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.
citing papers explorer
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When is randomization advantageous in quantum simulation?
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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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
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.
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Beyond Unitary Quantum Simulation: Open-System Approaches to Quantum Chemistry toward Quantum Advantage
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.