Critically damped quantum search

Abstract

Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a natural role. Remarkably, we have found that there is a critical damping value that divides between the quantum $O(\sqrt{N})$ and classical O(N) search regimes. In addition, by allowing the damping to vary in a fashion we describe, one obtains a fixed-point quantum search algorithm in which ignorance of the number of targets increases the number of oracle queries only by a factor of 1.5.

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• Optimal Conditions for Environment-Assisted Quantum Transport on the Fully Connected Network
• Measuring the degree of unitarity for any quantum process
• A Fast fixed-point Quantum Search Algorithm by using Disentanglement and Measurement
• Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
• Optimization of the damped quantum search
• Quantum Search with Prior Knowledge
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