Quantum Error Correction of Time-Correlated Errors

The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits $\mid 0_L>$ and $\mid 1_L>$ are entangled states of $2^{n}$ basis states in $\mathcal{H}_{2^n}$.Comment: 14 pages, 3 figure

Epigenomic and Transcriptional Regulation of Hepatic Metabolism by REV-ERB and Hdac3

Metabolic activities are regulated by the circadian clock, and disruption of the clock exacerbates metabolic diseases including obesity and diabetes. Transcriptomic studies in metabolic organs suggested that the circadian clock drives the circadian expression of important metabolic genes. Here we show that histone deacetylase 3 (HDAC3) is recruited to the mouse liver genome in a circadian manner. Histone acetylation is inversely related to HDAC3 binding, and this rhythm is lost when HDAC3 is absent. Diurnal recruitment of HDAC3 corresponds to the expression pattern of REV-ERBα, an important component of the circadian clock. REV-ERBα colocalizes with HDAC3 near genes regulating lipid metabolism, and deletion of HDAC3 or Rev-erbα in mouse liver causes hepatic steatosis. Thus, genomic recruitment of HDAC3 by REV-ERBα directs a circadian rhythm of histone acetylation and gene expression required for normal hepatic lipid homeostasis. In addition, we reported that the REV-ERBα paralog, REV-ERBβ also displays circadian binding similar to that of REV-ERBα. REV-ERBβ also recruits HDAC3 and protects the circadian clock and hepatic lipid homeostasis in the absence of REV-ERBα. REV-ERBs are indeed essential components of the circadian clock. Furthermore, we discovered that REV-ERBs competes with RORα for genomic binding at Bmal1 and Npas2 genes, and drives a diurnal binding of RORα. We then identified thousands of competing sites by RORα ChIP-seq, many of which are in close proximity of clock and metabolic genes. We also discovered many RORα binding sites with no rhythmic RORα binding or rhythmic RORα binding in-phase with REV-ERBs. Collectively, these findings indicate that REV-ERBs, HDAC3 and potentially RORα mediate the epigenomic and transcriptional regulation of liver metabolism by the circadian clock

A simple entanglement measure for multipartite pure states

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.Comment: 8 pages LaTe