Why Quantum Computing Exists

Why should you care? Because you will hear big claims about quantum computers. This chapter gives you a simple way to judge them.

Developers already pick between different chips. A CPU is the main chip in your laptop. It is good at general work with lots of if-this-then-that choices. A GPU does the same simple math on huge piles of numbers at once, which is great for graphics. An NPU speeds up a small set of tasks used by AI models.

A QPU, or quantum processing unit, is one more specialist. It controls a tiny physical system that follows the rules of quantum physics. It runs a planned list of steps on that system. Then it hands back samples of ordinary bits.

Think of a kitchen. A chef's knife does most jobs. A garlic press does one job very well, and is useless for slicing bread. These chips are like that. They have different roles. It is not a ranking. Moving work to any special chip only pays off when the problem, the method, and the cost of moving data all fit. The same is true for a QPU, only more strictly.

The state of n ordinary bits is one string of n zeros and ones. Qubits are the quantum version of bits. The state of n qubits is described by a list of amplitudes. An amplitude is a number that says how strongly the qubits lean toward one bit string. There is one amplitude for every possible bit string. It can be negative, or even a complex number (a number with two parts). And there are 2^n possible strings.

Work the numbers. For 10 qubits there are 2^10 = 1,024 amplitudes. A computer stores each amplitude as two numbers, because a complex number has two parts. Each of those numbers takes 8 bytes. So one amplitude takes 16 bytes. That gives 1,024 × 16 = 16,384 bytes, about 16 kB. Tiny.

Now try 50 qubits. That is 2^50 ≈ 1.13 × 10^15 amplitudes, which is roughly 18 petabytes. No ordinary computer memory can track that directly.

Here is the catch. That huge description is not something you can read out. To read a quantum computer you measure it. Measuring n qubits gives back just n ordinary bits per run. It is like a giant library where you are only allowed to borrow one page per visit.

Take 3 qubits. Their state has 2^3 = 8 amplitudes, one for each string from 000 to 111. A single run gives back exactly one of those strings.

How likely is each string? Square the size of its amplitude. Say the amplitude of 101 is 0.5. Then 0.5 × 0.5 = 0.25. So 101 shows up on 25% of runs. The other 75% of runs give other strings.

So a useful quantum method must set up the amplitudes so the strings you want come out often. It can't print all 8 values. It certainly can't print all 2^50.

A circuit is the planned list of steps you just ran. You read it from left to right. It starts one qubit in the state written |0⟩. Say it as "ket zero". It is a state that is sure to measure as 0.

Then comes the H gate, called the Hadamard gate. A gate is one step that changes the qubit. H moves the qubit to a state where both amplitudes are 1/√2 ≈ 0.7071.

Check it: square each amplitude. 0.7071 × 0.7071 ≈ 0.5. A shot is one full run of the circuit, ending in one measurement. So each shot reads 0 or 1 with a 50% chance. In 100 shots you might see 47 and 53, or 55 and 45.

Notice the workflow. An ordinary program described the circuit. A simulator (or a real QPU) ran it. Ordinary counts came back. That back-and-forth never goes away. Real quantum chips always sit inside an ordinary computer system. Try your own changes in the Lab.

Also notice what this is not. A coin flip made this way is no better than an ordinary random-number maker. "The quantum part works" and "it beats normal computers" are two separate claims.

A popular story says a quantum computer "tries every answer at the same time and picks the best one". The first half is misleading. The second half is false.

A state can have non-zero amplitudes for many strings at once. But measuring picks one string at random. Strings with bigger squared amplitudes get picked more often. Nothing reads out the whole list.

Real quantum methods use interference. That means amplitudes adding up or cancelling out, like two water waves in a pool. Where two peaks meet, the wave gets taller. Where a peak meets a dip, the water goes flat. A good quantum method plans the amplitudes so wrong answers cancel and right answers grow, before you measure. (Unlike pool waves, amplitudes are not made of anything you can touch. They are numbers in the math.)

This only works for problems with the right structure. That is why quantum speedups are specific, not universal.

Today's quantum chips have real limits:

• Gate errors. Each step goes slightly wrong a small part of the time.
• Limited connections. Each qubit can only work directly with a few neighbours.
• Drift. The settings, found by a process called calibration, slowly go off over time.
• Small circuits. Only short programs finish before errors pile up.

So a method can be faster in theory for very large problems. Yet today's devices can still lose to a laptop on the full task, from start to finish.

Keep three kinds of evidence apart. First, proven theory. Second, small tests or simulations. Third, what current hardware can really do. The scientist John Preskill coined the term NISQ for the current era. It stands for "noisy intermediate-scale quantum": machines of middle size that still make lots of errors. Browse real devices and their measured error rates at /hardware/qpus. Compare them side by side at /hardware/compare.