Quantum Computing: An Overview (original) (raw)

2008, Mathematical Aspects of Quantum Computing 2007

Elements of quantum computing and quantum infromation processing are introduced for mathematics students. Subjects inclulde quantum physics, qubits, quantum gates, quantum algorithms, decoherece, quantum error correcting codes and physical realizations. My lectures should serve as introduction to other lectures. i λ i |λ i λ i |, where A|λ i = λ i |λ i. Then the expectation value A of a after measurements with respect to many copies of |ψ is A = ψ|A|ψ. (2) Let us expand |ψ in terms of |λ i as |ψ = i c i |λ i. According to A 2, the probability of observing λ i upon measurement of a is |c i | 2 and therefore the expectation value after many measurements is i λ i |c i | 2. If, conversely, Eq. (2) is employed, we will obtain the same result since ψ|A|ψ = i,j c * j c i λ j |A|λ i = i,j λ i c * j c i δ ij = i λ i |c i | 2. This measurement is called the projective measurement. Any particular outcome λ i will be found with the probability |c i | 2 = ψ|P i |ψ , where P i = |λ i λ i | is the projection operator and the state immediately after the measurement is |λ i or equivalently P i |ψ / ψ|P i |ψ .

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