Quantum time-marching algorithms adapt LCU for diffusive dynamics and use method of images or direct unitary encoding for boundaries, achieving optimal success probabilities and linear complexity, shown via heat equation simulations.
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Generalizes iterative phase estimation to randomized Hamiltonians per step plus importance sampling, yielding fewer terms and sometimes fewer qubits for gapped chemical Hamiltonians.
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Quantum time-marching algorithms for solving linear transport problems including boundary conditions
Quantum time-marching algorithms adapt LCU for diffusive dynamics and use method of images or direct unitary encoding for boundaries, achieving optimal success probabilities and linear complexity, shown via heat equation simulations.
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Phase estimation with randomized Hamiltonians
Generalizes iterative phase estimation to randomized Hamiltonians per step plus importance sampling, yielding fewer terms and sometimes fewer qubits for gapped chemical Hamiltonians.