A brief introduction to quantum computing

Let’s start with some principles:

1. Any 2 level system can be used for quantum computing, like spin.

2. Due to dephase and decoherence, we need a clean background（closed box, out of touch with the outside universe), or topological protection.

3. A practical system should be able to be manipulated（the entanglement of qubit) and can be scaled up

Now let’s take a look at a simple example, IBM q

IBM q single gate

q[0] is a qubit with|0> and|1>, two eigenstates, you can imagine it as a spin. Initially, it’s|0>. label H is called Hadamard gate

the blue square is the operator, and the pink one is the measurement, after measurement, you get the following result:

what does it mean?

It means the probability at|0> or |1> is ~0.5.

why?

because H operator rotates the initial |0> state, and|0> becomes|+⟩=1/2(|0⟩+|1⟩), equivalently from Z-axis to X-axis.

The following is a multi-qubit version, a CNOT gate.

Conclusion: quantum computing has three steps, first prepare the initial state, and then add operators, finally measure the result.

Physically, there is ion trap, superconducting, semiconductor approaches to building quantum computing systems.

from arXiv:1009.2267v

superconducting

from arXiv:1009.2267v

semiconductor

from https://doi.org/10.1038/s41565-018-0207-y

ion trap

from arXiv:1009.2267v