NP-hardness of decoding quantum error-correction codes

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio

Unbounded-error quantum computation with small space bounds

We prove the following facts about the language recognition power of quantum Turing machines (QTMs) in the unbounded error setting: QTMs are strictly more powerful than probabilistic Turing machines for any common space bound $s$ satisfying $s(n)=o(\log \log n)$. For "one-way" Turing machines, where the input tape head is not allowed to move left, the above result holds for $s(n)=o(\log n)$. We also give a characterization for the class of languages recognized with unbounded error by real-time quantum finite automata (QFAs) with restricted measurements. It turns out that these automata are equal in power to their probabilistic counterparts, and this fact does not change when the QFA model is augmented to allow general measurements and mixed states. Unlike the case with classical finite automata, when the QFA tape head is allowed to remain stationary in some steps, more languages become recognizable. We define and use a QTM model that generalizes the other variants introduced earlier in the study of quantum space complexity.Comment: A preliminary version of this paper appeared in the Proceedings of the Fourth International Computer Science Symposium in Russia, pages 356--367, 200

Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Higher docosahexaenoic acid levels lower the protective impact of eicosapentaenoic acid on long-term major cardiovascular events

IntroductionLong-chain omega-3 polyunsaturated fatty acids (OM3 PUFA) are commonly used for cardiovascular disease prevention. High-dose eicosapentaenoic acid (EPA) is reported to reduce major adverse cardiovascular events (MACE); however, a combined EPA and docosahexaenoic acid (DHA) supplementation has not been proven to do so. This study aimed to evaluate the potential interaction between EPA and DHA levels on long-term MACE.MethodsWe studied a cohort of 987 randomly selected subjects enrolled in the INSPIRE biobank registry who underwent coronary angiography. We used rapid throughput liquid chromatography-mass spectrometry to quantify the EPA and DHA plasma levels and examined their impact unadjusted, adjusted for one another, and fully adjusted for comorbidities, EPA + DHA, and the EPA/DHA ratio on long-term (10-year) MACE (all-cause death, myocardial infarction, stroke, heart failure hospitalization).ResultsThe average subject age was 61.5 ± 12.2 years, 57% were male, 41% were obese, 42% had severe coronary artery disease (CAD), and 311 (31.5%) had a MACE. The 10-year MACE unadjusted hazard ratio (HR) for the highest (fourth) vs. lowest (first) quartile (Q) of EPA was HR = 0.48 (95% CI: 0.35, 0.67). The adjustment for DHA changed the HR to 0.30 (CI: 0.19, 0.49), and an additional adjustment for baseline differences changed the HR to 0.36 (CI: 0.22, 0.58). Conversely, unadjusted DHA did not significantly predict MACE, but adjustment for EPA resulted in a 1.81-fold higher risk of MACE (CI: 1.14, 2.90) for Q4 vs. Q1. However, after the adjustment for baseline differences, the risk of MACE was not significant for DHA (HR = 1.37; CI: 0.85, 2.20). An EPA/DHA ratio ≥1 resulted in a lower rate of 10-year MACE outcomes (27% vs. 37%, adjusted p-value = 0.013).ConclusionsHigher levels of EPA, but not DHA, are associated with a lower risk of MACE. When combined with EPA, higher DHA blunts the benefit of EPA and is associated with a higher risk of MACE in the presence of low EPA. These findings can help explain the discrepant results of EPA-only and EPA/DHA mixed clinical supplementation trials

Evaluation of a low-cost staining method for improved visualization of sweet potato whitefly (Bemisia tabaci) eggs on multiple crop plant species

BackgroundThe sweet potato whitefly (Bemisia tabaci) is a globally important insect pest that damages crops through direct feeding and by transmitting viruses. Current B. tabaci management revolves around the use of insecticides, which are economically and environmentally costly. Host plant resistance is a sustainable option to reduce the impact of whiteflies, but progress in deploying resistance in crops has been slow. A major obstacle is the high cost and low throughput of screening plants for B. tabaci resistance. Oviposition rate is a popular metric for host plant resistance to B. tabaci because it does not require tracking insect development through the entire life cycle, but accurate quantification is still limited by difficulties in observing B. tabaci eggs, which are microscopic and translucent. The goal of our study was to improve quantification of B. tabaci eggs on several important crop species: cassava, cowpea, melon, sweet potato and tomato.ResultsWe tested a selective staining process originally developed for leafhopper eggs: submerging the leaves in McBryde's stain (acetic acid, ethanol, 0.2% aqueous acid Fuchsin, water; 20:19:2:1) for three days, followed by clearing under heat and pressure for 15 min in clearing solution (LGW; lactic acid, glycerol, water; 17:20:23). With a less experienced individual counting the eggs, B. tabaci egg counts increased after staining across all five crops. With a more experienced counter, egg counts increased after staining on melons, tomatoes, and cowpeas. For all five crops, there was significantly greater agreement on egg counts across the two counting individuals after the staining process. The staining method worked particularly well on melon, where egg counts universally increased after staining for both counting individuals.ConclusionsSelective staining aids visualization of B. tabaci eggs across multiple crop plants, particularly species where leaf morphological features obscure eggs, such as melons and tomatoes. This method is broadly applicable to research questions requiring accurate quantification of B. tabaci eggs, including phenotyping for B. tabaci resistance