Optimizing Quantum Error Correction Codes with Reinforcement Learning

Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a reinforcement learning framework for optimizing and fault-tolerantly adapting quantum error correction codes. We consider a reinforcement learning agent tasked with modifying a family of surface code quantum memories until a desired logical error rate is reached. Using efficient simulations with about 70 data qubits with arbitrary connectivity, we demonstrate that such a reinforcement learning agent can determine near-optimal solutions, in terms of the number of data qubits, for various error models of interest. Moreover, we show that agents trained on one setting are able to successfully transfer their experience to different settings. This ability for transfer learning showcases the inherent strengths of reinforcement learning and the applicability of our approach for optimization from off-line simulations to on-line laboratory settings.Comment: 21 pages, 13 figures, 1 table, updated reference list, accepted for publication in Quantu

Integral solutions to boundary quantum Knizhnik–Zamolodchikov equations

We construct integral representations of solutions to the boundary quantum Knizhnik–Zamolodchikov equations. These are difference equations taking values in tensor products of Verma modules of quantum affine , with the K-operators acting diagonally. The integrands in question are products of scalar-valued elliptic weight functions with vector-valued trigonometric weight functions (boundary Bethe vectors). These integrals give rise to a basis of solutions of the boundary qKZ equations over the field of quasi-constant meromorphic functions in weight subspaces of the tensor product

Boundary quantum Knizhnik-Zamolodchikov equations and fusion

In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov equations with diagonal K-operators to higher-spin representations of quantum affine $\mathfrak{sl}_2$. First we give a systematic exposition of known results on $R$-operators acting in the tensor product of evaluation representations in Verma modules over quantum $\mathfrak{sl}_2$. We develop the corresponding fusion of $K$-operators, which we use to construct diagonal $K$-operators in these representations. We construct Jackson integral solutions of the associated boundary quantum Knizhnik-Zamolodchikov equations and explain how in the finite-dimensional case they can be obtained from our previous results by the fusion procedure

Computation of Entropy Production in Stratified Flames Based on Chemistry Tabulation and an Eulerian Transported Probability Density Function Approach

This contribution presents a straightforward strategy to investigate the entropy production in stratified premixed flames. The modeling approach is grounded on a chemistry tabulation strategy, large eddy simulation, and the Eulerian stochastic field method. This enables a combination of a detailed representation of the chemistry with an advanced model for the turbulence chemistry interaction, which is crucial to compute the various sources of exergy losses in combustion systems. First, using detailed reaction kinetic reference simulations in a simplified laminar stratified premixed flame, it is demonstrated that the tabulated chemistry is a suitable approach to compute the various sources of irreversibilities. Thereafter, the effects of the operating conditions on the entropy production are investigated. For this purpose, two operating conditions of the Darmstadt stratified burner with varying levels of shear have been considered. The investigations reveal that the contribution to the entropy production through mixing emerging from the chemical reaction is much larger than the one caused by the stratification. Moreover, it is shown that a stronger shear, realized through a larger Reynolds number, yields higher entropy production through heat, mixing and viscous dissipation and reduces the share by chemical reaction to the total entropy generated

Computation of Entropy Production in Stratified Flames Based on Chemistry Tabulation and an Eulerian Transported Probability Density Function Approach

This contribution presents a straightforward strategy to investigate the entropy production in stratified premixed flames. The modeling approach is grounded on a chemistry tabulation strategy, large eddy simulation, and the Eulerian stochastic field method. This enables a combination of a detailed representation of the chemistry with an advanced model for the turbulence chemistry interaction, which is crucial to compute the various sources of exergy losses in combustion systems. First, using detailed reaction kinetic reference simulations in a simplified laminar stratified premixed flame, it is demonstrated that the tabulated chemistry is a suitable approach to compute the various sources of irreversibilities. Thereafter, the effects of the operating conditions on the entropy production are investigated. For this purpose, two operating conditions of the Darmstadt stratified burner with varying levels of shear have been considered. The investigations reveal that the contribution to the entropy production through mixing emerging from the chemical reaction is much larger than the one caused by the stratification. Moreover, it is shown that a stronger shear, realized through a larger Reynolds number, yields higher entropy production through heat, mixing and viscous dissipation and reduces the share by chemical reaction to the total entropy generated

Large Eddy Simulation of Soot Formation in a Real Aero-Engine Combustor Using Tabulated Chemistry and a Quadrature-Based Method of Moments

Accepted manuscript of the ASME Journal of Engineering for Gas Turbines and Power Paper "Large Eddy Simulation of Soot Formation in a Real Aero-Engine Combustor Using Tabulated Chemistry and a Quadrature-Based Method of Moments"

Analysis of Local Exergy Losses in Combustion Systems Using a Hybrid Filtered Eulerian Stochastic Field Coupled with Detailed Chemistry Tabulation: Cases of Flames D and E

A second law analysis in combustion systems is performed along with an exergy loss study by quantifying the entropy generation sources using, for the first time, three different approaches: a classical-thermodynamics-based approach, a novel turbulence-based method and a look-up-table-based approach, respectively. The numerical computation is based on a hybrid filtered Eulerian stochastic field (ESF) method coupled with tabulated detailed chemistry according to a Famelet-Generated Manifold (FGM)-based combustion model. In this work, the capability of the three approaches to capture the effect of the Re number on local exergy losses is especially appraised. For this purpose, Sandia flames D and E are selected as application cases. First, the validation of the computed flow and scalar fields is achieved by comparison to available experimental data. For both flames, the flow field results for eight stochastic fields and the associated scalar fields show an excellent agreement. The ESF method reproduces all major features of the flames at a lower numerical cost. Next, the second law analysis carried out with the different approaches for the entropy generation computation provides comparable quantitative results. Using flame D as a reference, for which some results with the thermodynamic-based approach exist in the literature, it turns out that, among the sources of exergy loss, the heat transfer and the chemical reaction emerge notably as the main culprits for entropy production, causing 50% and 35% of it, respectively. This fact-finding increases in Sandia flame E, which features a high Re number compared to Sandia flame D. The computational cost is less once the entropy generation analysis is carried out by using the Large Eddy Simulation (LES) hybrid ESF/FGM approach together with the look-up-table-based or turbulence-based approach