Executive Summary : | Quantum computing is a powerful tool for solving complex and classically unattainable problems using properties like superposition and entanglement. Classical complexity theory classifies problems as either tractable or intractable based on the resources needed. Quantum computers can solve problems like factoring n-bit numbers and travelling salesman problems. To represent a state in a quantum computer, a complex vector with components is required. Quantum error correction protects quantum information from decoherence and quantum noise. However, classical computers can't be copied due to the 'No-cloning theorem'. Quantum computers also need to preserve phase information in entangled states, which requires a new approach for error-correcting codes. Fault-tolerance operations aim to prevent the spread of errors within a block, but quantum gates spread errors in both forward and backward directions. |