Quantum mechanics and classical computing

Certain Uncertainties

A common theme of this book is that quantum computers are much dierent than classical computers (such as your personal computer), because they require quantum mechanics for their working (and classical computers do not). To understand just how dierent a quantum computer is from a classical © 2010 Taylor & Francis Group, LLC computer, it is necessary to understand just how dierent quantum mechanics is from classical mechanics. I could just tell you they are dierent and get right to work on the story of the quantum computer, but then you would just have to take my word for this dierence. However, I don’t want you to just take my word for it. I don’t want you to just believe quantum mechanics is dierent than classical mechanics; I want you to know it. So my goal in this chapter is to show you that the quantum theory of Bohr and Heisenberg and Schrödinger is really dierent (and much stranger) from the classical theory of Kepler and Newton and Maxwell.

Bart D’Hooghe, Jarosław Pykacz

Lorenzo Catani, Dan E. Browne, Nadish de Silva

Spekkens’ toy model (SM) is a non-contextual hidden-variable model made to support the epistemic view of quantum theory, where quantum states are states of partial knowledge about a deeper underlying reality. Despite being a classical model, it has reproduced many features of quantum theory (entanglement, teleportation, . . .): (almost) everything but contextuality, which therefore seems to be the inherent quantum feature. In addition to the importance in foundation of quantum theory, the notion of contextuality seems to be a crucial resource for quantum computation. In particular it has been proven that, in the case of odd prime discrete dimensional systems, contextuality is necessary for universal quantum computation in state-injection schemes of computation based on stabilizer quantum mechanics (SQM). The latter is a subtheory of quantum mechanics which is very popular in the field of quantum computation and quantum error correction. State-injection schemes consist of a classically-simulable part (like SQM) and a resource state that boosts the computation to a quantum improvement. In the odd-dimensional case, SM is operationally equivalent to SQM. In the even-dimensional case, the equivalence only holds in terms of structure, not in terms of statistical predictions. This because qubit-SQM shows contextuality, while qudit(odd dimensions)-SQM does not. We believe that SM can be a valid tool to study contextuality as a resource in the field of quantum computation. Restricted versions of SM compatible with quantum mechanics (QM) can be used as the non-contextual classically-simulable part of state-injection schemes thus opening other scenarios where studying if contextuality is necessary for quantum computational speed-up.

Jasmeet Singh, Mohit Singh

With the skyrocketing needs of rapid processing speed and miniaturization, classical computers are not able to keep up the pace with these few necessary parameters. As classical computers work on classical mechanics there expansion is at zenith. Due to these limitation quantum mechanics is taking the role of game changer in race of computation. Quantum computing studies quantum computer with the quantum mechanics phenomenon of superposition, entanglement, tunneling and annealing to solve problems that can't be solved in life span of human beings. This review aims for summarizing timeline of the quantum computing along with quantum mechanics behind it.

Pooja Srivastava, Anushtup Mishra, Yogesh K. Srivastava