Quantum

Variational Programs with Open Clocks

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Briefings

A new quantum programming language VHamilton introduces open clock mechanisms allowing classical optimizers to set Hamiltonian evolution durations. The authors implement a compiler rewrite proving equivalence between open-clock programs and fixed-clock circuits, validate it via Agda, and test it on a two-qubit chemistry eigensolver. The system supports fusion of commuting blocks, exact error bounds between target precision and clock precision, and coordinate search where query complexity remains constant regardless of precision. On a benchmark of 134 million valuations, the algorithm reached the numerically verified optimum in 53 energy queries, though it found the grid optimum in only 21 of 30 validation settings.

Key points

• VHamilton is a minimal extension of the Hamilton quantum programming language that introduces open clocks for Hamiltonian evolution durations.
• The system supports a compiler rewrite proving equivalence between open-clock programs and fixed-clock circuits, with a formal proof in Agda.

Context

This research addresses the open problem of determining optimal Hamiltonian evolution durations in variational quantum algorithms. By allowing classical optimizers to set these durations, VHamilton enables a new class of hybrid algorithms that combine quantum circuit compilation with classical optimization.

Limitations

The benchmark results are conditional on the specific validation settings used. While the algorithm reached the numerically verified optimum in 53 queries, it only found the grid optimum in 21 of 30 validation settings, indicating the gain is not a global optimization guarantee.

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