Matrix realignment and partial transpose approach to entangling power of quantum evolutions

Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on qudits, and indicate that these two matrix rearrangements are not only powerful for studying separability problem of quantum states, but also useful in studying entangling capabilities of quantum operators.Comment: Four pages and no figure

Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations

In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which cannot be simulated with a classical computer due to the exponential increase of the Hilbert space with the size of the system and which cannot be measured or controlled in an actual experiment. The system will interact with the surrounding environment, with the other particles in the system and be implemented using imperfect controls making it subject to noise. It has been suggested that noise does not need to be controlled to the same extent as it must be for general quantum computing. However the effects of noise in quantum simulations and how to treat them are not completely understood. In this paper we study an existing quantum algorithm for the one-dimensional Fano-Anderson model to be simulated using a liquid-state NMR device. We calculate the evolution of different initial states in the original model, and then we add interacting spins to simulate a more realistic situation. We find that states which are entangled with their environment, and sometimes correlated but not necessarily entangled have an evolution which is described by maps which are not completely positive. We discuss the conditions for this to occur and also the implications.Comment: Revtex 4-1, 14 pages, 21 figures, version 2 has typos corrected and acknowledgement adde

Comparison of long and short axis quantification of left ventricular volume parameters by cardiovascular magnetic resonance, with ex-vivo validation

<p>Abstract</p> <p>Background</p> <p>The purpose of the study was to compare the accuracy and evaluation time of quantifying left ventricular (LV), left atrial (LA) volume and LV mass using short axis (SAX) and long axis (LAX) methods when using cardiovascular magnetic resonance (CMR).</p> <p>Materials and methods</p> <p>We studied 12 explanted canine hearts and 46 patients referred for CMR (29 male, age 47 ± 18 years) in a clinical 1.5 T CMR system, using standard cine sequences. In standard short axis stacks of various slice thickness values in dogs and 8 mm slice thickness (gap 2 mm) in patients, we measured LV volumes using reference slices in a perpendicular, long axis orientation using certified software. Volumes and mass were also measured in six radial long axis (LAX) views.</p> <p>LV parameters were also assessed for intra- and inter-observer variability. In 24 patients, we also analyzed reproducibility and evaluation time of two very experienced (> 10 years of CMR reading) readers for SAX and LAX.</p> <p>Results</p> <p>In the explanted dog hearts, there was excellent agreement between ex vivo data and LV mass and volume data as measured by all methods for both, LAX (r²= 0.98) and SAX (r²= 0.88 to 0.98). LA volumes, however, were underestimated by 13% using the LAX views. In patients, there was a good correlation between all three assessed methods (r²≥ 0.95 for all). In experienced clinical readers, left-ventricular volumes and ejection fraction as measured in LAX views showed a better inter-observer reproducibility and a 27% shorter evaluation time.</p> <p>Conclusion</p> <p>When compared to an ex vivo standard, both, short axis and long axis techniques are highly accurate for the quantification of left ventricular volumes and mass. In clinical settings, however, the long axis approach may be more reproducible and more time-efficient. Therefore, the rotational long axis approach is a viable alternative for the clinical assessment of cardiac volumes, function and mass.</p

Delegating Quantum Computation in the Quantum Random Oracle Model

A delegation scheme allows a computationally weak client to use a server's resources to help it evaluate a complex circuit without leaking any information about the input (other than its length) to the server. In this paper, we consider delegation schemes for quantum circuits, where we try to minimize the quantum operations needed by the client. We construct a new scheme for delegating a large circuit family, which we call "C+P circuits". "C+P" circuits are the circuits composed of Toffoli gates and diagonal gates. Our scheme is non-interactive, requires very little quantum computation from the client (proportional to input length but independent of the circuit size), and can be proved secure in the quantum random oracle model, without relying on additional assumptions, such as the existence of fully homomorphic encryption. In practice the random oracle can be replaced by an appropriate hash function or block cipher, for example, SHA-3, AES. This protocol allows a client to delegate the most expensive part of some quantum algorithms, for example, Shor's algorithm. The previous protocols that are powerful enough to delegate Shor's algorithm require either many rounds of interactions or the existence of FHE. The protocol requires asymptotically fewer quantum gates on the client side compared to running Shor's algorithm locally. To hide the inputs, our scheme uses an encoding that maps one input qubit to multiple qubits. We then provide a novel generalization of classical garbled circuits ("reversible garbled circuits") to allow the computation of Toffoli circuits on this encoding. We also give a technique that can support the computation of phase gates on this encoding. To prove the security of this protocol, we study key dependent message(KDM) security in the quantum random oracle model. KDM security was not previously studied in quantum settings.Comment: 41 pages, 1 figures. Update to be consistent with the proceeding versio

Decision problems with quantum black boxes

We examine how to distinguish between unitary operators, when the exact form of the possible operators is not known. Instead we are supplied with "programs" in the form of unitary transforms, which can be used as references for identifying the unknown unitary transform. All unitary transforms should be used as few times as possible. This situation is analoguous to programmable state discrimination. One difference, however, is that the quantum state to which we apply the unitary transforms may be entangled, leading to a richer variety of possible strategies. By suitable selection of an input state and generalized measurement of the output state, both unambiguous and minimum-error discrimination can be achieved. Pairwise comparison of operators, comparing each transform to be identified with a program transform, is often a useful strategy. There are, however, situations in which more complicated strategies perform better. This is the case especially when the number of allowed applications of program operations is different from the number of the transforms to be identified

Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs

In this paper, we present a quantum algorithm for dynamic programming approach for problems on directed acyclic graphs (DAGs). The running time of the algorithm is $O(\sqrt{\hat{n}m}\log \hat{n})$, and the running time of the best known deterministic algorithm is $O(n+m)$, where $n$ is the number of vertices, $\hat{n}$ is the number of vertices with at least one outgoing edge; $m$ is the number of edges. We show that we can solve problems that use OR, AND, NAND, MAX and MIN functions as the main transition steps. The approach is useful for a couple of problems. One of them is computing a Boolean formula that is represented by Zhegalkin polynomial, a Boolean circuit with shared input and non-constant depth evaluating. Another two are the single source longest paths search for weighted DAGs and the diameter search problem for unweighted DAGs.Comment: UCNC2019 Conference pape

Quantum Computing with Very Noisy Devices

In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is significantly higher than what was previously thought possible. However, the resources required for computing at such high error probabilities are excessive. Fortunately, they decrease rapidly with decreasing error probabilities. If we had quantum resources comparable to the considerable resources available in today's digital computers, we could implement non-trivial quantum computations at error probabilities as high as 1% per gate.Comment: 47 page

IL-17 Signaling triggers degradation of the constitutive NF-κB inhibitor ABIN-1

IL-17 activates NF-κB and induces expression of proinflammatory genes. IL-17 drives disease in autoimmune conditions, and anti–IL-17 Abs have shown impressive success in the clinic. Although produced by lymphocytes, IL-17 predominantly signals in fibroblasts and epithelial cells. IL-17–driven inflammation is kept in check by negative feedback signaling molecules, including the ubiquitin editing enzyme A20, whose gene TNFAIP3 is linked to autoimmune disease susceptibility. The A20 binding inhibitor of NF-κB activation 1 (ABIN-1) is an A20-binding protein encoded by the TNIP1 gene, which is also linked to autoimmune disease susceptibility including psoriasis. Accordingly, we hypothesized that ABIN-1 might play a role in negatively regulating IL-17 signaling activity. Indeed, ABIN-1 enhanced both tonic and IL-17–dependent NF-κB signaling in IL-17–responsive fibroblast cells. Interestingly, the inhibitory activities of ABIN-1 on IL-17 signaling were independent of A20. ABIN-1 is a known NF-κB target gene, and we found that IL-17–induced activation of NF-κB led to enhanced ABIN-1 mRNA expression and promoter activity. Surprisingly, however, the ABIN-1 protein was inducibly degraded following IL-17 signaling in a proteasome-dependent manner. Thus, ABIN-1, acting independently of A20, restricts both baseline and IL-17–induced inflammatory gene expression. We conclude that IL-17–induced signals lead to degradation of ABIN-1, thereby releasing a constitutive cellular brake on NF-κB activation

Enhancement mode double top gated MOS nanostructures with tunable lateral geometry

We present measurements of silicon (Si) metal-oxide-semiconductor (MOS) nanostructures that are fabricated using a process that facilitates essentially arbitrary gate geometries. Stable Coulomb blockade behavior free from the effects of parasitic dot formation is exhibited in several MOS quantum dots with an open lateral quantum dot geometry. Decreases in mobility and increases in charge defect densities (i.e. interface traps and fixed oxide charge) are measured for critical process steps, and we correlate low disorder behavior with a quantitative defect density. This work provides quantitative guidance that has not been previously established about defect densities for which Si quantum dots do not exhibit parasitic dot formation. These devices make use of a double-layer gate stack in which many regions, including the critical gate oxide, were fabricated in a fully-qualified CMOS facility.Comment: 11 pages, 6 figures, 3 tables, accepted for publication in Phys. Rev.