Entanglement And Interference: The Two Ideas Behind Quantum Algorithms

The previous article explained that a single qubit holds a weighted combination of 0 and 1, and that reading it gives one random result. On its own, that would make a rather unreliable coin. Two further ideas turn qubits into something that can compute: entanglement and interference.

Entanglement is the one that attracts headlines, often with talk of “spooky” connections across the universe. Interference gets less attention, but it does most of the work inside an algorithm. This article explains both in plain terms, clears up the most common misunderstanding about entanglement and shows why the two ideas together matter for anyone trying to judge what quantum computers can do.

Entanglement: Qubits That Only Make Sense Together

Normally you can describe a group of objects one at a time. Two coins on a table are each heads or tails, and knowing one tells you nothing about the other. Entangled qubits are different. Their shared state cannot be broken down into a separate description for each qubit. As NIST physicist Andrew Wilson puts it, entangled things “have no independent existence”.¹

The simplest example is called a Bell pair, and it takes only two operations to make. The steps below are the same ones IBM uses in its introductory tutorial for running a first circuit on real hardware.²

Look at either qubit alone and it behaves like a fair coin, giving 0 or 1 at random. Look at both and the results match. On its own, that proves little: two ordinary coins secretly set to the same face before being handed out would also always agree. The difference shows up when each side can choose between several different ways of measuring its qubit. A result called Bell’s theorem shows that, across those choices, entangled pairs agree and disagree in a pattern that no scheme of pre-set answers carried by each particle can reproduce.³ Three experiments published in 2015 tested this without the loopholes that had weakened earlier tests, and all three sided with quantum theory.⁴

What Entanglement Cannot Do

Because the correlation holds even when the two qubits are far apart, people often conclude that entanglement lets one qubit send a message to the other instantly. It does not. Each person holding one half of a Bell pair sees only random results. The match only becomes visible when the two sets of results are brought together and compared, and that comparison has to travel by ordinary means. Physicists call this the no-signalling principle: entanglement produces correlations, but it cannot be used to send information faster than light.⁵

Inside a quantum computer, entanglement is best thought of as a resource. Algorithms use it to tie qubits together so that a calculation over many qubits can behave as a single coordinated whole. Error correction relies on it too. When researchers report progress, entangling operations between protected “logical” qubits are one of the milestones they track. The Harvard, MIT and QuEra team, for example, reported entangling logical qubits as part of a 448-atom fault-tolerant architecture published in Nature in late 2025.⁶

Interference: Where The Computing Happens

Entanglement alone does not produce answers. If you build a large entangled state and measure it, you still get one random result. The step that turns a quantum state into a useful answer is interference.

Recall that each possible outcome carries an amplitude, which can be positive or negative. When different routes through a calculation lead to the same outcome, their amplitudes add together. If they have the same sign they reinforce. If they have opposite signs they cancel, in the same way that two water waves meeting peak to trough can flatten each other out.⁷

A quantum algorithm is, in effect, a recipe for arranging these additions and cancellations. The designer chooses the gates so that, by the end, the amplitudes for wrong answers have largely cancelled and the amplitude for the right answer has grown. Measurement then returns the right answer with high probability. Grover’s search algorithm, for instance, works by repeatedly nudging amplitudes in this way so that the marked item stands out.⁸

Interference is also visible in recent headline experiments. Google’s October 2025 “Quantum Echoes” experiment on its Willow chip ran a sequence forwards and then backwards and relied on constructive interference to make a faint signal measurable.⁹ Whatever one concludes about the speed claims attached to that experiment (covered later in this series), the mechanism is the one described here.

Why This Matters Beyond The Physics

These two ideas set realistic expectations. A quantum speed-up exists only where a problem has structure that interference can exploit. Shor’s algorithm finds such structure in the mathematics behind RSA and elliptic curve cryptography, which is why those schemes are at risk;¹⁰ the Quantum Threat section explains the consequences. For problems without that structure, entanglement and interference offer little or nothing.

They also explain why building the hardware is so hard. Entangled states and finely balanced amplitudes are easily disturbed, and a small error can spoil the cancellations an algorithm depends on. That fragility is the subject of the article on noise and error correction.