Physical synthesis of quantum circuits using Q-learning

Abstract

The present status of quantum computing is of the noisy intermediate-scale quantum (NISQ) era. In addition to the limited number of available qubits, NISQ devices generally possess two other physical constraints, quantum gate and interaction constraints. Those constraints should be satisfied in order for realizing a quantum circuit on an NISQ device. However, this often introduces extra CNOT gates into the circuit which harm the fidelity of the resulting circuit. Consequently, the number of extra CNOT gates needs to be reduced while compiling a quantum circuit onto an NISQ device. To this end, here, a solution that uses Q-learning (QL) is proposed by dividing physical synthesis of quantum circuits into qubit placement and routing. QL algorithms are designed for qubit placement and routing, respectively, by considering them as sequential decision-making problems. A physical synthesis method for quantum circuits is proposed by first using a QL algorithm to learn an optimally initial qubit mapping and then using another QL algorithm to learn an optimal routing scheme. A number of quantum circuits are compiled onto quantum architectures provided by IBM and grid architectures by using the proposed synthesis method. Compared to several methods for physical synthesis of quantum circuits, the proposed synthesis method can reduce the number of extra CNOT gates or the depth of the resulted physical quantum circuit in many cases. In a few cases, the QL algorithm designed for qubit placement can find an initial qubit mapping that makes all gates in a circuit being executed on a quantum architecture provided by IBM.