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 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 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.
The synthesis of efficient reversible logic circuits is critical for fault-tolerant quantum computing (FTQC). The primary motivation of this work is to overcome the inherent disadvantages of existing synthesis techniques: approximate heuristic methods often miss optimal solutions, while pure exact computational methods suffer from combinatorial explosion on deep circuits. While the strict NCT library (NOT, CNOT, Toffoli) is often preferred due to the high cost of distilling non-Clifford states required for arbitrary gates, standard physical implementations frequently utilize the broader NCV library (NOT, CNOT, V, V-dagger), requiring the decomposition of Toffoli gates into five elementary operations. To bridge this gap, this paper presents a unified, highly scalable methodology for the optimal design of reversible circuits across both libraries. First, a Mixed-Integer Non-Linear Programming (MINLP) formulation, linearized for the high-performance IBM ILOG CPLEX solver, is introduced to automate the exact generation of globally optimal strict NCT topologies. Second, a systematic four-phase optimization framework is proposed to reduce NCV costs. By replacing Toffoli gates with specific NCV decompositions, permuting control lines to match subsequent linear gates, and applying exact local searches via an extended MINLP solver on bounded sliding windows, significant gate cancellations are achieved. Applying this methodology to prominent primitives (MIG, SAYEM, URG, TSG, and MKG), we match global NCT optimality constraints and achieve highly optimized NCV Quantum Costs of 7, 14, and 12 for the MIG, TSG, and MKG gates, respectively, establishing best-known upper bounds that significantly outperform heuristic literature benchmarks.
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.
This paper considers the optimization of reversible circuits composed of multiple-control Toffoli gates to quantum circuits using the well-known NCV-1 (NCV) library and the recently introduced NCV-v1 library which both use a four-valued model for the quantum gates. The techniques introduced handle positive and negative controls which are central to many reversible circuit synthesis procedures. Experimental results confirm the methods are applicable to circuits obtained by diverse synthesis methods. The results also show the significant advantage of the NCV-v1 library.
Owing to the exponential nature of the memory or run-time complexity,many existing methods can only synthesize 3-qubit logic circuits using quantum logic gate library,however,a few can optimally synthesize 3-qubit logic circuits for quantum NOT,CNOT,Controlled-V and Controlled-V+(NCV)gates,the key approach reduces the NCV quantum circuit synthesis problem to four-valued logic synthesis.This paper proposes using NCV gates to create a new quantum logic gate library,which is exactly the same as NCV gate library in the synthesis of all optimal 3-qubit circuits,thus it also reduces the four-valued logic synthesis to easily solved two-valued logic synthesis.We present a 3-qubit efficient synthesis algorithms based on perfect hash function,which can quickly construct all optimal 3-qubit circuits——the average speed that synthesizes circuits with minimum cost is nearly 127 times faster than that of the best result of Maslov 2007.
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.