Quantum Mechanical Principles Behind Quantum Computing

Last Updated on December 8, 2025 by Dr. Sushanta Barman

Quantum computing is built upon the laws of quantum mechanics, which govern the behavior of extremely small particles such as electrons, photons, and ions. Classical physics accurately explains the motion of large objects like planets and cars.

However, at microscopic scales, nature behaves differently. Particles can act like both waves and particles, and their behavior is probabilistic rather than definite. Quantum mechanics provides the rules for describing this unusual behavior.

In quantum computing, qubits are physical quantum systems, such as trapped ions or superconducting circuits, that store and process information. To understand how qubits work, we must first learn two key ideas from quantum mechanics: the wave function and superposition. These concepts give quantum computers their unique power.

Wave-Particle Duality and the Wave Function

One of the earliest discoveries in quantum physics is that particles exhibit both particle-like and wave-like properties. This behavior is known as wave-particle duality. Instead of having an exact position and velocity at all times, a quantum particle is described by a mathematical function called the wave function \(\psi(x,t)\).

The wave function contains the full information about the quantum state of a system. It does not give a definite answer about where a particle is located. Instead, the square of the wave function, \(|\psi|^2\), gives the probability of finding the particle at a certain position.

This idea means that before measurement, the particle exists in a spread-out cloud of possibilities. When a measurement is performed, the wave function collapses, and the particle is found in a definite location.

This probabilistic nature of quantum mechanics is very different from classical physics and is central to how quantum computers operate.

Qubits: Information Stored as Waves

A classical bit can take only one value, either 0 or 1. A qubit, however, is a quantum system whose state is represented by a wave function. Because it is a wave, it can exist in multiple possibilities at the same time. This leads to the principle known as superposition.

Mathematically, the qubit state can be written as,

\[ |\psi\rangle = \alpha |0\rangle + \beta |1\rangle,\]

where, \(|0\rangle\) and \(|1\rangle\) are the two logical states of a qubit, and \(\alpha\) and \(\beta\) are complex numbers called probability amplitudes. The total probability must always be one,

\[|\alpha|^2 + |\beta|^2 = 1\]

This expression describes a qubit that simultaneously contains information corresponding to both 0 and 1, until a measurement forces it to choose one outcome. This is why qubits can explore many computational paths at once.

Superposition and Quantum Speed

Superposition has no classical equivalent. A helpful analogy is a spinning coin. While spinning, it is neither strictly heads nor tails, it is in a mixture of both. Only when it lands (measured) do we see a definite outcome. A qubit, however, can remain in this mixed state as long as it is isolated from the environment.

This ability to hold multiple states at once gives quantum computers a dramatic scaling advantage. For example:

• A single qubit can represent two (=2¹) states in superposition.
• Two qubits represent four (=2²) states.
• Ten qubits represent 1024 (=2¹⁰) states.
• Three hundred qubits can represent more quantum states than the number of atoms in the visible universe.

Even though we can observe only one outcome at the end, the computation leading to that outcome takes place over this vast quantum state space.

Quantum Phase and Interference

Quantum states are waves (probability waves), and waves have a property called phase. When waves interact, they can interfere, either reinforcing each other or cancelling out. Quantum algorithms are designed to manipulate phases so that wrong answers cancel out while correct answers become more likely to appear when measured.

This phenomenon distinguishes quantum computation from simple probabilistic guessing. The calculation is driven by structured interference, amplifying useful results.

Measurement and Collapse

Although superposition supports parallel computation, it is extremely fragile. When a qubit is measured or disturbed by its surroundings, its quantum state collapses to a definite classical value. This is one of the biggest challenges in quantum technology.

To obtain reliable results, quantum computers require careful isolation, fast operation, and often multiple repeated measurements.

Summary

Quantum mechanics provides a new foundation for computing. The wave function describes quantum information as a spread-out probability wave.

Superposition allows qubits to store multiple values at once, giving quantum computers the ability to process many possibilities in parallel. The wave nature of quantum states also enables interference, which is used to guide calculations toward correct answers.

Together, these quantum principles provide a powerful and fundamentally different model of computation, one that classical computers cannot replicate efficiently.

References

1. Sushanta Barman, “Types of Qubits in Quantum Computing,” MatterWaveX.Com, August 23 (2024).
2. Sushanta Barman, “Wave Function in Quantum Mechanics,” MatterWaveX.Com, August 30 (2024).
3. Sushanta Barman, “de Broglie Hypothesis: The Wave-Particle Duality of Matter,” MatterWaveX.Com, August 25 (2024).