Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in between

Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in between

Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as buil...

Decoherence, Control and Symmetry in Quantum Computers

Quantum Computers

We analyse dissipation in quantum computation and its destructive impact on eeciency of quantum algorithms. We discuss relations between decoherence and computational complexity and show that quantum factorisation algorithm must be modiied in order to be regarded as eecient and realistic. Our model od decoherence is quite general and incorporates reservoirs with a large coherence length.

Quantum Computers

This research paper gives an overview of quantum computers – description of their operation, differences between quantum and silicon computers, major construction problems of a quantum computer and many other basic aspects. No special scientific knowledge is necessary for the reader. Introduction to Quantum Computers Around 2030 computers might not have any transistors and chips. Think of a com...

Algorithms for Quantum Computers

Quantum computing is a new computational paradigm created by reformulating information and computation in a quantum mechanical framework [30, 27]. Since the laws of physics appear to be quantum mechanical, this is the most relevant framework to consider when considering the fundamental limitations of information processing. Furthermore, in recent decades we have seen a major shift from just obs...