bernhardt: Quantum Computing for Everyone, The MIT Press, 2020.
0 件のコメント:
コメントを投稿