Quantum Parallelism and Its Limits
A group of n qubits in an even blend holds 2^n amplitudes at once. But a measurement gives back just one n-bit string, picked at random. You never get to read the whole list. Quantum algorithms win only when interference piles the chance onto strings that reveal the answer, before you measure.
Does a quantum computer really try everything at once?
You have probably heard this line: "n qubits hold 2^n values at the same time, so a quantum computer tries every answer in parallel." Half of it is true. The other half is a myth. This chapter shows you which half is which. That skill will save you from a lot of hype.
First, some words. A qubit is a quantum bit. Its state is a pair of amplitudes. These are numbers tied to the values 0 and 1. They can be negative or even complex (a number with two parts). Square the size of an amplitude and you get the chance of reading that value. A superposition is any state where more than one amplitude is not zero. (A plain-words intro is on the superposition page.) For n qubits, the state is a list of 2^n amplitudes, one for each n-bit string.
That part is true. To describe 3 qubits you need 8 numbers. To describe 50 qubits you need 2^50 ≈ 1.1 quadrillion numbers.
Now the catch. A measurement is the only way to get data out. It gives back one n-bit string. The string is picked at random using those squared chances. After that, the superposition is gone. So if you make an even blend and measure right away, you have built a very costly random number maker. A normal computer can do that easily. The 2^n amplitudes are real, but you cannot read them like an array. "Tries everything at once" mixes up storing a description with handing you answers.
- Eight strings, one sample per shotINTERACTIVE
- What are the eight amplitudes, exactly?
- Why can't we just read all the amplitudes out?
- Undo the superposition with interferenceINTERACTIVE
- How does interference make amplitudes cancel?
- What does this mean for algorithm design?
- What do these two experiments look like on real devices?
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