Optimisation and synthesis of quantum circuits with global gates

Abstract

Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum hardware, and has the potential to significantly improve their performance when optimisation techniques are added to the process. One such optimisation technique is reducing the number of quantum gates that are needed to execute a circuit. For instance, methods for reducing the number of non-Clifford gates or CNOT gates from a circuit are an extensive research area that has gathered significant interest over the years. For certain hardware platforms such as trapped-ion quantum computers, we can leverage some of their special properties to further reduce the cost of executing a quantum circuit in them. In this work we use global interactions, such as the Global Mølmer–Sørensen (MS) gate present in trapped-ion hardware, to optimise and synthesise quantum circuits. We design and implement an algorithm that is able to compile an arbitrary quantum circuit into another circuit that uses global gates as the entangling operation, while optimising the number of global interactions needed. The algorithm is based on the ZX-calculus and uses a specialised circuit extraction routine that groups entangling gates into Global MS gates. We benchmark the algorithm in a variety of circuits, and show how it improves their performance under state-of-the-art hardware considerations in comparison to a naive algorithm and the Qiskit optimiser.