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Description
Two-qubit gates dominate error budgets on today's quantum hardware, so compiling a target unitary into a circuit with as few two-qubit gates as possible is central to accurate quantum computation. Standard exact decompositions apply a fixed construction to every target and overspend whenever a specific unitary admits a cheaper circuit---a gap that widens with system size. We ask whether a learned, target-specific search can do better by separating the combinatorial choice of circuit structure from the continuous optimization of rotation angles.
We adapt the generative quantum eigensolver, a generative model for ground-state preparation, to unitary synthesis. A decoder-only transformer, trained per target by group-relative policy optimization, autoregressively proposes discrete circuit structures over single-qubit rotations and CNOTs; classical optimization then fits each structure's rotation angles via an analytic coordinate sweep and quasi-Newton refinement. A Pareto archive retains non-dominated circuits trading process infidelity against two-qubit count.
We evaluate the generative unitary synthesiser on fifty Haar-random targets per qubit count from two to five. Every target compiles to process infidelity below $10^{-4}$. Discovered circuits use fewer CNOTs and lower depth than Qiskit's exact Quantum Shannon Decomposition on average, with mean CNOT savings reaching $10\%$ at five qubits and depth reduced by up to $1.8\times$. At two qubits the search recovers the provably optimal three-CNOT form; from three qubits it places isolated entangling gates rather than recursive blocks. A dedicated approximate compiler remains more compact at larger sizes, but the results establish reinforcement-learning-guided generative search as a viable framework for machine-learning-driven quantum compilation.
| Topic | Machine learning techniques for experimental quantum information science |
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