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I'm reading a book on quantum computing. It is a very non-technical book, and I do not need a very technical explanation. I keep on seeing the words quantum gate pop up, and I'm wondering whether this is the same thing as taking an observable? Or, am I confusing two concepts of physics?

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Physically, a quantum gate represents the operation of doing something to a quantum state in a reversible way. Reversible here means that there is no loss of information in the process and so, in principle, it is always possible to apply another (generally different) gate to come back to the initial state.

Mathematically, a quantum gate is simply a unitary operator, which applied to a state produces another state.

A measurement is very different from this because measuring a state collapses it to a specific classical output, and this process is markedly nonreversible.

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An observable is a way of representing some measurable quantity. The observable represents the set of possible outcomes of measuring that quantity. The observables together with the state give you the probability of each of the possible measurement outcomes.

A quantum gate represents a way of changing a quantum system. If a qubit has a value of 0 and you apply a quantum not gate to it then it will have a value of 1 after the gate is applied.

So a gate is not an observable since a gate represents a way of changing the state of a system, not a measurable quantity.

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    $\begingroup$ This is overly reductive. There are plenty of other gates beyond the NOT gate described in this answer, and omitting to mention them is just setting up a future misconception about what a quantum gate is. $\endgroup$ – Emilio Pisanty Nov 6 '18 at 9:25

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