QIP = PSPACE

We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the well-known equality IP = PSPACE, the equality QIP = PSPACE follows.Comment: 21 pages; v2 includes corrections and minor revision

Six-qubit permutation-based decoherence-free orthogonal basis

There is a natural orthogonal basis of the 6-qubit decoherence-free (DF) space robust against collective noise. Interestingly, most of the basis states can be obtained from one another just permuting qubits. This property: (a) is useful for encoding qubits in DF subspaces, (b) allows the implementation of the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting qubits, which completes a the method for quantum key distribution using DF states proposed by Boileau et al. [Phys. Rev. Lett. 92, 017901 (2004)], and (c) points out that there is only one 6-qubit DF state which is essentially new (not obtained by permutations) and therefore constitutes an interesting experimental challenge.Comment: REVTeX4, 5 page

Identification and Distance Measures of Measurement Apparatus

We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency significantly. A brief discussion on the problem of how to appropriately define distance measures of measurements is also provided based on the results of identification.Comment: 5 pages, RevTeX, 1 figure. Revised version with more examples and a reorganization of the content

Renormalization group equations as 'decoupling' theorems

We propose a simple derivation of renormalization group equations and Callan-Symanzik equations as decoupling theorems of the structures underlying effective field theories.Comment: 7 pages, no figure, revtex4, additional typos removed, published in Phys. Lett.

Minimal instances for toric code ground states

A decade ago Kitaev's toric code model established the new paradigm of topological quantum computation. Due to remarkable theoretical and experimental progress, the quantum simulation of such complex many-body systems is now within the realms of possibility. Here we consider the question, to which extent the ground states of small toric code systems differ from LU-equivalent graph states. We argue that simplistic (though experimentally attractive) setups obliterate the differences between the toric code and equivalent graph states; hence we search for the smallest setups on the square- and triangular lattice, such that the quasi-locality of the toric code hamiltonian becomes a distinctive feature. To this end, a purely geometric procedure to transform a given toric code setup into an LC-equivalent graph state is derived. In combination with an algorithmic computation of LC-equivalent graph states, we find the smallest non-trivial setup on the square lattice to contain 5 plaquettes and 16 qubits; on the triangular lattice the number of plaquettes and qubits is reduced to 4 and 9, respectively.Comment: 14 pages, 11 figure

From Ground States to Local Hamiltonians

Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles.Comment: 11 pages, 2 figures, to be published in PR

Advances in Metabolic Engineering of Saccharomyces cerevisiae for Cocoa Butter Equivalent Production

Cocoa butter is extracted from cocoa beans, and it is mainly used as the raw material for the production of chocolate and cosmetics. Increased demands and insufficient cocoa plants led to a shortage of cocoa butter supply, and there is therefore much interesting in finding an alternative cocoa butter supply. However, the most valuable component of cocoa butter is rarely available in other vegetable oils. Saccharomyces cerevisiae is an important industrial host for production of chemicals, enzyme and pharmaceuticals. Advances in synthetical biology and metabolic engineering had enabled high-level of triacylglycerols (TAG) production in yeast, which provided possible solutions for cocoa butter equivalents (CBEs) production. Diverse engineering strategies focused on the fatty acid-producing pathway had been applied in S. cerevisiae, and the key enzymes determining the TAG structure were considered as the main engineering targets. Recent development in phytomics and multi-omics technologies provided clues to identify potential targeted enzymes, which are responsible for CBE production. In this review, we have summarized recent progress in identification of the key plant enzymes for CBE production, and discussed recent and future metabolic engineering and synthetic biology strategies for increased CBE production in S. cerevisiae

Modeling the metabolic dynamics at the genome-scale by optimized yield analysis

The hybrid cybernetic model (HCM) approach is a dynamic modeling framework that integrates enzyme synthesis and activity regulation. It has been widely applied in bioreaction engineering, particularly in the simulation of microbial growth in different mixtures of carbon sources. In a HCM, the metabolic network is decomposed into elementary flux modes (EFMs), whereby the network can be reduced into a few pathways by yield analysis. However, applying the HCM approach on conventional genome-scale metabolic models (GEMs) is still a challenge due to the high computational demands. Here, we present a HCM strategy that introduced an optimized yield analysis algorithm (opt-yield-FBA) to simulate metabolic dynamics at the genome-scale without the need for EFMs calculation. The opt-yield-FBA is a flux-balance analysis (FBA) based method that can calculate optimal yield solutions and yield space for GEM. With the opt-yield-FBA algorithm, the HCM strategy can be applied to get the yield spaces and avoid the computational burden of EFMs, and it can therefore be applied for developing dynamic models for genome-scale metabolic networks. Here, we illustrate the strategy by applying the concept to simulate the dynamics of microbial communities

Machine learning for data integration in human gut microbiome

Recent studies have demonstrated that gut microbiota plays critical roles in various human diseases. High-throughput technology has been widely applied to characterize the microbial ecosystems, which led to an explosion of different types of molecular profiling data, such as metagenomics, metatranscriptomics and metabolomics. For analysis of such data, machine learning algorithms have shown to be useful for identifying key molecular signatures, discovering potential patient stratifications, and particularly for generating models that can accurately predict phenotypes. In this review, we first discuss how dysbiosis of the intestinal microbiota is linked to human disease development and how potential modulation strategies of the gut microbial ecosystem can be used for disease treatment. In addition, we introduce categories and workflows of different machine learning approaches, and how they can be used to perform integrative analysis of multi-omics data. Finally, we review advances of machine learning in gut microbiome applications and discuss related challenges. Based on this we conclude that machine learning is very well suited for analysis of gut microbiome and that these approaches can be useful for development of gut microbe-targeted therapies, which ultimately can help in achieving personalized and precision medicine