Sources: UCBerkeley, IBM Qiskit Textbook

Odd Features

• Quantum mechanics is inherently probabilistic. If we measure two quantum systems which were prepared in perfectly identical states, we may see completely different results.
• It is impossible to know the whole state of a quantum system. Moreover, the very act of measuring a system fundamentally disturbs its state.
• Elementary particles behave in some ways like waves, and in some ways like classical particles — this is often called the wave-particle duality. But it is more accurate to say that elementary particles behave neither like particles nor like waves, but in a uniquely quantum mechanical way.
• Elementary particles do not have trajectories. If an elementary particle starts at point A and was later measured at point B, quantum mechanics forbids us from asking about the path it took to get from A to B.

Young's Double Slit Experiment

• Wave-like behavior when we observe the interference patterns
• Particle-like nature when frequency of clicks of a photodetector decreases as the intensity of the light source is turned down

Heisenberg's Uncertainty Principle

• An electron is delicate
• Measurement disturbs system
• We can make light used for measurement of the electron fainter, but light is quantized
• Heisenberg's Uncertainty Principle states that it is impossible to design apparatus that detects which slit the electron passed through without disturbing the interference pattern

Qubits

Suppose we store a bit of information in the state of an electron in a Hydrogen atom. Recall that the orbitals of a hydrogen atom are discrete, or quantized: there is a ground state, a first excited, and so on. So we could let the ground state represent 0, and the first excited state represent 1. However, we know that the electron is governed by the laws of quantum mechanics.

• How do we represent the general quantum state of the system?
• Some examples of qubits

Geometric Interpretation