Learning State Separation for Quantum Circuit Synthesis

Many applications of quantum computing require the system to be initialized in a specific state before additional processing steps or algorithms can be applied. How to prepare such a state with the gate set available on a quantum computer is a task known as Quantum Circuit Synthesis (QCS). QCS is challenging due to the vastness of the search space and the cost of simulating candidate quantum circuits. As the cost of simulating a quantum circuit grows exponentially with the number of qubits, performing QCS over all qubits becomes unfeasible for even moderate numbers of qubits. In this paper, we present a Reinforcement Learning (RL) ap- proach aimed at reducing the simulation cost in QCS for state preparation. Our approach transforms the state that is supposed to be synthesized into a separable state, i.e., a state that can be written as the Kronecker product of two states of smaller dimensionality. These sub-states can then be synthesized in isolation using existing QCS frameworks. Finally, the synthesized sub-states can be trans- formed into the original target state by applying the inverse of the generated gate sequence. We evaluate the ability of our RL-based approach to achieve separation on 10 000 randomly created 5-qubit quantum states. Our approach achieved a mean success rate of between 77% and 93%, depending on the complexity of the evaluated states. For all states, the amount of gates used to achieve separability was far below the number of gates used to initially create these states. This highlights the potential a preliminary state separation step holds for QCS.