Spin qubits in solid-state structures

Abstract

It is remarkable that today’s computers, after the tremendous developmentduring the last 50 years, are still essentially described by themathematical model formulated by Alan Turing in the 1930’s. Turing’smodel describes computers which operate according to the laws ofclassical physics. What would happen if a computer was operatingaccording to the quantum laws? Physicists and computer scientistshave been interested in this question since the early 1980’s,but research in quantum computation really started to flourish after1994 when Peter Shor discovered a quantum algorithm to find primefactors of large integers efficiently, a problem which is intrinsicallyhard for any classical computer (see [1] for an introduction intoquantum computation). The lack of an algorithm for efficient factoringon a classical machine is actually the basis of the widely usedRSA encryption scheme. Phase coherence needs to be maintained fora sufficiently long time in the memory of a quantum computer. Thismay sound like a harmless requirement, but in fact it is the mainreason why the physical implementation of quantum computation isso difficult. Usually, a quantum memory is thought of as a set oftwo-level systems, named quantum bits, or qubits for short. In analogyto the classical bit, two orthogonal computational basis states|0ñ and |1ñ are defined. The textbook example of a quantum two-levelsystem is the spin 1/2 of, say, an electron, where one can identifythe “spin up��? state with |0ñ and the “spin down��? statewith |1ñ. While several other two-level systems have been proposedfor quantum computing, we will devote the majority of our discussionto the potential use of electron spins in nanostructures (such asquantum dots) as qubits.