From Easy to Hard: Tackling Quantum Problems with Learned Gadgets For Real Hardware

Building quantum circuits that perform a given task is a notoriously difficult problem. Reinforcement learning has proven to be a powerful approach, but many limitations remain due to the exponential scaling of the space of possible operations on qubits. In this paper, we develop an algorithm that automatically learns composite gates ("$gadgets$") and adds them as additional actions to the reinforcement learning agent to facilitate the search, namely the Gadget Reinforcement Learning (GRL) algorithm. We apply our algorithm to finding parameterized quantum circuits (PQCs) that implement the ground state of a given quantum Hamiltonian, a well-known NP-hard challenge. In particular, we focus on the transverse field Ising model (TFIM), since understanding its ground state is crucial for studying quantum phase transitions and critical behavior, and serves as a benchmark for validating quantum algorithms and simulation techniques. We show that with GRL we can find very compact PQCs that improve the error in estimating the ground state of TFIM by up to $10^7$ fold and make it suitable for implementation on real hardware compared to a pure reinforcement learning approach. Moreover, GRL scales better with increasing difficulty and to larger systems. The generality of the algorithm shows the potential for applications to other settings, including optimization tailored to specific real-world quantum platforms.