Quantum optimization offers a unique approach to globally optimizing unknown quantum states. Quantum computers operate on superpositions of all classical search states, allowing them to evaluate the properties of all the states in about the same time a classical machine requires for a single evaluation. This property is known as quantum parallelism.
Most quantum search algorithms focus on decision problems. Quantum computers give a quadratic improvement in search speed when compared with classical computers. Optimization searches can be treated as a series of decision problems with different assumed values for the minimum cost. Each quantum state has an associated cost and the goal is to find a minimum-cost state.
“However beautiful the strategy,
you should occasionally
look at the results.”
QUANTUM DATA COMPRESSION
"Opportunities are problems
in search of solutions."
Quantum data compression allows for the encoding of quantum information into a quantum state. The von Neumann entropy of a quantum source determines the minimum asymptotic number of qubits into which its signals can be compressed by a quantum encoder and still be faithfully recovered by a quantum decoder. This is the analogue of classical data compression or source coding, by which redundant classical data is compressed and faithfully regenerated. A quantum encoder is like a discreet telegrapher, who transmits messages without even remembering them.