In the past years, quantum computers more and more have evolved from an academic idea to an upcoming reality. IBM's project IBM Q can be seen as evidence of this progress. Launched in March 2017 with the goal to provide access to quantum computers for a broad audience, this allowed users to conduct quantum experiments on a 5-qubit and, since June 2017, also on a 16-qubit quantum computer (called IBM QX2 and IBM QX3, respectively). Revised versions of these 5-qubit and 16-qubit quantum computers (named IBM QX4 and IBM QX5, respectively) are available since September 2017. In order to use these, the desired quantum functionality (e.g. provided in terms of a quantum circuit) has to be properly mapped so that the underlying physical constraints are satisfied -a complex task. This demands solutions to automatically and efficiently conduct this mapping process.In this paper, we propose a methodology which addresses this problem, i.e. maps the given quantum functionality to a realization which satisfies all constraints given by the architecture and, at the same time, keeps the overhead in terms of additionally required quantum gates minimal. The proposed methodology is generic, can easily be configured for similar future architectures, and is fully integrated into IBM's SDK. Experimental evaluations show that the proposed approach clearly outperforms IBM's own mapping solution. In fact, for many quantum circuits, the proposed approach determines a mapping to the IBM architecture within minutes, while IBM's solution suffers from long runtimes and runs into a timeout of 1 hour in several cases. As an additional benefit, the proposed approach yields mapped circuits with smaller costs (i.e. fewer additional gates are required). All implementations of the proposed methodology is publicly available at http://iic.

e recent progress in the physical realization of quantum computers (the first publicly available ones-IBM's QX architectureshave been launched in 2017) has motivated research on automatic methods that aid users in running quantum circuits on them. Here, certain physical constraints given by the architectures which restrict the allowed interactions of the involved qubits have to be satisfied.us far, this has been addressed by inserting SWAP and H operations. However, it remains unknown whether existing methods add a minimum number of SWAP and H operations or, if not, how far they are away from that minimum-an N P-complete problem. In this work, we address this by formulating the mapping task as a symbolic optimization problem that is solved using reasoning engines like Boolean satisfiability solvers. By this, we do not only provide a method that maps quantum circuits to IBM's QX architectures with a minimal number of SWAP and H operations, but also show by experimental evaluation that the number of operations added by IBM's heuristic solution exceeds the lower bound by more than 100% on average. An implementation of the proposed methodology is publicly available at h p://iic.jku.at/eda/research/ibm qx mapping.

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Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum computers are in their infancy, a significant amount of research in this domain still relies on simulations of quantum computations on conventional machines. This causes a significant complexity which current state-of-the-art simulators try to tackle with a rather straight forward array-based representation and by applying massive hardware power. There also exist solutions based on decision diagrams (i.e. graph-based approaches) that try to tackle the exponential complexity by exploiting redundancies in quantum states and operations. However, these existing approaches do not fully exploit redundancies that are actually present.In this work, we revisit the basics of quantum computation, investigate how corresponding quantum states and quantum operations can be represented even more compactly, and, eventually, simulated in a more efficient fashion. This leads to a new graph-based simulation approach which outperforms state-of-the-art simulators (array-based as well as graph-based). Experimental evaluations show that the proposed solution is capable of simulating quantum computations for more qubits than before, and in significantly less run-time (several magnitudes faster compared to previously proposed simulators). An implementation of the proposed simulator is publicly available online at http://iic.jku.at/eda/research/quantum_simulation. Robert Wille Robert Wille (M'06-SM'09) received the Diploma and Dr.-Ing. degrees in computer science from the University of Bremen, Bremen, Germany, in 2006 and 2009, respectively. He was with the Group of Computer Architecture, University of Bremen, from 2006 to 2015, and has been with the German Research Center for Artificial Intelligence (DFKI), Bremen, since 2013. He was a Lecturer with the

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e Noisy Intermediate-Scale antum (NISQ) technology is currently investigated by major players in the eld to build the rst practically useful quantum computer. IBM QX architectures are the rst ones which are already publicly available today. However, in order to use them, the respective quantum circuits have to be compiled for the respectively used target architecture. While rst approaches have been proposed for this purpose, they are infeasible for a certain set of SU(4) quantum circuits which have recently been introduced to benchmark corresponding compilers. In this work, we analyze the bo lenecks of existing compilers and provide a dedicated method for compiling this kind of circuits to IBM QX architectures. Our experimental evaluation (using tools provided by IBM) shows that the proposed approach signi cantly outperforms IBM's own solution regarding delity of the compiled circuit as well as runtime. Moreover, the solution proposed in this work has been declared winner of the IBM QISKit Developer Challenge. An implementation of the proposed methodology is publicly available at h p://iic.jku.at/eda/research/ibm qx mapping.

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum functionality. In the classical domain, decision diagrams have been successfully employed as a powerful alternative to straightforward means such as truth tables. This motivated extensive research on whether decision diagrams provide similar potential in the quantum domain-resulting in new types of decision diagrams capable of substantially reducing the complexity of representing quantum states and functionality. From an implementation perspective, many concepts and techniques from the classical domain can be re-used in order to implement decision diagrams packages for the quantum realm. However, new problems-namely how to efficiently handle complex numbersarise. In this work, we propose a solution to overcome these problems. Experimental evaluations confirm that this yields improvements of orders of magnitude in the runtime needed to create and to utilize these decision diagrams. The resulting implementation is publicly available as a quantum DD package at http://iic.jku.at/eda/research/quantum dd.

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