Probabilistic Quantum Computation and Linear Optical Realizations
Norbert Lütkenhaus · 2016
Quantum computation is usually thought of as a sequence of quantum gates. This sequence of gates decomposes the desired total unitary operation of the computation. It is followed by a measurement that extracts the result of the computation. This chapter introduces a concept of computation that allows one to incorporate probabilistic elements into a computation, which in the end becomes deterministic again. It also shows that computation can be performed not only in the paradigm of quantum gates but also by preparing entangled auxiliary states, measurements, and single-qubit operations. It turns out that the Bell measurements required in the Gottesman-Chuang trick cannot be implemented perfectly with linear optics. Moreover, the generation of entangled auxiliary states is hard to achieve in general. Knill, Laflamme, and Milburn solved this problem in several steps. The chapter describes each steps of the Knill-Laflamme-Milburn (KLM) scheme.