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Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Stability of topological quantum memories in contact with a thermal bath

Stefano Chesi, Basel

joint work with Beat Röthlisberger, Daniel Loss, Sergey Bravyi, and Barbara M. Terhal

We discuss several aspects related to the thermal stability of quantum memories. These are typically represented by spin lattice Hamiltonians encoding one or several qubits in a degenerate eigenspace. A self-correcting quantum memory has an infinite lifetime in the thermodynamic limit, even if the individual spins of the lattice are short-lived. While several candidate quantum memories were proposed to be self-correcting, many have revealed inadequate or difficult to analyze. In our work: a) We discuss general criteria to establish the stability of a quantum memory and derive a rigorous upper bound to the relaxation rate of a general quantum memory and b) We examine a generalization of the two-dimensional toric code which includes long-range repulsive interactions. By analytical arguments and direct numerical simulations we establish that such long-range interactions lead to stable memories. The lifetime scales polynomially with system size and the exponent is large for a super-ohmic thermal environment. We also show that such long-range interactions are physically relevant.