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Public-key Cryptography: Theory and Practice by C. E. Veni Madhavan, Abhijit Das

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8.2. Quantum Computation

We start with a formal description of quantum computation. Quantum mechanical laws govern this paradigm. We will pay little attention to the physical interpretations of these laws. A mathematical formulation suffices for our purpose.

For defining a quantum mechanical system, we need to enrich our mathematical vocabulary. Let V be a vector space over (or ). Using Dirac’s ket notation we denote a vector ψ in V as |ψ〉.

Definition 8.1.

An inner product (also called a dot product or a scalar product) on V is a function satisfying ...

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