The basic unit of information in a classical computer is a bit, which is a little register that can take on two possible values usually called “0” and “1.” If one bit can take two values (0 and 1), then two bits can take four (22) values (00, 01, 10, and 11). Three bits offers a total of eight (23) values: (000, 001, 010, 011, 100, 101, 110, and 111). As you can see, the number of possible values increases as the square of the number of bits. In computer jargon, 8 bits is known as a byte, And it can take on 1 of 256 possible values.
The bits of classical computers are made using classical physical quantities such as voltage levels between the plates of a tiny capacitor in a microprocessor. If a charge is applied to the capacitor, for example, it has the value 1. If uncharged, the value is zero. Arrays of capacitors then build up multiple bits into bytes, kilobytes, megabytes, and more.
As their name suggests, computers are good for more than just storing information in a sea of bits. Computers utilize specific rules to flip bits in certain ways to perform computations. These rules are known as algorithms. Algorithms generally perform simple functions, but these can be combined to perform more sophisticated tasks using sets of instructions known as computer programs.
You will recall that quantum particles have a property that lends itself quite naturally to the concept of the bit. Quantum spin tells us that some quantum particles (like an electron) can exist in two possible states, normally called “down” and “up.” The names are arbitrary, and we could have also called them “0” and “1.”
For example, let’s write Ψ0 for an electron in the “down” state and Ψ1 for an electron in the “up” state. The electron in this case, which jumps between two well-defined, observable states, is a physical entity that behaves like a bit. In the terminology of quantum computing, the electron represents a quantum bit, otherwise known as a qubit.
ATOM TRAP
We are focusing here on the property of quantum spin. More generally, though, a qubit can be formed from any two-state quantum system. Another example would be the ground state and some excited state of an atom. There is no difference from a theoretical perspective. The only difference would arise in how you actually build your quantum computer.
Aside from swapping out copper capacitors for electrons, we’ve so far introduced nothing new. However, if you recall that quantum systems can take on numerous values at the same time, through the property of superposition, you’ll see that our qubits offer many more possibilities than their classical counterparts.
For example, an electron could be in its “down” state, its “up” state, or some arbitrary superposition in between. We could write out such a superposition state as Ψ = aΨ0 + bΨ1, where a and b are just a pair of constant numbers. Recall that in such a superposition state, the probability of finding the electron in state Ψ0 is |a|2 and the probability of finding it in state Ψ1 is |b|2. In their most general form, a and b can be complex numbers, which adds a whole new dimension of flexibility into the system. This leads us to the basic advantage of a quantum computer over a classical computer. In contrast to classical bits, which can take only one value at any time, qubits can take on multiple values simultaneously. This property is called parallelism.
DEFINITION
A qubit, which stands for quantum bit, can be formed from a physical entity (like an electron) that has two well-defined quantum states (like spin “down” and spin “up”). It is the quantum analog to the computer bit.
Parallelism refers to the ability of qubits to take on multiple values at the same time, thanks to the property of quantum superposition.
Things get even better when we add in more qubits. Consider the case of three. We saw in the classical case that a three-bit system can take on one, but only one, of eight possible values (000, 001, 010, 011, 100, 101, 110, and 111). A qubit, on the other hand, can simultaneously take on all of the eight possible values (which we could write as Ψ0, Ψ1, Ψ2, Ψ3, Ψ4, Ψ5, Ψ6, and Ψ7). This can be written as a superposition of the form Ψ = aΨ0 + bΨ1 + cΨ2 + dΨ3 + eΨ4 + fΨ5 + gΨ6 + hΨ7. Again, the letters out front (called coefficients) represent arbitrary values, the size of which is an indication of how much any particular component state is mixed in.
You can see that as the number of qubits increases, the range of possible values that can be assumed at one time increases exponentially. This rapid increase (or parallelism) can be used to make quantum computers faster than classical computers. Conversely, it could be used to make quantum computers smaller than their classical counterparts, since the number of qubits needed to perform sophisticated computations would be far less than the corresponding number of bits.
Furthermore, groups of two or more qubits can exist not just in superposition states, but also in states that are entangled as we defined. This property allows for even more possibilities.
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