Asymptotically Good Quantum Codes

Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.Comment: 15 pages, 1 figur

The Finite Basis Problem for Kiselman Monoids

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke--Kiselman monoids including the Kiselman monoids $\mathcal{K}_n$. As a consequence, we conclude that the identities of $\mathcal{K}_n$ are nonfinitely based for every $n\ge 4$ and exhibit a finite identity basis for the identities of each of the monoids $\mathcal{K}_2$ and $\mathcal{K}_3$. In the third version a question left open in the initial submission has beed answered.Comment: 16 pages, 1 table, 1 figur

Clustered Error Correction of Codeword-Stabilized Quantum Codes

Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an algorithm that employs a single measurement to test all errors located on a given set of t qubits. Compared with exhaustive error screening, this reduces the total number of measurements required for error recovery by a factor of about 3^t.Comment: 4 pages, 2 figures, revtex4; number of editorial changes in v

Effect of HIV-1-related protein expression on cardiac and skeletal muscles from transgenic rats

<p>Abstract</p> <p>Background</p> <p>Human immunodeficiency virus type 1 (HIV-1) infection and the consequent acquired immunodeficiency syndrome (AIDS) has protean manifestations, including muscle wasting and cardiomyopathy, which contribute to its high morbidity. The pathogenesis of these myopathies remains partially understood, and may include nutritional deficiencies, biochemical abnormalities, inflammation, and other mechanisms due to viral infection and replication. Growing evidence has suggested that HIV-1-related proteins expressed by the host in response to viral infection, including Tat and gp120, may also be involved in the pathophysiology of AIDS, particularly in cells or tissues that are not directly infected with HIV-1. To explore the potentially independent effects of HIV-1-related proteins on heart and skeletal muscles, we used a transgenic rat model that expresses several HIV-1-related proteins (e.g., Tat, gp120, and Nef). Outcome measures included basic heart and skeletal muscle morphology, glutathione metabolism and oxidative stress, and gene expressions of atrogin-1, muscle ring finger protein-1 (MuRF-1) and Transforming Growth Factor-β₁(TGFβ₁), three factors associated with muscle catabolism.</p> <p>Results</p> <p>Consistent with HIV-1 associated myopathies in humans, HIV-1 transgenic rats had increased relative heart masses, decreased relative masses of soleus, plantaris and gastrocnemius muscles, and decreased total and myosin heavy chain type-specific plantaris muscle fiber areas. In both tissues, the levels of cystine (Cyss), the oxidized form of the anti-oxidant cysteine (Cys), and Cyss:Cys ratios were significantly elevated, and cardiac tissue from HIV-1 transgenic rats had altered glutathione metabolism, all reflective of significant oxidative stress. In HIV-1 transgenic rat hearts, MuRF-1 gene expression was increased. Further, HIV-1-related protein expression also increased atrogin-1 (~14- and ~3-fold) and TGFβ₁(~5-fold and ~3-fold) in heart and plantaris muscle tissues, respectively.</p> <p>Conclusion</p> <p>We provide compelling experimental evidence that HIV-1-related proteins can lead to significant cardiac and skeletal muscle complications independently of viral infection or replication. Our data support the concept that HIV-1-related proteins are not merely disease markers, but rather have significant biological activity that may lead to increased oxidative stress, the stimulation of redox-sensitive pathways, and altered muscle morphologies. If correct, this pathophysiological scheme suggests that the use of dietary thiol supplements could reduce skeletal and cardiac muscle dysfunction in HIV-1-infected individuals.</p

Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes

On a class of memoryless quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R). The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity.Comment: Ver.4. In vers.1--3, I claimed Theorem 1 for general quantum channels. Now I claim this only for a slight generalization of depolarizing channel in this paper because Lemma 2 in vers.1--3 was wrong; the original general statement is proved in quant-ph/0112103. Ver.5. Text sectionalized. Appeared in PRA. The PRA article is typographically slightly crude: The LaTeX symbol star, used as superscripts, was capriciously replaced by the asterisk in several places after my proof readin

How to correct small quantum errors

The theory of quantum error correction is a cornerstone of quantum information processing. It shows that quantum data can be protected against decoherence effects, which otherwise would render many of the new quantum applications practically impossible. In this paper we give a self contained introduction to this theory and to the closely related concept of quantum channel capacities. We show, in particular, that it is possible (using appropriate error correcting schemes) to send a non-vanishing amount of quantum data undisturbed (in a certain asymptotic sense) through a noisy quantum channel T, provided the errors produced by T are small enough.Comment: LaTeX2e, 23 pages, 6 figures (3 eps, 3 pstricks

Закономерности изменения адсорбционных свойств глин, активированных давлением и ионами железа

The purpose of the work is to consider the patterns of adsorption of water vapor by clay soils that have been treated with pressure and saturated with iron ions, and also to study the processes of adsorption and desorption of Fe3+ ions by bentonite and kaolin clays. The study of changes in the adsorption properties of clay soils is necessary to understand the processes occurring in soils, both in natural and anthropogenic conditions, especially in the case of soil contamination. As a result of the experiment, it was found that the adsorption capacity of clays in relation to water vapor increases when they are treated with pressure. When clay is treated with pressure and subsequently saturated with iron ions in bentonite clay, the adsorption activity decreases in the range of 0-150 MPa, at higher pressures it changes irregularly. In kaolin, adsorption increases at pressures up to 200 MPa, but it decreases at pressures from 200 to 800 MPa.Цель работы: рассмотреть закономерности адсорбции водяного пара глинистыми грунтами, которые были обработаны под разными давлениями и насыщены ионами железа, а также изучить процессы адсорбции и десорбции ионов Fe3+ бентонитовой и каолиновой глинами. Изучение изменений адсорбционных свойств глинистых грунтов необходимо для понимания процессов, происходящих в грунтах как в природных, так и в антропогенных условиях, особенно в случае загрязнения грунтов. В результате эксперимента было установлено, что адсорбционная способность глин по отношению к водяному пару возрастает при обработке их давлением. При обработке глин давлением и при последующем насыщении их ионами железа в бентонитовой глине адсорбционная активность снижается в диапазоне 0–150 МПа, при более высоких давлениях изменяется незакономерно. В каолине происходит рост адсорбции при давлениях до 200 МПа, но она уменьшается при давлениях от 200 до 800 МПа

Lower bound for the quantum capacity of a discrete memoryless quantum channel

We generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel. For the depolarizing channel, our lower bound coincides with that obtained by Bennett et al. We also slightly improve the quantum Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof is restricted to the binary quantum channels, but its extension of to l-adic channels is straightforward.Comment: 16 pages, REVTeX4. To appear in J. Math. Phys. A critical error in fidelity calculation was corrected by using Hamada's result (quant-ph/0112103). In the third version, we simplified formula and derivation of the lower bound by proving p(Gamma)+q(Gamma)=1. In the second version, we added an analogue of the quantum Gilbert-Varshamov bound for linear stabilizer code

Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit

A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize our work to show that for subsystem stabilizer codes in $d$ dimensional Hilbert space, such a universal set of transversal gates cannot exist for even one encoded qudit, for any dimension $d$, prime or nonprime. This result strongly supports the idea that other primitives, such as quantum teleportation, are necessary for universal fault-tolerant quantum computation, and may be an important factor for fault tolerance noise thresholds.Comment: 16 pages, 3 figure