Self-Correcting Quantum Computers

Abstract

Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we first give a sufficient condition on the connect- edness of excitations for a stabilizer code model to be a self-correcting quantum memory. We then study the two main examples of topological stabilizer codes in arbitrary dimensions and establish their self-correcting capabilities. Also, we address the transversality properties of topological color codes, showing that 6D color codes provide a self-correcting model that allows the transversal and local implementation of a universal set of operations in seven spatial dimensions. Finally, we give a procedure to initialize such quantum memories at finite temperature.

RevTeX, 24 pages, version revised to increase readability: added sketch of proof of stability criterion, rewritten section on implementation of quantum computation, revised introduction and conclusions

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• Topological Quantum Distillation
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• Topological Computation without Braiding
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Cited by in corpus (2)

• Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
• Implementation of Single-qubit and CNOT Gates by Anyonic Excitations of Two-body Topological Color Code