Maths
There is a lot more to a qubitโs state than just itโs probability however. Each qubit on its own is stored with two numbers. (
It gets even more complicated when qubits interact with each other.)
If you square the top number, you get the probability that when
measured, this qubit will be on. If you square the bottom number, you get the probability that when
measured, this qubit will be off.
These numbers can also be negative or complex. (If it is complex, the magnitude squared is the probability.)
Maths
The
not gate (and most other gates) can be represented by a matrix.
When you apply the gate, you multiply the matrix for the gate by the
vector for the qubit.
Maths
The
hadamard gate (and most other gates) can be represented by a matrix.
When you apply the gate, you multiply the matrix for the gate by the
vector for the qubit.
Notice if you apply a
hadamard gate to (โ0.5 ๐๐น๐น+ โ0.5 ๐๐), the ๐๐s cancel, making the qubit 100% off.
Notice also that applying the
hadamard gate twice will always do nothing.
Maths
When there are two qubits involved instead of each being represented by a
2d vector we represent both in one 4d vector.
Thus a
controlled not gate can be written using the following matrix:
The qubit block is the most important block in the mod, as all other blocks connect to it. The qubit block represents one quantum switch, which can be on, off or a combination of the two. The number on the block shows the probability that it will be on when measured (rounded to the nearest 10%).
Quantum tendrils act as an extension to the qubit block, allowing gates to be connected to it. Qubit blocks cannot be connected together with tendrils.
Not gate blocks act on the qubit block they are connected to. Not gates swap the probabilities of being on and off. They are activated by redstone.
Hadamard gate blocks act on the qubit block they are connected to. hadamard gates create/cancel basic superpositions. They are activated by redstone.
If a qubit is originally 100% off, then the hadamard gate will make it 50/50. Applying the hadamard gate again will get the qubit back to 100% off.
Gate controls must be placed next to another gate (but not next to a measurement). The attached gate will now only act when the qubit block the control is attached to is on.
In this setup, first, a hadamard gate is applied to the bottom qubit, this creates a superposition of ON + OFF in the bottom qubit. A controlled not is then applied to the two qubits, and since the top qubit only changes when the bottom qubit is ON, the two qubits are now ON, ON or OFF, OFF. This is entanglement, where the two states arenโt independent of each other.
A measurement may be used to measure a qubit block and get a redstone output from a qubit. The measurement is updated when the redstone input is on, and the output of the measurement can be obtained using a comparator.