Related papers: Error threshold in optimal coding, numerical crite…
We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra…
Analyses in high energy physics aim to put the Standard Model---the commonly accepted theory---to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is equivalent to the Bayesian posterior for a high-dimensional…
We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures $\beta>0$. To characterize the free energy,…
A recently introduced Renormalization Group approach to frustrated spin models is applied in three dimensions through Monte Carlo computations. A class of spin glass models is analysed, with correlated disorder variables given by a Z_2…
In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
The description of a three-dimensional Ising-like magnet in the presence of an external field in the vicinity of the critical point by the collective variables method is proposed. Using the renormalization group transformations, the scaling…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
These are notes for a mini-course on the extremes of correlated random fields which I gave in the spring 2013 in Marseille. The first chapter recalls the paradigmatic random energy models with finitely many scales introduced by B. Derrida…
Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of…
One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the…
We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…
A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last $n$ symbols. If the algorithm is randomized, then at each time instant it produces an incorrect…