AAI_2025_Capstone_Chronicles_Combined

Breast Tumor Classification Using Quantum Neural Networks

10

Figure 7

Equal chance of a pair of qubits collapsing to 00 or 11.

1 √2

1 √2

|00⟩+

|11⟩

An oversimplified way to think of this combination of entanglement and superposition is

allows computation to be carried out in parallel. With 8 qubits one could effectively compute

using all 256 (2 8 ) values at once, whereas on a classical computer you’d have to go through

each of the 256 values one at a time. This is what gives quantum computers a computational

advantage over classical computers. As with classical computers, these qubits are operated on

via gates 4 - albeit quantum gates.

There are additional differences, such as requiring quantum computations to be

reversable (Kaye, Laflamme, & Mosca, 2007) and not being able to copy quantum information-

also known as the no cloning theorem 5 (Meglicki, 2008). Further details will not be covered here,

but the important thing to note is that computation with qubits is a fundamentally different way of

computing when compared to classical bits. To dispel a common myth: quantum computers

aren’t universally faster 6 than classical computers, they just compute fundamentally differently-

and that difference can be exploited in certain cases to make them faster.

Famous applications of quantum computing include factoring large numbers via Shor’s

algorithm and faster unsorted database searching with Grover’s algorithm. It should be noted

that the quantum piece of these algorithms is only for specific parts- the rest is classical

computation. For a comprehensive overview of quantum computing the reader is referred to the

4 Such as an OR, NOT, or AND gate. 5 Essentially copy and paste is not allowed, however cut and paste is allowed. 6 For example, a classical and quantum computer can perform addition of two numbers with the same operations- meaning neither has a faster run time than the other.

263