Why Noise Exists in Quantum Systems

Overview

In the ideal circuit model, qubits evolve exactly as the gates say they should. On real hardware, qubits are physical systems: tiny oscillators, spins, ions, or superconducting circuits. They interact with their surroundings and with imperfect control electronics.

Noise matters because it turns “perfect quantum logic” into something that slowly (and sometimes quickly) drifts away from the intended state. That drift is why today’s devices are called NISQ (Noisy Intermediate-Scale Quantum): we can run nontrivial circuits, but only up to limited depth and accuracy.

This page builds the core reality check:

• quantum states are fragile
• isolation is never perfect
• “noise” in quantum mechanics has extra consequences compared to classical noise

Intuition

Fragility is a feature, not a bug

Quantum information depends on phase relationships between amplitudes. Those phase relationships are what enable interference, and interference is where quantum advantage comes from.

The same feature makes quantum systems sensitive:

• A tiny, uncontrolled interaction can change relative phases.
• A small amount of energy exchange can move population between basis states.

The environment is always there

Even in a vacuum and at low temperatures, a device still couples to:

• stray electromagnetic fields
• thermal excitations from imperfect cooling
• vibrations and mechanical noise
• defects in materials
• control lines and measurement apparatus

“Perfect isolation” would mean no ability to control or read out the qubit either. In practice, you must couple the qubit to something to operate it, and that coupling is also a pathway for noise.

Classical vs quantum noise (conceptual difference)

In classical computing, noise often looks like:

• a random fluctuation you can average away
• a small analog error that stays small

In quantum systems, noise can do something qualitatively different:

• it can destroy coherence, meaning the system loses the phase relationships that make interference work
• it can turn a pure state into a mixed state (a statistical mixture)

You can sometimes correct classical noise by repetition because the bit value is still well-defined. Quantum noise often attacks the structure of the state itself.

Formal Description

We’ll define “noise” operationally.

Ideal evolution

In the ideal circuit model, a state evolves by unitary gates:

• start with some state $|\psi\rangle$
• apply a unitary gate $U$
• new state is $U|\psi\rangle$

The only randomness comes from measurement at the end.

Real evolution (conceptual)

In real hardware, the system is not completely closed. So the actual evolution is closer to:

• intended unitary evolution from your control pulses
• plus unintended interaction with uncontrolled degrees of freedom (“the environment”)

Instead of “apply $U$ exactly,” what happens is “apply something close to $U$, then the environment nudges the state.”

Two broad classes of effects show up:

• Energy relaxation: the qubit exchanges energy with the environment (population changes).
• Dephasing: the qubit’s phase drifts randomly (relative phase is scrambled).

These are the two pillars of decoherence (next page).

Why isolation is never perfect

There is always some coupling because:

• materials are imperfect
• temperature is not absolute zero
• electromagnetic fields cannot be perfectly shielded
• control and measurement lines are physical connections

Even if each coupling is small, it accumulates over time and over many gates.

Worked Example

Imagine you prepare $|+\rangle$ and want it to remain unchanged for a while. In an ideal world, it stays $|+\rangle$.

In reality, suppose the qubit’s phase drifts by a small random angle each microsecond. After many microseconds, different runs accumulate different phases.

Result:

• Each individual run is still a valid quantum state.
• But across runs, the relative phase becomes unpredictable.
• Interference-based circuits that rely on a stable phase stop working reliably.

This is why “small random phase noise” is not just a nuisance—it directly attacks the mechanism that makes quantum algorithms work.

Turtle Tip

Common Pitfalls

Quick Check

What’s Next

Next we make the two major noise processes concrete: T1 energy relaxation and T2 dephasing. These timescales are the simplest way experimentalists summarize “how long quantum information survives.”