Basis and Native Gates
A native gate is one the chip can do directly, as a single tuned control pulse. Every other gate must be rewritten using native gates. A small set of the right gates can build any gate, either exactly or within a stated error. So a chip with a short list of native gates is not weaker because of it.
Why can't the chip just run an H gate?
Why care? Every gate you did not write yourself is extra work for the chip, and extra work means extra error. Knowing the chip's own gates helps you guess what the compiler will add.
On a real chip, a gate is not a button in a menu. It is a physical action. It is a shaped pulse of microwaves or laser light. That pulse is tuned, or calibrated, for one gate on one qubit. The short list of gates a chip can do this way is its native gate set.
Every other gate must be rewritten. The compiler picks a basis. That is the set of gates it will aim for, usually the native ones. These are the basis gates. Then it does basis translation. It swaps each gate in your circuit for a short sequence of basis gates that does the same job.
An everyday example: a recipe says "whisk". Your kitchen has no whisk, only a fork. So you write "stir fast with a fork for two minutes." Same result, different tools. This is also a lot like how a normal compiler turns code into the few instructions a computer chip knows.
The example breaks in two places. First, a quantum rewrite must track something called global phase. We explain it below. Second, some quantum rewrites are close but not exact on purpose. They are correct only within a stated error limit, and that limit must be reported with the result.
- Worked example: building H from native-style gates
- What does the textbook Bell pair give?INTERACTIVE
- Does the same Bell pair work with only CZ?INTERACTIVE
- Worked example: making CX out of CZ
- What happens to CZ without the H gates around it?INTERACTIVE
- Which gate sets do real devices use?
You’ve read the opening of chapter 2. Pro unlocks the other 6 sections — plus every chapter of every course, with circuits you can run right on the page. That’s $11.99 a month, about the price of a coffee, or $99.99 a year (save 30%). The first chapter of every course, and the whole math course, stay free.