Quantum assisted quantum compiling

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. Here we propose to use the Hilbert-Schmidt inner product between a target unitary $U$ and a trainable unitary $V$ as the cost function to be evaluated on the quantum computer. We introduce two circuits for evaluating this cost. One circuit avoids using controlled unitaries (and hence is shorter depth) and gives $| {\rm Tr} (V^\dagger U)|$. We use this circuit for gradient-free compiling. Our other circuit gives ${\rm Tr}(V^\dagger U)$ and is a generalization of the power-of-one-qubit circuit that we call the power-of-two-qubits. We use this circuit for gradient-based compiling. We illustrate both our gradient-free and gradient-based methods by compiling various one-qubit gates to the native gate alphabets on IBM's and Rigetti's quantum computers, and we also compile multiqubit gates on a simulator.

PDF Abstract