By Michel Le Bellac
Quantum info and computation is a swiftly increasing and cross-disciplinary topic. This e-book supplies a self-contained advent to the sphere for physicists, mathematicians and desktop scientists who need to know extra approximately this fascinating topic. After a step by step creation to the quantum bit (qubit) and its major homes, the writer offers the mandatory historical past in quantum mechanics. The middle of the topic, quantum computation, is illustrated by means of an in depth remedy of 3 quantum algorithms: Deutsch, Grover and Shor. the ultimate chapters are dedicated to the actual implementation of quantum desktops, together with the newest facets, reminiscent of superconducting qubits and quantum dots, and to a brief account of quantum info. Written at a degree appropriate for undergraduates in actual sciences, no past wisdom of quantum mechanics is believed, and basically uncomplicated notions of physics are required. The e-book contains many brief workouts, with ideas on hand to teachers via [email protected]
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Extra info for A Short Introduction to Quantum Information and Quantum Computation
Number has no pre-image, this function is not onto. g. (2, 3) and (3, 2), that map to the same integer, the function is also not one-to-one. 16: An invertible function is one-to-one. Proof Suppose f is not one-to-one, and let x1 and x2 be distinct elements of the domain such that f (x1 ) = f (x2 ). Let y = f (x1 ). Assume for a contradiction that f is invertible. The definition of inverse implies that f −1 (y) = x1 and also f −1 (y) = x2 , but both cannot be true. 17: An invertible function is onto.
To take the negative of a number, use as a unary operator (as in -9). Exponentiation is represented by the binary operator **, and truncating integer division is //. Finding the remainder when one integer is divided by another (modulo) is done using the % operator. As usual, ** has precedence over * and / and //, which have precedence over + and -, and parentheses can be used for grouping. To get Python to carry out a calculation, type the expression and press the Enter/Return key: >>> 44+11*4-6/11.
The value of that expression is 9, so y is bound to 18. In the third assignment, x is bound to 12. This does not change the fact that y is bound to 18. 3 Conditional expressions There is a syntax for conditional expressions: ⟨expression⟩ if ⟨condition⟩ else ⟨expression⟩ 22 CHAPTER 0. THE FUNCTION 23 The condition should be a Boolean expression. Python evaluates the condition; depending on whether it is True or False, Python then evaluates either the first or second expression, and uses the result as the result of the entire conditional expression.
A Short Introduction to Quantum Information and Quantum Computation by Michel Le Bellac