Speaker
Description
Optimization problems are commonly formulated through Hamiltonians whose ground states encode the desired solutions. We have recently approached such problems using tensor-network methods and variational ground-state search, applying these techniques to real-world challenges such as RSA factorization [1] and satellite mission planning [2]. Here we introduce an alternative quantum route based on equational reasoning [3], where symbolic expressions are connected by rewriting rules that generate equivalence classes. The rewriting rules define a sparse Laplacian Hamiltonian whose ground-state space consists of orbit states—equal-amplitude superpositions of all expressions in an equivalence class—making the word problem and class-size estimation accessible through quantum overlap measurements. We then extend this framework to optimization within an equivalence class, demonstrating a quantum algorithm for compiling quantum circuits on quantum computers: the search for hardware-optimized circuits is recast as ground-state preparation of an infidelity Hamiltonian, capturing global simplifications beyond standard heuristic compilers [4].
References
[1]M. Tesoro, I. Siloi, D. Jaschke, G. Magnifico and S. Montangero, arXiv:2410.16355; [2] M. Tesoro et al. (in preparation); [3] D. Rattacaso, D. Jaschke, M. Ballarin, I. Siloi and S. Montangero, arXiv:2508.21122; [4] D. Rattacaso, D. Jaschke, M. Ballarin, I. Siloi and S. Montangero, PRR 7 (3), 033268, (2025).
| Sessions | Quantum Simulation |
|---|---|
| Invited | No |