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He imagined a topological quantum computer built on anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (one temporal plus two spatial dimensions). In 1997, having this problem in mind, Russian physicist Alexei Kitaev imagined a different approach to quantum computing: stable qubits could theoretically be formed from pairs of hypothetical particles called “non-abelian anyons”. If you want a hundred logical qubits you’d need tens of thousands of physical qubits in the computer.” Enormous progress has been achieved in this direction, but, to quote John Preskill: “That gives you a big overhead cost.
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For this, a quantum computer requires each unit of information to be shared among an elaborate network of many qubits cleverly arranged to prevent an environmental disturbance of one from leading to the collapse of them all. We have already introduced these problems when speaking about quantum error correction: to fight decoherence, one has to completely isolate the computer from its environment, and careful eliminate of noise, and protocols for quantum correction of unavoidable errors. Decoherence arises when the quantum system that encodes the qubits becomes entangled with its environment, which is a bigger, uncontrolled system. This effect, called decoherence, abruptly ends quantum computations. The outstanding problem with entangled superpositions of spinning electrons, polarized photons or most other particles that might serve as qubits is that they are very unstable: even a slight interaction with the environment will collapse qubit’s superposition, forcing it into a definite state of or. Yet, we haven’t talk much about practicalities. We have talked about its theoretical principles ( quantum entanglement, no-cloning theorem, …) and its applications, especially in the contexts of cryptography and complexity. We have been talking about quantum computing for a few weeks now.