Quantum circuits

Colin P. Williams

Daniel Escánez-Expósito, Pino Caballero‐Gil, Marcos Rodriguez-Vega +2 more

Abstract The use of graphical language in quantum computing for the representation of algorithms, although intuitive, is not very useful for different tasks such as the description of quantum circuits in text environments, the calculation of quantum states or the optimization of quantum circuits. While classical circuits can be represented either by circuit graphs or by Boolean expressions, quantum circuits have until now predominantly been illustrated as circuit graphs because no formal language for quantum circuits that allows algebraic manipulations has so far been accepted. This work proposes a means to represent quantum circuits in a convenient and concise manner, similar to the way Boolean expressions are used in classical circuits. The proposed notation allows the consistent and parameterized description of quantum algorithms, as well as the easy handling of the elements that compose it to achieve powerful optimizations in the number of gates of the circuits. To visualize it, a software implementation of an algebraic quantum circuit framework has been made, which allows describing quantum circuits, as well as their respective state vectors, using the proposed algebraic language.

Madhusudan Singh Irish Singh, Bharat S. Rawal

Einar Pius

The main focus of this work is to implement a program that can be used to parallelise quantum circuits. This is done by translating the quantum circuits to the Measurement Based Quantum Computing (MBQC) model, applying a number of optimising techniques to the computation in MBQC, and by translating it back to a quantum circuit. As a side result of implementing this method, a new algorithm for creating and optimising an MBQC graph from a quantum circuit is designed. The implemented program is used to investigate quantum circuits known from the literature: the QFT, and a specific type of circuits. We show that our program will parallelise the circuit to logarithmic depth, and increase the depth of QFT by a logarithmic factor. Finally, three new classes of quantum circuits are presented: the Toffoli staircase circuit, the Toffoli + CNOT staircase circuit, and a circuits consisting of quantum gates ∧Z, CNOT , ω , Z(α), and J(−2 ). In the computational experiments we perform, those classes of circuits will benefit from the parallelisation method implemented in this dissertation.

Huinan Chen, Yanying Zhu, CAI BinBin +1 more

Serpent, one of the AES candidate algorithms, is known for its high security and attack resistance. It is suitable for areas with high information security requirements. Serpent's distinctive nonlinear structure is the S-boxes. This paper studies how to build the quantum circuit for Serpent algorithm with lower costs. By combining with the quantum circuits of S-boxes with fewer qubits and quantum gates and the inverse quantum circuits of S-boxes, the key expansion quantum circuit can be constructed. Moreover, by decomposing the 3-controlledCNOT gates appearing in the quantum circuits of the S-boxes and optimizing the decomposed quantum circuits, the number of Toffoligates is further reduced. In conjunction with the proposed quantum circuits, two types of quantum circuits requiring 448 qubits and 92288 T gates and 384 qubits and 118944 T gates are given to realize the Serpent algorithm. In comparison with the previous study, which required 800 qubits and 132608 T gates, the quantum circuit in this paper requires fewer resources. Furthermore, the S-boxes and key expansion quantum circuits used in the study can reduce the quantum resources in implementing Serpent, reducing the quantum circuit scale required to attack Serpent by the Grover algorithm.