How Does Relative Phase Affect Quantum Results?

Starter
Article
Ages 10+
4 min read
Updated November 5, 2026

Relative phase tells whether two parts of a quantum state meet peak to peak or peak to trough. Peak to peak, they add; peak to trough, they cancel. Because the amplitude of each result is what sets its probability when measured, relative phase can change the outcome distribution when the components interfere.

Contents

In phase, two waves add into a bigger wave; offset by half a cycle, they cancel into a flat line.

Two waves in phase
Sum: wave twice as tall
Sum: cancels to a flat line

What you will learn

Understand relative phase as the offset between two waves.
Say why phase makes two parts add or cancel.
See why quantum computers need to control phase.

Before you start

No prior knowledge is needed. You only need to have seen two ripples on water meet.

What is relative phase?

Relative phase is the offset between two waves. Look at two ripples on water. If the peak of one lines up with the peak of the other, they are in phase. If a peak of one meets a trough of the other, they are out of phase. That difference is the relative phase.

The Physics Classroom page on wave interference describes two outcomes. Two identical upward pulses meeting make the medium take an upward pulse of twice the amplitude: constructive interference. An upward and a downward pulse of the same shape meeting cancel each other's effect: destructive interference.

The gap between matching peaks of the two waves shows the phase offset.

First wave
Second wave, lagging
Offset between the peaks

How does relative phase change a measured result?

It changes probabilities, because probabilities come from wave-like amplitudes. IBM describes qubits in a collective superposition as structuring information like waves, with amplitudes associated with each outcome. An outcome probability is the squared magnitude of its amplitude in the chosen measurement basis; amplitude is not itself probability.

IBM also says these waves can build on each other when many peak at a particular outcome, or cancel each other out. If two parts of a state are in phase at one outcome, that outcome becomes more likely. If they are opposite in phase, it can become less likely; complete cancellation also requires equal magnitudes. Microsoft Quantum makes the same point: when a particle is in a superposition of multiple states, those states can interfere with each other, leading to constructive or destructive interference.

Changing phase and immediately measuring in the same basis need not change the probabilities. AWS Quantum Technologies explains that states differing only in relative phase can give identical statistics in that basis. A transformation that mixes the components, or a suitable measurement basis, is needed to reveal phase through interference. A measurement basis is the set of outcomes a measurement distinguishes.

Two arrows in the same direction add into a tall probability column; opposite arrows leave it near zero.

In phase: high probability
Out of phase: probability near zero

Why do quantum computers need to control phase?

Because phase is how they choose which outcomes get amplified. According to Microsoft Quantum, by controlling the relative phases of the states, interference can be used to amplify certain outcomes and suppress others. An algorithm combines phase control with transformations to increase the probability of desired outcomes. This does not mean the computer already knows the answer or always measures it.

Phase control combined with amplitude mixing can change the probability distribution. A phase shift alone followed by measurement in the same basis is not enough.

Two equal outcomes at the start
Phase control and amplitude mixing
One outcome amplified

Real-world example

Noise-cancelling headphones are an example of waves cancelling, though they belong to sound and not to quantum physics. The headphones make a wave that is out of phase with the noise so the two nearly wipe each other out. Quantum phase follows the same add-or-cancel principle, but it acts on the probabilities of measured results. This is only a comparison to help picture it.

Common misunderstandings

Phase is an extra kind of energy. Phase is an offset between two waves, not an amount of energy.

Phase cannot matter because we only measure probabilities. Probabilities come from wave-like amplitudes, so relative phase decides whether they add or cancel.

Two parts that meet always get stronger. Only in phase do they add. Out of phase they can cancel.

Relative phase is the offset between two waves: peak to peak or peak to trough.
Probabilities are squared magnitudes of amplitudes, so phase decides add or cancel.
Controlling phase lets a computer amplify wanted outcomes and suppress others.

Terms in this article

English and Vietnamese terms, with the meanings used here. Hover, tap or Tab to a term with a dotted underline for an explanation as you read.

relative phasepha tương đối: The offset between two waves or two parts of a state: peak meeting peak, or peak meeting trough.
superpositionchồng chập: A state made of several possibilities at once, each with its own amplitude.
amplitudebiên độ: The wave-like number attached to an outcome, from which the outcome's probability follows.
interferencegiao thoa: The effect of waves meeting and adding to or cancelling each other.
qubit: The unit of information in a quantum computer.

This article is not marked as viewed

Spotted something wrong or unsafe?

Tell the administrator by email. The message already has the article title and address.

Report this article

Starter
What Is Quantum Technology?
Explore technologies using quantum effects in computing and sensing, distinguishing the underlying principles, potential uses and limitations.
6 min read
Starter
What Are Atoms Made Of?
Explore the nucleus, protons, neutrons and electrons, and learn to read an atom model without mistaking it for a miniature solar system.
4 min read
Starter
Why Do Atoms Have Discrete Energy Levels?
See how matching matter-wave patterns explain discrete atomic energy levels, how transitions emit photons, and where the Bohr model has limits.
5 min read
Starter
How Do Photons Describe Light?
A photon is a discrete packet of light energy with wave and particle sides: its energy sets the radiation type, and the photon count sets brightness.
5 min read