Everything You Always Wanted to Know About Quantum Circuits

Abstract

The development of circuits for quantum computing has been motivated by the proliferation of quantum algorithms which promise up to a superpolynomial factor speedup over classical equivalents. The quantum algorithms developed have the potential to impact fields such as number theory, encryption, scientific computation [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]. The design of quantum algorithms remains an active area of research and new algorithms continue to appear in the literature (see [17] for a representative listing of quantum algorithms). In order to realize the potential performance gains of these proposed quantum algorithms, they must be implemented on quantum hardware. The quantum computers developed by entities such as IBM or Honeywell are examples of quantum hardware platforms which could be used to implement quantum algorithms [18] [19] [20] [21] [22]. To implement quantum algorithms on these hardware platforms, we require quantum datapath systems which are composed of quantum circuits. In this work we shall introduce the design and resource cost assessment of quantum circuits. These quantum circuits are composed of quantum gate networks. Quantum machines developed from entities such as IBM and Honeywell support gate based quantum computation. Gate based quantum circuit design has applications in fault tolerant quantum computation and in quantum circuit design automation [23] [24] [25] [26] [27] [28] [16] [29]. Each quantum gate represents a quantum mechanical operation. As a result, the designer working with quantum circuits shall have to contend with novel properties and challenges. For instance, quantum circuits are one-to-one and all information is preserved. The design of quantum circuits for the implementation of quantum algorithms has caught the attention of researchers. Circuits for elementary functions such as basic arithmetic functions (such as addition or division) have been proposed such as [30] [31][32] [33] [34] [35] [36] [37]. These basic circuits are used as building blocks for more complex datapath systems such as higher level mathematical functions for applications in scientific computing, image processing or machine learning [38] [39] [40] [12] [41] [42] [43].