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Quantum Computing

Matrixes are linear operators, what's the main implication of this?

That if the domain an orthonormal space, the image will also be one (Therefore if input is an unit vector, so will the output)

Quantum Computing

What's the point of the Gramm Schmidt theorem?

Given an arbitrary basis that spans the space S, it allows us to obtain a new orthonormal basis that has as it’s the first element the unit vector v and spans S still.

Quantum Computing

What does orthonormal mean?

That the vectors that form the basis are unit vectors (modulus 1 in the euclidean distance) and orthogonal in their Hilbert space

Quantum Computing

What are the requirements for an alternative basis for your states?

Given an arbitrary basis of two states, an state can be represented in terms of it and it will be possible to measure as long as this new base is orthonormal

Quantum Computing

What are the base components of any multi-qubit quantum gate?

They are composed by CNOTs and single-qubit gates

Quantum Computing

Are quantum gates invertible?

Yes, as the inverse of an unitary matrix is an unitary, and therefore, the reverse gate is also a valid quantum gate

Quantum Computing

What does an irreversible gate mean?

That given its output, we are not capable of reconstructing the input state

Quantum Computing

Inverse of an unitary matrix...

is still an unitary matrix

Quantum Computing

What's the universal gate on classical computing?

The NAND gate. With them, you can build any other function.

Quantum Computing

Do phase multipliers affect our quantum state? e^iθ * |ψ>

No, as the probabilities remain constant

Quantum Computing

What's the parity of a binary string?

It’s the number of 1’s in the binary representation of a number. This number can be odd or even and it’s used as the most basic form of error correction.

Quantum Computing

What do we mean with the decomposition of single-qubit gates?

Every single-qubit gate can be broken in the product of three rotation matrixes. With a finite set of rotation angles α, β & γ, we can produce an arbitrary gate

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