- 1 -
Welcome to the world of Quantum Cellular Automata!
In this tutorial, you will learn how to build interesting circuits using Qubits.
There are the three kind of blocks you can place:
- Influencer: sets the adjacent qubits to its value (0 or 1)
- Qubit: stores and transmits quantum information, can be in an undeterminate state (?)
or determinate state (0 or 1) when measured
- Output: allow to measure the value of one qubit
- 2 -
Negative influence
Since electrons repel each other, it is possible to invert the polarity of qubits as such:
- 3 -
One output, many inputs
Let's build a more complex logic gate. By having many inputs joined into one output, a majority gate can be built. The output corresponds to the value of the major input.
- 4 -
More complex logic gates: AND gate
Let's now build another logic gate: the AND gate. The AND gate takes two inputs, A and B and one output, Z.
The output Z's value is 1 when both of the input A and B's values are 1. Otherwise, the output Z's value is 0.
The truth table for the AND logic gate is:
| A |
B |
Z |
| 0 |
0 |
0 |
| 0 |
1 |
0 |
| 1 |
0 |
0 |
| 1 |
1 |
1 |
- 5 -
More complex logic gates: XOR gate
Another logic gate is the eXclusive-OR, or XOR gate. The output Z's value is 1 when only one
of the two inputs is 1 and the other is 0.
| A |
B |
Z |
| 0 |
0 |
0 |
| 0 |
1 |
1 |
| 1 |
0 |
1 |
| 1 |
1 |
0 |
- 6 -
Combining circuits: a binary half-adder
By combining logic gates, we can build more complex and interesting circuits. If we combine
the AND and XOR logic gate, we can build an half-adder, which computes the binary sum of
its two inputs, A and B.
An half-adder has two outputs: S, the sum of A and B, and C, the carry (or overflow of the
sum into the next digit, if we were to build a more complex adder).
The truth table is:
| Inputs |
Outputs |
| A |
B |
C |
S |
| 0 |
0 |
0 |
0 |
| 1 |
0 |
0 |
1 |
| 0 |
1 |
0 |
1 |
| 1 |
1 |
1 |
0 |
By looking at the truth table, we can see that C = A AND B, and S = A XOR B. Thus, we can
easily build an half-adder out of the AND and XOR we build in the two previous missions.
The logical structure is widely used in computer processors to compute the sum of two binary
numbers.
