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By David McMahon
A self-contained therapy of the basics of quantum computing
This transparent, sensible e-book takes quantum computing out of the world of theoretical physics and teaches the basics of the sector to scholars and execs who've no longer had education in quantum computing or quantum info idea, together with desktop scientists, programmers, electric engineers, mathematicians, physics scholars, and chemists. the writer cuts during the conventions of average jargon-laden physics books and as a substitute provides the fabric via his specified "how-to" procedure and pleasant, conversational style.
Readers will how to perform calculations with particular information and may achieve a basic seize of:
* Quantum mechanics
* Quantum computation
* Teleportation
* Quantum cryptography
* Entanglement
* Quantum algorithms
* mistakes correction
A variety of labored examples are integrated so readers can see how quantum computing is completed with their very own eyes, whereas solutions to related end-of-chapter difficulties are supplied for readers to envision their very own paintings as they discover ways to grasp the information.
Ideal for execs and graduate-level scholars alike, Quantum Computing defined promises the basics of quantum computing readers have to be in a position to comprehend present learn papers and cross directly to learn extra complicated quantum texts.
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Additional info for Quantum Computing Explained
Sample text
2. Two quantum states are given by |a = −4i , 2 |b = 1 −1 + i (A) Find |a + b . (B) Calculate 3|a − 2|b . (C) Normalize |a , |b . 3. Another basis for C2 is |+ = |0 + |1 , √ 2 |− = |0 − |1 √ 2 Invert this relation to express {|0 , |1 } in terms of {| + , | − }. 4. A quantum system is in the state |ψ = 3i|0 + 4|1 5 (A) Is the state normalized? (B) Express the state in the | + , | − basis. 5. 6. Photon horizontal and vertical polarization states are written as |h and |v , respectively. Suppose √ 1 3 |ψ1 = |h + |v 2 2 √ 1 3 |ψ2 = |h − |v 2 2 |ψ3 = |h Find | ψ1 |ψ2 |2 , | ψ1 |ψ3 |2 , | ψ3 |ψ2 |2 3 MATRICES AND OPERATORS An operator is a mathematical rule that can be applied to a function to transform it into another function.
4) |a = ⎜ .. ⎠ an This type of notation can be used with qubits. 1). 1. 4), which we call the components of the vector, are complex—something we’ve already mentioned. 5) α|a = α ⎜ .. ⎟ = ⎜ .. ⎠ ⎝ . ⎠ an αan It’s easy to see that this produces another column vector with n complex numbers, so the result is another element in Cn . So Cn is closed under scalar multiplication. 6) |a + |b = ⎜ .. ⎟ + ⎜ .. ⎟ = ⎜ .. ⎠ ⎝ . ⎠ an bn an + bn This should all be pretty straightforward, but let’s illustrate it with an example.
If a vector is not normalized, we can generate a normalized vector by computing the norm (which is just a number) and dividing the vector by it. For the vectors√in the previous√example, |u , |v are not normalized, since we found that u = 20 and v = 11. But the vectors 25 ORTHONORMALITY |u˜ = 1 |u = √ |u u 20 |v˜ = |v 1 = √ |v v 11 are normalized. This is easy to see. Check the first case: u| ˜ u˜ = 1 √ u| 20 1 √ |u 20 = 1 20 u|u = =1 20 20 If each element of a set of vectors is normalized and the elements are orthogonal with respect to each other, we say the set is orthonormal .