Requirements for a Quantum Computer
ARTUR K. EKERT, Alastair Kay · 2016
This chapter explores how computation is a physical process, and the workings of a computer are governed by the laws of physics. This has caused to replace the classical description of a process, using probabilities and stochastic matrices, with a new description using probability amplitudes and unitary matrices. Many interesting quantum operations can be obtained by parallel and sequential compositions of quantum gates. Building large quantum circuits requires large supplies of preselected quantum gates. Many classical mathematical techniques and conclusions translate to the new scenario, such as the composition of gates by tensor products and matrix multiplication, or that all possible operations can be decomposed in terms of a small number of building blocks, the universal gates. It should be stressed, however, that not all probability vectors of composed systems and not all stochastic matrices operating on such systems can be written as tensor products.