Approximation of quantum control correction scheme using deep neural networks

We study the functional relationship between quantum control pulses in the idealized case and the pulses in the presence of an unwanted drift. We show that a class of artificial neural networks called LSTM is able to model this functional relationship with high efficiency, and hence the correction scheme required to counterbalance the effect of the drift. Our solution allows studying the mapping from quantum control pulses to system dynamics and then analysing the robustness of the latter against local variations in the control profile.Comment: 6 pages, 3 figures, Python code available upon request. arXiv admin note: text overlap with arXiv:1803.0516

An initialization strategy for addressing barren plateaus in parametrized quantum circuits

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ans\"atze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method

Geometrical versus time-series representation of data in quantum control learning

Recently machine learning techniques have become popular for analysing physical systems and solving problems occurring in quantum computing. In this paper we focus on using such techniques for finding the sequence of physical operations implementing the given quantum logical operation. In this context we analyse the flexibility of the data representation and compare the applicability of two machine learning approaches based on different representations of data. We demonstrate that the utilization of the geometrical structure of control pulses is sufficient for achieving high-fidelity of the implemented evolution. We also demonstrate that artificial neural networks, unlike geometrical methods, posses the generalization abilities enabling them to generate control pulses for the systems with variable strength of the disturbance. The presented results suggest that in some quantum control scenarios, geometrical data representation and processing is competitive to more complex methods.Comment: 12 pages, 14 figures, Python code available upon the reques

Claude Ambrose Rogers. 1 November 1920 — 5 December 2005

Claude Ambrose Rogers and his identical twin brother, Stephen Clifford, were born in Cambridge in 1920 and came from a long scientific heritage. Their great-great-grandfather, Davies Gilbert, was President of the Royal Society from 1827 to 1830; their father was a Fellow of the Society and distinguished for his work in tropical medicine. After attending boarding school at Berkhamsted with his twin brother from the age of 8 years, Ambrose, who had developed very different scientific interests from those of his father, entered University College London in 1938 to study mathematics. He completed the course in 1940 and graduated in 1941 with first-class honours, by which time the UK had been at war with Germany for two years. He joined the Applied Ballistics Branch of the Ministry of Supply in 1940, where he worked until 1945, apparently on calculations using radar data to direct anti-aircraft fire. However, this did not lead to research interests in applied mathematics, but rather to several areas of pure mathematics. Ambrose's PhD research was at Birkbeck College, London, under the supervision of L. S. Bosanquet and R. G. Cooke, his first paper being on the subject of geometry of numbers. Later, Rogers became known for his very wide interests in mathematics, including not only geometry of numbers but also Hausdorff measures, convexity and analytic sets, as described in this memoir. Ambrose was married in 1952 to Joan North, and they had two daughters, Jane and Petra, to form a happy family

Mechanistic modeling of the SARS-CoV-2 disease map.

Here we present a web interface that implements a comprehensive mechanistic model of the SARS-CoV-2 disease map. In this framework, the detailed activity of the human signaling circuits related to the viral infection, covering from the entry and replication mechanisms to the downstream consequences as inflammation and antigenic response, can be inferred from gene expression experiments. Moreover, the effect of potential interventions, such as knock-downs, or drug effects (currently the system models the effect of more than 8000 DrugBank drugs) can be studied. This freely available tool not only provides an unprecedentedly detailed view of the mechanisms of viral invasion and the consequences in the cell but has also the potential of becoming an invaluable asset in the search for efficient antiviral treatments

Secreted Amyloid β-Proteins in a Cell Culture Model Include N-Terminally Extended Peptides That Impair Synaptic Plasticity

Evidence for a central role of amyloid β-protein (Aβ) in the genesis of Alzheimer’s disease (AD) has led to advanced human trials of Aβ-lowering agents. The “amyloid hypothesis” of AD postulates deleterious effects of small, soluble forms of Aβ on synaptic form and function. Because selectively targeting synaptotoxic forms of soluble Aβ could be therapeutically advantageous, it is important to understand the full range of soluble Aβ derivatives. We previously described a Chinese hamster ovary (CHO) cell line (7PA2 cells) that stably expresses mutant human amyloid precursor protein (APP). Here, we extend this work by purifying an sodium dodecyl sulfate (SDS)-stable, ∼8 kDa Aβ species from the 7PA2 medium. Mass spectrometry confirmed its identity as a noncovalently bonded Aβ40 homodimer that impaired hippocampal long-term potentiation (LTP) in vivo. We further report the detection of Aβ-containing fragments of APP in the 7PA2 medium that extend N-terminal from Asp1 of Aβ. These N-terminally extended Aβ-containing monomeric fragments are distinct from soluble Aβ oligomers formed from Aβ1-40/42 monomers and are bioactive synaptotoxins secreted by 7PA2 cells. Importantly, decreasing β-secretase processing of APP elevated these alternative synaptotoxic APP fragments. We conclude that certain synaptotoxic Aβ-containing species can arise from APP processing events N-terminal to the classical β-secretase cleavage site

Coupled Maps on Trees

We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. As the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to effect. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatio-temporal structures. We find that a mean-field like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys. Rev.

Club does not imply the existence of a Suslin tree

We prove that club does not imply the existence of a Suslin tree, so answering a question of I. Juhasz