1,614 research outputs found
Stable quantum memories with limited measurement
We demonstrate the existence of a finite temperature threshold for a 1D
stabilizer code under an error correcting protocol that requires only a
fraction of the syndrome measurements. Below the threshold temperature, encoded
states have exponentially long lifetimes, as demonstrated by numerical and
analytical arguments. We sketch how this algorithm generalizes to higher
dimensional stabilizer codes with string-like excitations, like the toric code.Comment: 11 Pages, 7 Figure
Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime
We present an analysis of the relaxation dynamics of finite-size topological
qubits in contact with a thermal bath. Using a continuous-time Monte Carlo
method, we explicitly compute the low-temperature nonequilibrium dynamics of
the toric code on finite lattices. In contrast to the size-independent bound
predicted for the toric code in the thermodynamic limit, we identify a
low-temperature regime on finite lattices below a size-dependent crossover
temperature with nontrivial finite-size and temperature scaling of the
relaxation time. We demonstrate how this nontrivial finite-size scaling is
governed by the scaling of topologically nontrivial two-dimensional classical
random walks. The transition out of this low-temperature regime defines a
dynamical finite-size crossover temperature that scales inversely with the log
of the system size, in agreement with a crossover temperature defined from
equilibrium properties. We find that both the finite-size and
finite-temperature scaling are stronger in the low-temperature regime than
above the crossover temperature. Since this finite-temperature scaling competes
with the scaling of the robustness to unitary perturbations, this analysis may
elucidate the scaling of memory lifetimes of possible physical realizations of
topological qubits.Comment: 14 Pages, 13 figure
Stroboscopic Generation of Topological Protection
Trapped neutral atoms offer a powerful route to robust simulation of complex
quantum systems. We present here a stroboscopic scheme for realization of a
Hamiltonian with -body interactions on a set of neutral atoms trapped in an
addressable optical lattice, using only 1- and 2-body physical operations
together with a dissipative mechanism that allows thermalization to finite
temperature or cooling to the ground state. We demonstrate this scheme with
application to the toric code Hamiltonian, ground states of which can be used
to robustly store quantum information when coupled to a low temperature
reservoir.Comment: 5 pages, 2 figures. Published versio
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