A linear time quantum algorithm for 3SAT using irreversible quantum operations
Zachary B. Walters
TL;DR
This paper introduces a quantum algorithm that solves the NP-complete problem 3SAT in linear time by extending the Deutsch model to include irreversible operations, enabling rapid probability concentration.
Contribution
It presents a novel quantum algorithm leveraging irreversible operations to achieve linear time complexity for 3SAT, an NP-complete problem.
Findings
Achieves linear time solution for 3SAT
Uses irreversible quantum operations for probability concentration
Extends Deutsch model to include thermodynamically irreversible processes
Abstract
The Deutsch model of quantum computation is extended to allow for thermodynamically irreversible operations by allowing the system of interest to interact with an outside reservoir. A set of irreversible logical error correction superoperators are constructed which allow the rapid concentration of probability from an exponentially large search space into a small number of logically defined states. These capabilities are used to construct a linear time solution algorithm for the NP complete problem 3SAT.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Neural Networks and Reservoir Computing · Quantum Information and Cryptography