Randomized sparse-QSVT reduces gate counts by up to 10x for inhomogeneous many-term Hamiltonians at moderate error (around 10^{-3}), but deterministic QSVT becomes cheaper for higher precision.
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Quantum algorithm finds eigenvalues of parameterized matrix families by minimizing singular values and applies it to Schrödinger equation collocation with O(sqrt(N)) scaling.
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.
Review arguing that open-system approaches integrating dissipation into quantum chemistry simulations on fault-tolerant computers offer practical advantages for robustness and potential quantum advantage over purely unitary methods.
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Quantum algorithm for solving generalized eigenvalue problems with application to the Schr\"odinger equation
Quantum algorithm finds eigenvalues of parameterized matrix families by minimizing singular values and applies it to Schrödinger equation collocation with O(sqrt(N)) scaling.