A quantum computer processes information through quantum-mechanical states and operations. It is most promising for specialized problems where classical resource requirements grow exponentially, while quantum resources may grow polynomially. section 1.0 section 1.3
A quantum computing system is understood through these programming-facing ideas:
- A qubit is the fundamental unit, analogous to a classical bit but capable of encoding changing outcome probabilities rather than only switching between 0 and 1. section 1.4.2
- A computation changes the state probabilities and then measures the system, producing one outcome whose repeated frequencies approximate the encoded distribution. section 1.4.2
- Quantum parallelism represents multiple possible outcomes in the system state, while measurement converts that state into an observed result. section 1.3
- Quantum approaches are considered for Fourier transforms, chemical and physical simulation, random sampling, optimization, and selected machine-learning problems. section 1.0 section 12.1
From probability distribution to measurement
A simple probabilistic-bit model changes the chance of heads and tails before measurement. If the tails probability changes from 0.7 to 0.3, ten repetitions are expected to produce roughly seven heads and three tails; more repetitions generally approach that distribution. Quantum amplitudes add directional information to these probabilities, affecting how the system changes even though measurement frequencies depend on squared amplitude lengths. section 1.4.2
Table 1.1 Eight outcome–probability pairs
|
Outcome
|
Probability
|
|---|---|
|
0
|
0.05
|
|
1
|
0.11
|
|
2
|
0.13
|
|
3
|
0.02
|
|
4
|
0.34
|
|
5
|
0.17
|
|
6
|
0.06
|
|
7
|
0.12
|
Use the outcome–probability table to inspect how a quantum state represents several possible computational results whose probabilities sum to one. section 1.3
