Circuit Synthesis and Compilation

Abstract

Practical quantum computation may be achievable in the next few years, but applications will need to be error-tolerant and make the best use of a relatively small number of quantum bits and operations. Compilation tools will play a critical role in achieving these goals. The job of a quantum compiler is to translate a quantum program written in a high-level programming language into native instructions recognizable by the hardware, through a series of transformations and optimizations. Traditional wisdom from compilation for classical computers can occasionally be inherited or adapted to the quantum case, such as resolving control flows and allocating registers. This chapter puts particular emphasis on the aspects of compilation that are unique to quantum computers. Notably, compilation under strict resource constraints has proven challenging, and optimization will have to break traditional abstractions and be customized to algorithmic and device characteristics in a manner never before seen in classical computing. We call attention to a number of important steps specialized for quantum compilation to help ensure the efficiency and correctness needed. To name a few, unitary synthesis focuses on exactly or approximately expressing arbitrary unitary transformations (such as single qubit rotations by an arbitrary angle) in a sequence of elementary gates. The goal of gate scheduling is to utilize commutation relations to determine the ordering of the (possibly parallel) operations, and to use circuit equivalence to simplify quantum programs. Qubit mapping is another challenge, in that we aim to strategically assign the variables in a quantum program to the qubits available in the system, under multiple constraints such as limited connectivity between qubits, fluctuations in the reliability of qubits and links, and potential opportunities for reclamation and reuse of qubits, etc.