AAI_2025_Capstone_Chronicles_Combined

Breast Tumor Classification Using Quantum Neural Networks

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classical bit 2 , but also a blend (superposition) of the two. As can be seen by Figure 5, these

qubits exist in a higher dimensional space than bits or probabilistic bits. The act of observing, or

measuring, at the end of the quantum computation causes a qubit in superposition to “collapse”

probabilistically to the classical value of 0 or 1. Thus the output of a quantum computation is a

classical result. Since that measurement is probabilistic, the result may be non-deterministic as

well.

Figure 6

Example of a single qubit being put in an equal superposition, then being measured. This is repeated 20 times, essentially resulting in a series of 20 bits being 0 or 1 due to the nondeterministic nature of the qubit being in superposition.

The state of qubits can be linked together, through a property known as entanglement.

For example, a pair of qubits could be in a state where they both collapse to the value of 0 or

the value of 1, but not a mix of 0 and 1. Another way to think of this would be to have a pair of

coins spinning. If one is slammed down as heads the other also becomes heads instantly. The

“instantly” part is worth highlighting: this occurs regardless of the distance between the qubits 3 .

Einstein himself struggled with acknowledging this, referring to entanglement as “spooky action

at a distance” (Muller, 2022). Figure 7 represents two qubits entangled to collapse to either 00

or 11 with equal probability, in Dirac notation. The coefficients of 1/√2 are squared to give the

probability of collapsing to that state- resulting in a probability of 0.5 for each state in this case.

2 The north pole and south pole being the values of 0 and 1. 3 This is even if the qubits are light years apart. There is no information transmitted when this happens, so the principle of information not being able to travel faster than light is not violated.

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