How powerful is the adiabatic quantum calculation

This is how a quantum computer works

Today's computers, smartphones, smartwatches and pocket calculators have one thing in common: they work with bits. A bit can only have two states: either a [1] or a [0]. These two states are represented in the processors of today's computers with electricity: "Power on" means [1] and "Power off" [0].

Quantum computers, on the other hand, work quite differently and with "qubits". This is nothing more than a shortening of “quantum bits”. Like a bit in a classic computer, a qubit can either be in the state [1] or [0]. It gets interesting, however, when the qubit shows its special property that the classic bit does not have: A qubit can be in state [1] and [0] at the same time or in theoretically an infinite number of states in between. The best way to understand this is with a coin: If it is to represent a classic bit, it can be placed either head or tails up, that would be a [0] or a [1]. A qubit, on the other hand, would be a coin tossed into the air that rotates quickly on itself. With her you cannot say whether heads or tails are up, she is in both states at the same time.

And this ability of the qubit makes the quantum computer more efficient in principle: For the same calculation it needs significantly fewer qubits than today's computer bits. This is made clear by the following example.

A normal computer can represent the numbers from 0 to 3 with two bits. The two bits [0,0] result in the number 0, with [0,1] the number 1 is meant. With [1,0] the number 2 and with [1,1] the 3. Two bits can only represent one number at a time in a classic computer. In a quantum computer, on the other hand, a qubit can assume an infinite number of different states and that at the same time. The four combinations of states that represent the numbers 0 to 3 can theoretically be represented by just one qubit and at the same time. The quantum computer is therefore significantly faster. At the moment, however, the practice is not ready and only a few qubit states can be used. But even if one only assumes two different states that a qubit can occupy at the same time, each additional qubit doubles the number of states that can be represented at the same time. This advantage grows exponentially: three qubits can take on 8 states at the same time, 300 qubits even 2 to the power of 300 = 203703597633448608626844568840937816105146839366593625063614044935438129976333 6706183397376. That is a larger number than there are particles in the universe! A task that cannot be mastered for a classic computer. This example shows the unachievable advantage that quantum computers have in principle.

Calculating with faster than light speed

The qubits in a quantum computer can also be quantum entangled, colloquially one would say that they are connected to one another. If a qubit is brought into a certain state, the state of the other qubits quantum entangled with it also changes at this moment. This happens at faster than light speed. Since several qubits are quantum entangled with one another, i.e. their own state is dependent on that of the other qubits, the calculation in the quantum computer can also be carried out faster than light. This is also an advantage of quantum computers over today's computers.