Quantum circuit simplification cuts gate counts for optimization problems
Exact Diagonal Completion on Reachable Subspaces: Application to QAOA Placement
Hardware ArchitectureEmerging Technologies
Summary
Quantum computers use quantum bits that can represent a huge number of states, but many of these states go unused in certain problems. This paper studies how to fill in those unused parts of a quantum operation exactly, without changing the intended outcome, to simplify the circuits. The authors show this technique can significantly reduce the number of key operations called controlled-NOT gates needed to run a quantum optimization algorithm for placing components on a chip. However, in the end-to-end chip design flow, these improvements did not clearly make the whole process better.
What this means in practice
- •For quantum circuit designers: Reduce controlled-NOT gate counts in QAOA circuits for placement by optimizing unused encoding states using exact diagonal completion.
- •For chip design engineers: Improve the phase construction step in quantum-assisted chip placement workflows integrating QAOA with classical design tools.
Authors
Owen Friedewald, Ali Shiri Sichani, Chi-Ren Shyu
Abstract
Unused encoding states offer opportunities to simplify quantum circuits. For algorithms restricted to reachable subspaces, unspecified diagonal-operator entries can be optimized without changing ideal computation. We investigate exact diagonal completion for the quantum approximate optimization algorithm (QAOA) applied to placement, using permutation-preserving register swaps. We construct exact Manhattan-distance operators through weighted-$\ell_1$ optimization of Walsh coefficients and a sparse recurrence requiring $O(\sqrt{m})$ terms on balanced rectangles, avoiding $O(m^4)$ dense constraint storage. Across 160 geometries, weighted-$\ell_1$ completion reduces controlled-NOT (CX) counts relative to four alternative extensions in all 96 cases with unused binary codes under Gray-code synthesis. On an independently specified 60-case cohort, median reductions relative to virtual-coordinate extension are 28.0\%, 53.9\%, and 21.6\% at six, nine, and twelve sites. Under generic diagonal synthesis, reductions decrease to 10.9\%, 1.3\%, and 0.7\%, demonstrating compiler dependence. Additional ancillas reduce mixer serialization, but token circuits remain deeper than one-hot baselines. Ideal placement simulations show baseline-dependent solution quality, with classical search performing better. OpenROAD integration takes 72 QAOA and 216 classical placements across six RTL designs through clock-tree synthesis and global routing with zero overflow. Completion improves phase construction; no end-to-end advantage is established.