please elaborate the process in detail and legible manner :)

Problem 4 Quantum computers are a computers which use quantum states (called qubits} to process information. The best hardware to physically realize a qubit is active area of research in materials chemistry. Common choices include superconductors, trapped ions, neutral atoms, and even the vibronic states of molecules. Compare this with your own classical computer which use electronic transistors to emulate classical bits of information (i.e. 0's and 1's). Mathematically qubits are represented by column vectors and the logical operations to manipulate them (called gates) are represented by matrices. Consider the 0-bit and 1-bit, was) M) These form the basis of a single qubit Ma) which is generally a complex linear combination of the two bits, I4?) = ca ID) + c1|1), with 90,81 6 (I. Consider the simplest possible case where the qubit is prepared in either one of the basis vectors, namely M9) = |0) or I?) = |1} (a) [Spts] Compute the action of the X-gate on |D). Do this though matrix X |0} where, he s)- (b) [Spts] Repeat your calculation in (a), but this time calculating X |1). (c) [4pts] X is called the NOT-gate. Explain this in terms of your results from (a)-(b}. It will help to think of |0) corresponding to FALSE, |1) corresponding to TRUE, and what the action of the matrix does