What is quantum interference?
Interference is what happens when amplitudes combine. Amplitudes, unlike probabilities, can be positive or negative (or complex), so when a calculation brings several of them together they can add up, making a result more likely, or cancel out, making it less likely or impossible. Quantum algorithms are designed so that the paths leading to wrong answers cancel and those leading to the right answer reinforce. Interference is central to many quantum algorithms, and entanglement matters in many algorithms that use several qubits. Neither guarantees a speed-up on its own, and neither works by "trying every answer at once".
A two-step example
Start a qubit at 0 and apply a Hadamard gate (the H gate): it becomes an equal superposition, 50% each. Apply the same gate again and it returns to 0 every time. There are two routes to the result 1, and their amplitudes are +½ and −½, so they cancel. The two routes to 0 are both +½, so they add up to 1.
| Route via 0 | Route via 1 | Total amplitude | Chance | |
|---|---|---|---|---|
| Ending at 0 | +½ | +½ | 1 | 100% |
| Ending at 1 | +½ | −½ | 0 | 0% |
The same effect in light
Interference isn't special to computers. In an interferometer, a single photon is split into two paths and recombined; with the paths set up right, it always leaves through one exit and never the other, because the two ways of reaching the second exit cancel. Block either path and the cancellation is lost: photons that get past the block leave by either exit, half the time each.
How algorithms use it
Shor's algorithm uses interference to make the period of a hidden pattern stand out, which is what lets it factor large numbers. Grover's algorithm uses repeated rounds of interference to make one marked item steadily more likely. Designing that cancellation is hard, and that's why only some problems have known quantum speed-ups.
Common confusions
- "Quantum computers try every answer and pick the best." They can't read every answer. They use interference so the best one is likely when measured.
- "Probabilities cancel." Probabilities can't be negative. It's the amplitudes that cancel, before they're turned into probabilities.
- "Interference makes every problem faster." No. It helps only where an algorithm can arrange the cancellation, which is why quantum computers are expected to help with some tasks, not all.
Written by Muhammad Atif · Reviewed 19 October 2026 · How sources are chosen and checked · Report a correction
Sources and further reading
Tags show what kind of source each one is (how sources are used). Checked against these sources on 19 October 2026. Spotted an error? Email hello@plainquantum.com and it will be corrected, with a note.
- BookQuantum Computation and Quantum Information (10th anniversary edition)Michael Nielsen and Isaac Chuang, Cambridge University Press, 2010
- CourseBasics of quantum information (free course)IBM Quantum Learning
- Peer-reviewed paperPolynomial-time algorithms for prime factorization and discrete logarithms on a quantum computerPeter Shor, SIAM Journal on Computing, 1997
- Peer-reviewed paperA fast quantum mechanical algorithm for database searchLov Grover, STOC, 1996