In recent years, quantum computing has gained a lot of importance due to its property of increasing computational power exponentially. In the current literature, it has observed that the quantum computing has potential to solve many complex problems with less complexity based on the theoretical analysis. But in contrast to hardware implementation of quantum technology, it expands in a linear way. Moreover, there is a close relation between quantum computing and reversible computing. More precisely, quantum computing operations are reversible. In this paper, we propose an extended approach of mapping flow for describing reversible circuits to its equivalent quantum circuits. Here, we consider the reversible circuits of n-inputs and n-outputs with NCT and GT library, which is mapped to the quantum circuits with the NCV-|v1〉 library. Finally, we provide our experimental results in terms of quantum costs for mapping the reversible circuits to quantum circuits.
In recent years, quantum computing has gained a lot of importance due to its property of increasing computational power exponentially. In the current literature, it has observed that the quantum computing has potential to solve many complex problems with less complexity based on the theoretical analysis. But in contrast to hardware implementation of quantum technology, it expands in a linear way. Moreover, there is a close relation between quantum computing and reversible computing. More precisely, quantum computing operations are reversible. In this paper, we propose an extended approach of mapping flow for describing reversible circuits to its equivalent quantum circuits. Here, we consider the reversible circuits of n-inputs and n-outputs with NCT and GT library, which is mapped to the quantum circuits with the NCV-|v1〉 library. Finally, we provide our experimental results in terms of quantum costs for mapping the reversible circuits to quantum circuits.
Motivated by the prospects of quantum computation, the design of quantum circuits received significant attention in the recent past. Due to the complex representation of the underlying quantum mechanical phenomena, a two-stage design flow was established in which the desired functionality is first realized in terms of a reversible circuit and, afterwards, mapped into an equivalent quantum circuit. This paper proposes a new metric for estimating nearest neighbor cost at the reversible circuit level. Research works are mostly carried out considering nearest neighbor constraints at the quantum circuit level. Various quantum gate libraries and mapping schemes have been reported in the literature to realize the circuit operation at quantum level. One such mapping scheme exploiting a well established quantum gate library (NCV) is explored in defining the cost metric. Experimental evaluations confirmed both the accuracy as well as the applicability of the proposed metric.
In the recent past, significant effort has been put on the investigation of design methods for quantum circuits. Based on different physical realizations, several gate libraries have been proposed for this purpose. Recently, the so-called NCV-|v1> library has been introduced in this context. In contrast to established libraries, the NCV-|v1> library seems to inherit some significant advantages compared to established ones, e.g. with respect to the mapping from reversible circuits or the satisfaction of nearest neighbour constraints. However, all these conclusions have been drawn based on heuristically results. In this work, we perform a more in-depth examination of the NCV-|v1> library based on minimal circuits. For this purpose, an exact synthesis scheme is proposed which utilizes the power of solvers for Boolean satisfiability. Our examination clearly unveiled that, from a logic design perspective, the NCV-|v1> library indeed superiors the currently established library.
In previous work and motivated by a theoretical discussion on physical realizations, a new quantum gate library (the NCV-v1 library) for electronic design automation of quantum circuits has been proposed. Here, qudits instead of qubits are assumed, i.e. a basic building block which does not rely on a two level quantum system but a (multiple-valued) d-level quantum system is assumed. However, the descriptions on the foundation of this new library remained brief. This technical report provides an extended description of the applied ideas and concepts.
Quantum information processing is of interest as it offers the potential for a new generation of very powerful computers supporting novel computational paradigms. Over the last couple of decades, different aspects of quantum computers ranging from quantum algorithms to quantum physical design have received growing attention. One of the most important research areas is the synthesis and post-synthesis optimization of reversible and quantum circuits. Many synthesis and optimization approaches can be found in the literature, yet, due to the complexity of the problem, finding approaches leading to optimal, or near optimal, results is still an open problem. The synthesized circuits are usually evaluated based on quantum cost models. Therefore, they are often technology mapped to circuits of more primitive gates. To this end, various technology mapping approaches have also been proposed in the past few years. Related work shows an existing gap in optimized technology mapping for reversible and quantum circuits. In this dissertation, an optimized technology mapping design flow is introduced for mapping reversible circuits to quantum circuits. The contributions of this dissertation are classified as follows: - New reversible circuit optimization methods. - Optimized reversible to quantum mapping approaches. - New quantum gate libraries and new cost models for reversible gates based on the new libraries. - Quantum circuit optimization approaches. The steps above, form an optimized flow for mapping reversible circuits to quantum circuits. At each step of the design flow optimized and consistent approaches are suggested with the goal of reducing the quantum cost of the synthesized reversible circuits. The evaluations show that the proposed mapping methodology leads to significant improvement in the quantum cost of the existing benchmark circuits.
The synthesis of reversible logic circuits is a fundamental step in the design of fault-tolerant quantum arithmetic. Existing literature frequently minimizes Quantum Cost (QC) by utilizing the NCV library, which permits controlled-V and Vdagger gates. However, in the context of Fault-Tolerant Quantum Computing (FTQC), the strict NCT library (NOT, CNOT, Toffoli) is often preferred due to the high cost of distilling non-Clifford states required for arbitrary V-gates. Moreover, in the classical design of reversible circuits, only the NCT library can be used as V-gates are not available. In this paper, a new design method for reversible circuits is proposed, based on Mixed-Integer Non-Linear Programming (MINLP) within the Strict NCT Library. By formulating the problem as an MINLP model in GAMS, we successfully automated the optimization of five prominent reversible primitives (TSG, MKG, MIG, SAYEM, and URG) within the strict NCT library. Comparative analysis with the NCV costs found in the literature shows that the costs within the NCT library are comparable or better.
The synthesis of reversible logic circuits is a fundamental step in the design of fault-tolerant quantum arithmetic. Existing literature frequently minimizes Quantum Cost (QC) by utilizing the NCV library, which permits controlled-V and Vdagger gates. However, in the context of Fault-Tolerant Quantum Computing (FTQC), the strict NCT library (NOT, CNOT, Toffoli) is often preferred due to the high cost of distilling non-Clifford states required for arbitrary V-gates. Moreover, in the classical design of reversible circuits, only the NCT library can be used as V-gates are not available. In this paper, a new design method for reversible circuits is proposed, based on Mixed-Integer Non-Linear Programming (MINLP) within the Strict NCT Library. By formulating the problem as an MINLP model in GAMS, we successfully automated the optimization of five prominent reversible primitives (TSG, MKG, MIG, SAYEM, and URG) within the strict NCT library. Comparative analysis with the NCV costs found in the literature shows that the costs within the NCT library are comparable or better.