Speed limits for quantum gates in multi-qubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.Comment: 7 pages (two-column), 2 figures, 2 table

Large N Duality, Lagrangian Cycles, and Algebraic Knots

We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.Engineering and Physical Sciences Research CouncilSimons Foundatio

Role of conventional oral antidiabetic drugs in management of type 2 diabetes mellitus

Type 2 diabetes mellitus (T2DM) is caused by insulin resistance and characterized by progressive pancreatic β-cell dysfunction. Recent innovative treatment approaches target the multiple pathophysiological defects present in type 2 diabetes. The targets for glycemic control as set by the American Diabetes Association (HbA1C<7%) and the American Association of Clinical Endocrinologists (HbA1C<6.5%) sometimes appear daunting and unattainable. It is therefore of the utmost importance to have an excellent understanding of the mechanism of action of these drugs in order to optimize patient therapy. Here, we present a corresponding discussion of all the available oral antidiabetic drugs according to the different classes, their mechanisms of action and pharmacological profiles

A Similarity Measure for GPU Kernel Subgraph Matching

Accelerator architectures specialize in executing SIMD (single instruction, multiple data) in lockstep. Because the majority of CUDA applications are parallelized loops, control flow information can provide an in-depth characterization of a kernel. CUDAflow is a tool that statically separates CUDA binaries into basic block regions and dynamically measures instruction and basic block frequencies. CUDAflow captures this information in a control flow graph (CFG) and performs subgraph matching across various kernel's CFGs to gain insights to an application's resource requirements, based on the shape and traversal of the graph, instruction operations executed and registers allocated, among other information. The utility of CUDAflow is demonstrated with SHOC and Rodinia application case studies on a variety of GPU architectures, revealing novel thread divergence characteristics that facilitates end users, autotuners and compilers in generating high performing code

An Arbitrary Two-qubit Computation In 23 Elementary Gates

Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 CNOTs. To this end, we constructively prove a worst-case upper bound of 23 elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail much larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of 61 gates of which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie theory as well as the polar and spectral (symmetric Shur) matrix decompositions from numerical analysis and operator theory. They are related to the canonical decomposition of a two-qubit gate with respect to the ``magic basis'' of phase-shifted Bell states, published previously. We further extend this decomposition in terms of elementary gates for quantum computation.Comment: 18 pages, 7 figures. Version 2 gives correct credits for the GQC "quantum compiler". Version 3 adds justification for our choice of elementary gates and adds a comparison with classical library-less logic synthesis. It adds acknowledgements and a new reference, adds full details about the 8-gate decomposition of topC-V and stealthily fixes several minor inaccuracies. NOTE: Using a new technique, we recently improved the lower bound to 18 gates and (tada!) found a circuit decomposition that requires 18 gates or less. This work will appear as a separate manuscrip

On the Effect of Quantum Interaction Distance on Quantum Addition Circuits

We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any $\Omega(\log n)$-depth quantum adder circuit for two $n$-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates. Unfortunately, on the chosen $k$-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer $\Omega(\log {n})$, but $\Omega(\sqrt[k]{n})$. This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing System

Quantum algorithm for simulating the dynamics of an open quantum system

In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment and their interaction: one basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system+environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.Comment: 5 figures, two table

Broad features of surface ozone variations over Indian region

Surface ozone concentration at three Indian stations - New Delhi (28.6 deg N), Pune (18.5 deg N) and Thiruvananthapuram (formerly Trivandrum (8.3 deg N) - has been measured since 1973 with the help of an electrochemical continuous ozone recorder. These stations show diurnal, seasonal and annual cycles in surface ozone. Daily changes show that the minimum value occurs at sunrise and maximum in the afternoon. As regards seasonal variations, Thiruvananthapuram and Pune have a minimum value during monsoon season (June to August) while at New Delhi the minimum value occurs in January. However, New Delhi also records low ozone amount during monsoon season identical to the amounts show at Thiruvananthapuram and Pune. The annual cycles at these stations have been compared with similar measurements in the northern and southern hemispheres. The Indian measurements agree well with the annual cycles at these stations. Further, the analysis of the Indian data indicates that the major contribution in surface ozone comes from the natural sources like stratospheric-tropospheric exchange, turbulence, and mixing in the boundary layer; however, a small contribution from anthropogenic sources cannot be ruled out at Pune and probably at New Delhi, especially in winter and summer seasons

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author

Role of insulin in management of type 2 diabetes mellitus

The prevalence of type 2 diabetes mellitus and its resultant morbidity and mortality is rapidly increasing. An important factor in reducing the microvascular complications of diabetes is strict glycemic control. Most patients require additional insulin therapy in spite of regularly taking oral anti-diabetic drugs. Though classically used later in the natural course of the disease, newer treatment guidelines suggest early initiation of insulin analogues. The discovery of insulin has been hailed as one of the most dramatic events in the history of diabetes, improving the life-span of most diabetics. Replacement insulin therapy should mimic physiological insulin release patterns. Modern insulin and its analogues have been developed to serve as an ideal replacement therapy. There are various insulin preparations available in the market and each of them has their own advantages and disadvantages. The modern insulin’s have been developed to overcome certain side effects of the older preparations. A range of insulin products are under development that aim to increase absorption prolong action and provide alternative delivery methods. Greater patient adherence is important since most patients are reticent about insulin therapy.  This review describes the role of insulin in the management of type 2 diabetes mellitus