Adrian Hutter

Efficient Markov chain Monte Carlo algorithm for the surface code

Minimum-weight perfect matching (MWPM) has been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108, 180501 (2012)]. A Markov chain Monte Carlo (MCMC) algorithm [Phys. Rev. Lett. 109, 160503 (2012)] is able to achieve lower logical error rates and higher thresholds than MWPM, but requires a classical runtime complexity, which is super-polynomial in L, the linear size of the code. In this work we present an MCMC algorithm that achieves significantly lower logical error rates than MWPM at the cost of a runtime complexity increased by a factor O(L-2). This advantage is due to taking correlations between bit-and phase-flip errors (as they appear, for example, in depolarizing noise) as well as entropic factors (i.e., the numbers of likely error paths in different equivalence classes) into account. For depolarizing noise with error rate p, we present an efficient algorithm for which the logical error rate is suppressed as O((p/3)(L/2)) for p -< 0-an exponential improvement over all previously existing efficient algorithms. Our algorithm allows for tradeoffs between runtime and achieved logical error rates as well as for parallelization, and can be also used for correction in the case of imperfect stabilizer measurements.

Enhanced thermal stability of the toric code through coupling to a bosonic bath

We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at nonzero temperature. This is achieved by locally coupling a two-dimensional

Almost all quantum states have low entropy rates for any coupling to the environment.

L\ifmmode\times\else\texttimes\fi{}L

Quantum computing with parafermions

toric code to a three-dimensional (3D) bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with

Breakdown of surface-code error correction due to coupling to a bosonic bath

L

Dynamic Generation of Topologically Protected Self-Correcting Quantum Memory

. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with

Parafermions in a Kagome lattice of qubits for topological quantum computation

\mathrm{ln}(L)

Improved HDRG decoders for qudit and non-Abelian quantum error correction

. For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing, respectively, exponentially and polynomially with

Dependence of a quantum-mechanical system on its own initial state and the initial state of the environment it interacts with

L

Effective quantum-memory Hamiltonian from local two-body interactions

. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its low-energy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.