Optimized Quantum Gate Library for Various Physical Machine Descriptions

Quantum logic circuits consist of a cascade of quantum gates. These gates are realized using primitive quantum operations that are supported by a quantum physical machine description (PMD). Since different quantum systems are associated with different Hamiltonians, a specific quantum operation may be more easily realizable in one quantum system than another. Thus, different quantum systems have different PMDs. Also, the quantum cost for implementing a quantum operation may differ from one PMD to another. Thus, a quantum logic circuit needs to be realized with and optimized for only the set of primitive quantum operations supported by the given PMD. Quantum logic design that can be targeted at multiple PMDs has not been attempted before, to the best of our knowledge. In this paper, we target quantum logic design with respect to the set of primitive quantum operations that are supported by six different PMDs: quantum dot, superconducting, ion trap, neutral atom, and two photonics systems. Our aim is to build a quantum gate library that targets these PMDs. This is akin to a cell library in traditional logic design that enables logic gates to be mapped to cells realizable in an underlying technology. To make our quantum gate library efficient in terms of the number of primitive quantum operations involved and the associated delay, we explore one- and two-qubit quantum identity rules that can help remove redundancies in the quantum gate implementation. We show that, using these identities, each gate in the library can be efficiently mapped to just the set of primitive operations supported by each of the six PMDs. Each mapping results in a different circuit structure and quantum cost, which is measured in terms of the number of primitive quantum operations and the number of execution cycles required. Thus, such a library provides the foundation for quantum logic synthesis, just like a cell library provides the foundation for technology-dependent logic synthesis (i.e., technology mapping) in traditional synthesis.