Entanglement and its Role in Shor's Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not included in the end); v4 is improved following referee comments, expanded explanations and added reference

A computer algebra user interface manifesto

Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and allowing easy fine grain control over the form of the result even by amateurs. This wizard integrates ideas including: * flexible subexpression selection; * complete control over the ordering of variables and commutative operands, with well-chosen defaults; * interleaving the choice of successively less main variables with applicable function choices to provide detailed control without incurring a combinatorial number of applicable alternatives at any one level; * quick applicability tests to reduce the listing of inapplicable transformations; * using an organizing principle to order the alternatives in a helpful manner; * labeling quickly-computed alternatives in dialog boxes with a preview of their results, * using ellipsis elisions if necessary or helpful; * allowing the user to retreat from a sequence of choices to explore other branches of the tree of alternatives or to return quickly to branches already visited; * allowing the user to accumulate more than one of the alternative forms; * integrating direct manipulation into the wizard; and * supporting not only the usual input-result pair mode, but also the useful alternative derivational and in situ replacement modes in a unified window.Comment: 38 pages, 12 figures, to be published in Communications in Computer Algebr

ADB–OECD Study on Enhancing Financial Accessibility for SMEs: Lessons from Recent Crises

During the era of global financial uncertainty, stable access to appropriate funding sources has been much harder for small and medium-sized enterprises (SMEs). The global financial crisis impacted SMEs and entrepreneurs disproportionately, exacerbating their traditional financing constraints. The financial conditions of many SMEs were weakened by the drop in demand for goods and services and the credit tightening. The sovereign debt crisis that hit several European countries contributed to further deterioration in bank lending activities, which negatively affected private sector development. The global regulatory response to financial crises, such as the Basel Capital Accord, while designed to reduce systemic risks may also constrain bank lending to SMEs. In particular, Basel III requires banks to have tighter risk management as well as greater capital and liquidity. Resulting asset preference and deleveraging of banks, particularly European banks with significant presence in Asia, could limit the availability of funding for SMEs in Asia and the Pacific. Lessons from the recent financial crises have motivated many countries to consider SME access to finance beyond conventional bank credit and to diversify their national financial system. Improving SME access to finance is a policy priority at the country and global level. Poor access to finance is a critical inhibiting factor to the survival and growth potential of SMEs. Financial inclusion is thus key to the development of the SME sector, which is a driver of job creation and social cohesion and takes a pivotal role in scaling up national economies. The Asian Development Bank (ADB) and the Organisation for Economic Co-operation and Development (OECD) have recognized that it is crucial to develop a comprehensive range of policy options on SME finance, including innovative financing models. With this in mind, sharing Asian and OECD experiences on SME financing would result in insightful discussions on improving SME access to finance at a time of global financial uncertainty. Based on intensive discussions in two workshops organized by ADB in Manila on 6–7 March 2013 and by OECD in Paris on 21 October 2013, the two organizations together compiled this study report on enhancing financial accessibility for SMEs, especially focusing on lessons from the past and recent crises in Asia and OECD countries. The report takes a comparative look at ADB and OECD experiences, and aims to identify promising policy solutions for creating an SME base that is resilient to crisis, from a viewpoint of access to finance, and which can help drive growth and development