Quantum computation received a steadily growing attention in recent years, especially supported by the emergence of publicly available quantum computers like the popular IBM QX series. In order to execute a reversible or quantum circuit on those devices, a mapping is required that replaces each reversible or quantum gate by an equivalent cascade of elementary, i.e. directly executable, gates-a task which tends to induce a significant mapping overhead. Several approaches have been proposed for this task which either rely on the swapping of physically adjacent qubits or the use of precomputed templates, so-called remote CNOT gates. In this paper, we show that combining both, swapping and remote gates, at the reversible circuit level has the prospect of significantly reducing the mapping overhead. We propose a methodology to compute the optimal combination of swaps and templates for Multiple-Controlled Toffoli gates. By using a formulation as a single-source shortest-path problem, a complete database of optimal combinations can be computed efficiently. Experimental results indicate that the mapping overhead can be significantly reduced.

Quantum computers offer enormous speed advantages over their classical counterparts. Still, optimization on quantum circuits is necessary to further increase their potential. Additionally, physical realizations of quantum computers place restrictions on quantum circuits, regarding the available quantum gates. In order to satisfy these restrictions, non-native gates need to be expressed as an equivalent cascade of natively available quantum gates which induces a mapping overhead. Two complementary approaches to this problem are to move around the qubits (using SWAP gates) or to apply so-called remote gates, i.e. pre-computed cascades of native gates which keep the qubit placement.In this paper, we explore how combinations of movements and remote gates can be employed to reduce the required overhead regarding the number of native gates as well as the circuit depth. We also discuss ways to find out which qubits to address with the movements in order to optimize these metrics. Our general evaluation is supplemented by evaluations on two IBM quantum computer architectures to show how quantum circuits can be optimized by the presented patterns.

With more and more powerful quantum computers becoming available, there is an increasing interest in the efficient mapping of a given quantum circuit to a particular quantum computer (so-called technology mapping). In most cases, the limitations of the targeted quantum hardware have not been taken into account when generating these quantum circuits in the first place. Thus, the technology mapping is likely to induce a considerable overhead for such circuits. In this paper, we consider the realization of reversible circuits consisting of multiple-controlled Toffoli gates on IBM quantum computers. We show that choosing different quantum-level decompositions can indeed have a significant impact on the mapping overhead. Based on this observation, we present an approach to perform design space exploration to obtain quantum circuits with reduced overhead by exploiting information about the targeted quantum hardware as well as the reversible circuit. An experimental evaluation shows that this approach often leads to considerable reductions of the technology mapping overhead with negligible runtime.

Near zero-energy computing describes the concept of executing logic operations below the ( k B T ln 2) energy limit. Landauer discussed that it is impossible to break this limit as long as the computations are performed in the conventional, non-reversible way. But even if reversible computations were performed, the basic energy needed for operating circuits realized in conventional technologies is still far above the ( k B T ln 2) energy limit (i.e., the circuits do not operate in a physically reversible manner). In contrast, novel nanotechnologies like Quantum-dot Cellular Automata (QCA) allow for computations with very low energy dissipation and hence are promising candidates for breaking this limit. Accordingly, the design of reversible QCA circuits is an active field of research. But whether QCA in general and the proposed circuits in particular are indeed able to operate in a logically and physically reversible fashion is unknown thus far, because neither physical realizations nor appropriate simulation approaches are available. In this work, we address this gap by utilizing an established theoretical model that has been implemented in a physics simulator enabling a precise consideration of how energy is dissipated in QCA designs. Our results provide strong evidence that QCA is indeed a suitable technology for near zero-energy computing. Further, the first design of a logically and physically reversible adder circuit is presented, which serves as proof of concept for future circuits with the ability of near zero-energy computing.

Quantum computation promises to solve many hard or infeasible problems substantially faster than classical solutions. The involvement of big players like Google, IBM, Intel, Rigetti, or Microsoft furthermore led to a momentum which increases the demand for automated design methods for quantum computations. In this context, decision diagrams for quantum computation provide a major pillar as they allow to efficiently represent quantum states and quantum operations which, otherwise, have to be described in terms of exponentially large state vectors and unitary matrices. However, current decision diagrams for the quantum domain suffer from a tradeoff between accuracy and compactness, since: 1) small errors that are inevitably introduced by the limited precision of floating-point arithmetic can harm the compactness (i.e., the size of the decision diagram) significantly and 2) overcompensating these errors (to increase compactness) may lead to an information loss and introduces numerical instabilities. In this article, we describe and evaluate the effects of this tradeoff which clearly motivates the need for a solution that is perfectly accurate and compact at the same time. More precisely, we show that the tradeoff indeed weakens current design automation approaches for quantum computation (possibly leading to corrupted results or infeasible run-times). To overcome this, we propose an alternative approach that utilizes an algebraic representation of the occurring complex and irrational numbers and outline how this can be incorporated in a decision diagram which is suited for quantum computation. Evaluations show that-at the cost of an overhead which is moderate in many cases-the proposed algebraic solution indeed overcomes the tradeoff between accuracy and compactness that is present in current numerical solutions.

Quantum computation is a promising research field since it allows to conduct certain tasks exponentially faster than on conventional machines. As in the conventional domain, decision diagrams are heavily used in different design tasks for quantum computation like synthesis, verification, or simulation. However, unlike decision diagrams for the conventional domain, decision diagrams for quantum computation as of now suffer from a trade-off between accuracy and compactness that requires parameter fine-tuning on a case-by-case basis. In this work, we-for the first time-describe and evaluate the effects of this trade-off. Moreover, we propose an alternative approach that utilizes an algebraic representation of the occurring irrational numbers and outline how this can be incorporated in a decision diagram in order to overcome this trade-off.

The Clifford+T library provides robust and fault-tolerant realizations for quantum computations. Consequently, (logic) synthesis of Clifford+T quantum circuits became an important research problem. However, previously proposed solutions are either only applicable to very small quantum systems or lead to circuits that are far from being optimal- mainly caused by a local, i.e. column-wise, consideration of the underlying transformation matrix to be synthesized. In this paper, we suggest an improved approach that considers the matrix globally and, by this, overcomes many of these drawbacks. Preliminary evaluations show the promises of this direction.

Quantum-Dot Cellular Automata (QCA) are an emerging nanotechnology with remarkable performance and energy efficiency. Computation and information transfer in QCA is based on field forces rather than electric currents. As a consequence, new strategies are required for design automation approaches in order to cope with the arising challenges. One of these challenges rises from the fact that QCA is a planar technology. That means, logic gates as well as interconnection elements are mostly located in the same layer. Hence, it is expected that interconnections have higher influence on the final design costs than in conventional integrated technologies. For the first time, this paper presents an extensive study on the quantification of this impact. Therefore, we consider the entire design flow for QCA circuits from the initial synthesis (using different synthesis approaches) to the corresponding placement on a QCA grid. Then, we characterize the respectively obtained QCA circuits in terms of area, delay and energy costs. The obtained results indicate that the impact of interconnections in QCA is indeed substantial. Design costs including or not including interconnections differ by several orders of magnitudes, which motivates to completely re-think how logic synthesis for QCA circuits shall be conducted in the future.

Quantum-dot cellular automata (QCA) are an emerging field-coupled nanotechnology with remarkable performance and energy efficiency. In order to enable the exploration of this technology, we propose a model for the logic synthesis of QCA circuits that, for the first time, considers and abstracts all main physical aspects-in particular, energy dissipation. To this end, we review in detail how energy is dissipated in QCA cells and present a corresponding environment that allows for the estimation of the energy dissipation with respect to any specific set of technology parameters. Based on that, we derive a model for logic synthesis. A case study confirms the accuracy of the proposed model and reveals that interconnections have a significant impact in this technology-motivating a more rigorous consideration. These findings eventually provide the basis for a new generation of synthesis approaches at the logic level that are explicitly dedicated to QCA systems.

UML/OCL models are used to describe system models in early stages of the design process. In order to detect design flaws in these models as soon as possible (ideally before the implementation phase starts), various methods for the validation and verification of UML/OCL models have been proposed. In particular, automatic solutions (so-called model finders) are of interest here. They provide designers with quick feedback, e. g., on the consistency of their models in a push-button fashion. But thus far, all proposed approaches support a (small) subset of UML/OCL only or employ substantial restrictions. In fact, there are only few solutions that support the extended type system including the irregular values null and invalid - although these values play an important role for covering exceptional cases. Moreover, these solutions either heavily rely on manual interaction or significantly restrict the supported UML/OCL description means. In this work, we propose a generic formal representation of UML/OCL which can be used for the validation and verification of corresponding models and, at the same time, addresses these shortcomings.

Verification and validation of UML/OCL models is a crucial task in the design of complex software/hardware systems. The behavior in those models is expressed in terms of operations with pre- and postconditions. These, however, are often not precise enough to describe what may or may not be modified in a transition between two system states. This frame problem is commonly addressed by providing additional constraints in terms of so-called frame conditions and has already been considered in different research areas in the last decades - except for UML/OCL where corresponding approaches have been investigated only recently. Besides that, several approaches for the verification of the behavior specified in UML/OCL models have been proposed. They rely on a symbolic representation of all possible system states and transitions between them. But here, frame conditions have not been considered yet - a significant drawback for the underlying verification approaches. In this paper, we describe how to integrate frame conditions to symbolic representations. This enables designers to verify the behavior of UML/OCL models while, at the same time, respecting the given frame conditions.

Quantum mechanical phenomena such as phase shifts, superposition, and entanglement show promise in use for computation. Suitable technologies for the modeling and design of quantum computers and other information processing techniques that exploit quantum mechanical principles are in the range of vision. Quantum algorithms that significantly speed up the process of solving several important computation problems have been proposed in the past. The most common representation of quantum mechanical phenomena are transformation matrices. However, the transformation matrices grow exponentially with the size of a quantum system and, thus, pose significant challenges for efficient representation and manipulation of quantum functionality. In order to address this problem, first approaches for the representation of quantum systems in terms of decision diagrams have been proposed. One very promising approach is given by Quantum Multiple-Valued Decision Diagrams (QMDDs) which are able to efficiently represent transformation matrices and also inherently support multiple-valued basis states offered by many physical quantum systems. However, the initial proposal of QMDDs was lacking in a formal basis and did not allow, e.g., the change of the variable order-an established core functionality in decision diagrams which is crucial for determining more compact representations. Because of this, the full potential of QMDDs or decision diagrams for quantum functionality in general has not been fully exploited yet. In this paper, we present a refined definition of QMDDs for the general quantum case. Furthermore, we provide significantly improved computational methods for their use and manipulation and show that the resulting representation satisfies important criteria for a decision diagram, i.e., compactness and canonicity. An experimental evaluation confirms the efficiency of QMDDs.

In behavioral modeling, operation contracts defined by pre- and postconditions describe the effects on model properties (i.e., model elements such as attributes, links, etc.) that are enforced by an operation. However, it is usually omitted which model properties should not be modified. Defining so-called frame conditions can fill this gap. But, thus far, these have to be defined manually - a time-consuming task. In this work, we propose a methodology which aims to support the modeler in the definition of the frame conditions by extracting suggestions based on an automatic analysis of operation contracts provided in OCL. More precisely, the proposed approach performs a structural analysis of pre- and postconditions together with invariants in order to categorize which class and object properties are clearly “variable” or “unaffected” - and which are “ambiguous”, i.e. indeed require a more thorough inspection. The developed concepts are implemented as a prototype and evaluated by means of several example models known from the literature.

Quantum circuits established themselves as a promising emerging technology and, hence, attracted considerable attention in the domain of computer-aided design. As a result, many approaches for synthesis of corresponding netlists have been proposed in the last decade. However, as the design of quantum circuits faces serious obstacles caused by phenomena such as superposition, entanglement, and phase shifts, automatic synthesis still represents a significant challenge. In this paper, we propose an automatic synthesis approach for quantum circuits that implement Clifford Group operations. These circuits are essential for many quantum applications and cover core aspects of quantum functionality. The proposed approach exploits specific properties of the unitary transformation matrices that are associated to quantum operations. Furthermore, Quantum Multiple-Valued Decision Diagrams (QMDDs) are employed for an efficient representation of these matrices. Experimental results confirm that this enables a compact realization of the respective quantum functionality.