Quantum Recap: Representing Qubits
This is going to be a series where I brush up on my quantum mechanics and physics knowledge, hoping that one day I’ll be able to have conversations about these topics without being completely clueless. I have a Master’s in Physics and a Master’s in Artificial Intelligence, plus 6+ years of experience in software engineering. I’m hoping all that knowledge can help me on this journey! All thoughts are my own unless otherwise noted.
Physical Systems
Physical systems form the foundation for creating both classical and quantum bits. Transistors are used to create classical bits, while particles such as electrons and photons are used to create quantum bits.
Note: While technically any particle with a two-level quantum state could be used (such as spin states, polarization states, or vibrational modes), not all are practical. Neutrons, for example, have two spin states but are difficult to trap and control effectively.
Controlling Quantum States
Many factors can affect the delicate quantum states of qubits, with thermal energy being particularly problematic. At room temperature, electrons vibrate with so much energy that precisely controlling their spin states becomes extremely difficult. This is why electrons must be cooled to near absolute zero (around 15 millikelvin, or ~0.015 K) to minimize thermal vibrations, allowing researchers to use precision microwaves to flip spin states with high fidelity.
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Photons present a different case entirely. Since photons are particles of electromagnetic energy, they cannot be “cooled” in the traditional sense. Instead, their polarization states can be manipulated using optical elements like waveplates and beam splitters.
Note: You might wonder why microwaves are used instead of radio waves for electron spin control. The energy required to flip an electron’s spin state corresponds to microwave frequencies, roughly 1–100 GHz. This relationship follows Planck’s equation: E = hν, where E is the photon energy, h is Planck’s constant (≈ 6.626×10⁻³⁴ J·s), and ν is the frequency. Interestingly, radio waves are used in nuclear magnetic resonance (NMR) quantum computing, where atomic nuclei are manipulated instead of electrons, requiring lower energies and thus lower frequencies.
Mathematical Representation of Qubits
Unlike classical bits that exist in definite states of 0 or 1, qubits can exist in any point on the surface of a sphere — this visualization is called the Bloch sphere. Since a qubit’s state represents a combination of being in both the |0⟩ and |1⟩ positions simultaneously, we need mathematical notation to express this clearly.
Enter bra-ket notation, developed by Paul Dirac. This describes the qubit’s position on the Bloch sphere as a vector:
|Ψ⟩ = α₀|0⟩ + α₁|1⟩
Where:
- |Ψ⟩ (psi) represents the qubit’s quantum state
- α₀ is the probability amplitude for finding the qubit in state |0⟩
- α₁ is the probability amplitude for finding the qubit in state |1⟩
An important convention to remember: |0⟩ typically represents the ground state (lower energy), while |1⟩ represents the excited state (higher energy). Energy must be added to the system to transition from |0⟩ to |1⟩.
