Physical Principles of Bloch Sphere

Bloch Sphere is a 3D ball. Each point on the sphere corresponds to a quantum state (Points in the sphere are called mixed states). A single qubit can be represented as a 2*1 complex vector. After extracting a global phase, the 2*1 complex vector can be represented by a 3*1 real vector. So, it is complete to represent a quantum state by a 3-D sphere.

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In classical computer, the state of bits can be 0 or 1. However, for a quantum bit (or qubit), it will be at a state of 0 or 1, or a superposition state of 0 and 1. It means that the state of 0 and 1 can exist in a qubit at the same time. In the representation of a Bloch Sphere, (0, 0, 1) is the state of 0 and (0, 0, -1) is the state of 1. For a classical bit, these 2 states are complete. However, for a qubit, it can be all the points on the sphere. For example, the points (1, 0, 0) and (0, 1, 0) are two superposition states. The different points on the sphere mean the different amplitudes of 0 and 1.

In the game Bloch Sphere, you need to choose different single-qubit quantum gates (operations) to move the yellow point (start point) to the white point (goal point) to win. Surely it will need some 3D imagination. Now, just try it!

Physical Principles in Quantum Escape

Quantum Escape involves quantum entanglement, multi-qubit operation, and quantum teleportation. After passing this game, you will understand how quantum computer works.

Level 1: Find the Schrödinger’s Cat

In the first level we consider a coin as a 2-level quantum system. The coin’s up and down stands for the quantum state of 0 and 1, respectively. First, we assume two coins are in the entanglement state of 01 and 10. We randomly choose a cup in which we do not know the state of coin in it before opening the cup, then we open one of it (it is called measurement in quantum computing) and we can know about the state of coin in another cup. This will not be limited by the distance of two coins. In this level, we aim to show you the characteristics of quantum entanglement.

Level 2: Single-qubit Operation

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In quantum algorithm, we already know that all quantum gates can be decomposed into a series of CNOT gates and single-qubit operations like X and H. In level 2 and level 3, we need to know about what’s the mean of quantum operations. And we can choose suitable quantum gate to change the wave function on the key into what the password told you. And then you pass!

Level 3: Multi-qubit Operation and Multi-Step Operations

In level 3 you need to know how to prepare a Bell’s pair. We already gave you some tips in the clue.

Level 4: Quantum Teleportation

First, you need to find the qubits to operate. Second, you need to find the order of qubits corresponding to the quantum circuit.

The principles of quantum teleportation:
Ion A and Ion C are too far away from each other and operations cannot be done to both of them. Ion B and Ion C are in the Bell state. Ion A and Ion B are at the same position. Teleportation transfers the quantum state of Ion A to Ion C through operations on Ions A, B, and C in the following procedure:
1. Perform Bell state measurement on Ion A and Ion B and obtain one of the four possible classical results.
2. Send the classical result to Ion C.
3. Perform corresponding operations on Ion C based on the result and recover the initial quantum state of Ion A at the position of Ion C.

Level 5: Quantum Revival

Use three steps to complete the work you did in level 4. Be careful about the order of qubits.