Efficient feedback controllers for continuous-time quantum error correction

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model

Collective processes of an ensemble of spin-1/2 particles

When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1/2 particles in order to efficiently describe these more general collective processes. The corresponding collective states span a subspace which grows quadratically with the number of spins. We also derive explicit formulae for expressing arbitrary identical, local decoherence in terms of these states.Comment: 12 pages, see 0805.2910 for simulations using these method

Generalized Limits for Single-Parameter Quantum Estimation

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$ where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.Comment: 4 pages, 1 figure. v2 typos correcte

Bio-products from algae-based biorefinery on wastewater: A review

Increasing resource demand, predicted fossil resources shortage in the near future, and environmental concerns due to the production of greenhouse gas carbon dioxide have motivated the search for alternative ‘circular’ pathways. Among many options, microalgae have been recently ‘revised’ as one of the most promising due to their high growth rate (with low land use and without competing with food crops), high tolerance to nutrients and salts stresses and their variability in biochemical composition, in so allowing the supply of a plethora of possible bio-based products such as animal feeds, chemicals and biofuels. The recent raising popularity of Circular Bio-Economy (CBE) further prompted investment in microalgae, especially in combination with wastewater treatment, under the twofold aim of allowing the production of a wide range of bio-based products while bioremediating wastewater. With the aim of discussing the potential bio-products that may be gained from microalgae grown on urban wastewater, this paper presents an overview on microalgae production with particular emphasis on the main microalgae species suitable for growth on wastewater and the obtainable bio-based products from them. By selecting and reviewing 76 articles published in Scopus between 1992 and 2020, a number of interesting aspects, including the selection of algal species suitable for growing on urban wastewater, wastewater pretreatment and algal-bacterial cooperation, were carefully reviewed and discussed in this work. In this review, particular emphasis is placed on understanding of the main mechanisms driving formation of microalgal products (such as biofuels, biogas, etc.) and how they are affected by different environmental factors in selected species. Lastly, the quantitative information gathered from the articles were used to estimate the potential benefits gained from microalgae grown on urban wastewater in Campania Region, a region sometimes criticized for poor wastewater management

A relative-error inertial-relaxed inexact projective splitting algorithm

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters and study the interplay between them in order to guarantee weak convergence of sequences generated by our algorithm. Additionally, the proposed algorithm also benefits from inexact subproblem solution within a relative-error criterion. Simple numerical experiments on LASSO problems indicate some improvement when compared with previous (noninertial and exact) versions of projective splitting

Developing HIV-1 Protease inhibitors through stereospecific reactions in protein crystals

Protease inhibitors are key components in the chemotherapy of HIV infection. However, the appearance of viral mutants routinely compromises their clinical efficacy, creating a constant need for new and more potent inhibitors. Recently, a new class of epoxide-based inhibitors of HIV-1 protease was investigated and the configuration of the epoxide carbons was demonstrated to play a crucial role in determining the binding affinity. Here we report the comparison between three crystal structures at near-atomic resolution of HIV-1 protease in complex with the epoxide-based inhibitor, revealing an in-situ epoxide ring opening triggered by a pH change in the mother solution of the crystal. Increased pH in the crystal allows a stereospecific nucleophile attack of an ammonia molecule onto an epoxide carbon, with formation of a new inhibitor containing amino-alcohol functions. The described experiments open a pathway for the development of new stereospecific protease inhibitors from a reactive lead compound