Synthesis of quantum circuits is essential for building quantum computers. It is important to verify that the circuits designed perform the correct functions. In this paper, we propose an algorithm which can be used to verify the quantum circuits synthesized by any method. The proposed algorithm is based on BDD (Binary Decision Diagram) and is called X-decomposition Quantum Decision Diagram (XQDD). In this method, quantum operations are modeled using a graphic method and the verification process is based on comparing these graphic diagrams. We also develop an algorithm to verify reversible circuits even if they have a different number of garbage qubits. In most cases, the number of nodes used in XQDD is less than that in other representations. In general, the proposed method is more efficient in terms of space and time and can be used to verify many quantum circuits in polynomial time.
Synthesis of quantum circuits is essential for building quantum computers. It is important to verify that the circuits designed perform the correct functions. In this paper, we propose an algorithm which can be used to verify the quantum circuits synthesized by any method. The proposed algorithm is based on BDD (Binary Decision Diagram) and is called X-decomposition Quantum Decision Diagram (XQDD). In this method, quantum operations are modeled using a graphic method and the verification process is based on comparing these graphic diagrams. We also develop an algorithm to verify reversible circuits even if they have a different number of garbage qubits. In most cases, the number of nodes used in XQDD is less than that in other representations. In general, the proposed method is more efficient in terms of space and time and can be used to verify many quantum circuits in polynomial time.
X-decomposition Quantum Decision Diagram (XQDD) can represent a quantum operation and perform matrix operations. It can be used to verify quantum and reversible circuits even if the reversible circuits have different number of garbage qubits. It is efficient in terms of space and time. In this paper, we extend the original XQDD to multiple-valued quantum logic. The extended XQDD can represent a multiple-valued quantum operation and perform matrix operations. It can be used to check the equivalence of two multiple-valued quantum or reversible circuits which are synthesized by different approaches. In this paper, we show that the space in multiple-valued XQDD is less than other representations and it is much better than multiple-valued QuIDD and very close to QMDD in terms of time.
Reversible logic became a promising alternative to traditional circuits because of its applications in emerging technologies such as quantum computing, low-power design, DNA computing, or nanotechnologies. As a result, synthesis of the respective circuits is an intensely studied topic. However, most synthesis methods are limited, because they rely on a truth table representation of the function to be synthesized. In this paper, the authors present a synthesis approach that is based on Binary Decision Diagrams (BDDs). The authors propose a technique to derive reversible or quantum circuits from BDDs by substituting all nodes of the BDD with a cascade of Toffoli or quantum gates, respectively. Boolean functions containing more than a hundred of variables can efficiently be synthesized. More precisely, a circuit can be obtained from a given BDD using an algorithm with linear worst case behavior regarding run-time and space requirements. Furthermore, using the proposed approach, theoretical results known from BDDs can be transferred to reversible circuits. Experiments show better results (with respect to the circuit cost) and a significantly better scalability in comparison to previous synthesis approaches.
With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of them supports symbolic computation. Algorithmic manipulations of symbolic objects, however, have been identified as crucial, if not indispensable, for several verification tasks. This paper proposes the first decision-diagram approach for operating symbolic objects and verifying quantum circuits with symbolic terms. As a notable example, our symbolic tensor decision diagrams (symbolic TDD) could verify the functionality of the 160-qubit quantum Fourier transform circuit within three minutes. Moreover, as demonstrated on Bernstein-Vazirani algorithm, Grover's algorithm, and the bit-flip error correction code, the symbolic TDD enables efficient verification of quantum circuits with user-supplied oracles and/or classical controls.
Quantum information processing technology is in its pioneering stage and no proficient method for synthesizing quantum circuits has been introduced so far. This paper introduces an effective analysis and synthesis framework for quantum logic circuits. The proposed synthesis algorithm and flow can generate a quantum circuit using the most basic quantum operators, i.e., the rotation and controlled-rotation primitives. The paper introduces the notion of quantum factored forms and presents a canonical and concise representation of quantum logic circuits in the form of quantum decision diagrams (QDD's), which are amenable to efficient manipulation and optimization including recursive unitary functional bi-decomposition. This paper concludes by presenting the QDD-based algorithm for automatic synthesis of quantum circuits
Synthesis of reversible and quantum logic has become an intensely studied topic in the last years. However, most synthesis methods are limited, since they rely on a truth table representation of the function to be synthesized. BDD-based synthesis offers an alternative. Here, reversible or quantum circuits are derived from a function given as Binary Decision Diagram (BDD) by substituting all nodes of the BDD with a cascade of Toffoli or elementary quantum gates, respectively. As a result, the application of the approach is not limited by the truth table of the function but by the (quite more efficient) BDD representation. Furthermore, many optimization techniques for BDDs exist which can be exploited. In this work, we evaluate the effect of three optimization methods for BDDs (namely shared nodes, complement edges, and advanced orderings) on the resulting reversible and quantum circuits. We describe in detail the adjustments, which have to be done to support these optimizations for synthesis, and discuss possible improvements and drawbacks. In a case study, the effects are experimentally evaluated. The results showed, that applying these optimization techniques leads to significant smaller circuits (with respect to number of gates and lines) in most of the cases.
Recently much attentions have been paid to quantum circuit design to prepare for the future ldquoquantum computation era.rdquo Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated quantum circuits. For that purpose, we propose an efficient verification method for quantum circuits under a practical restriction. Thanks to the restriction, we can introduce an efficient verification scheme based on decision diagrams called Decision Diagrams for Matrix Functions (DDMFs). Then, we show analytically the advantages of our approach based on DDMFs over the previous verification techniques. In order to introduce DDMFs, we also introduce new concepts, quantum functions and matrix functions, which may also be interesting and useful on their own for designing quantum circuits.