The power of quantum computing

We’ve seen that quantum computing differs from classical computing in a lot of ways. The power of quantum computers for certain problems becomes apparent when we compare them to their classical counterpart. While a classical computer with \(n\) bits can represent only one state, a quantum computer with \(n\) qubits can represent \(2^n\) states simultaneously. For example, a conventional computer with 2 bits can be in the state \(\ket{10}\), thus representing the number 2. However, a quantum computer with 2 qubits can be in a superposition of the states \(\ket{00}\), \(\ket{01}\), \(\ket{10}\) and \(\ket{11}\), thus representing the numbers 0,1,2 and 3 simultaneously.

One giant supercomputer has the memory capacity to store around 50 qubits. Storing 51 qubits would require already two of these machines. With a quantum computer, we would just need to add one qubit. Taking this further, it just takes 300 qubits to represent more numbers simultaneously than there are atoms in the universe.

While classical computers are in one state and only process this one state, quantum computers allow operating on a superposition that represents multiple results. But only one result can be obtained with one measurement. Therefore, we need clever algorithms that take advantage of the peculiarities of qubits (namely superposition and entanglement) and ensure that the correct measurement results become very likely.

In practice, the correct results are barely measured 100% of the times. Thus, a program on a quantum computer needs to be executed more often than on a conventional computer and will often deliver a range of answers instead of a single one.

Obtaining multiple possible answers from a quantum computer may sound less accurate than the results we obtain with conventional computers. With the addition of 44 and 32 we don’t want the answer to be most likely 76, but precisely 76. Unsurprisingly, for tasks like running a web server or addition, we are most likely not going to see quantum computers replacing conventional computers.

However, there are a variety of problems, where reducing the number of possible answers to just a few will result in great time savings. In the next module, you will learn how those use cases look like.