Quantum algorithms achieve polylog(N) complexity for high-dimensional linear SDEs by amplitude-encoding the solution and noise via Dyson series or Euler-Maruyama approximations plus quantum linear systems solvers.
Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm
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D-VQLS with FWHT Pauli decomposition and 1% thresholding reduces circuit evaluations by 256x for 10-qubit tridiagonal systems while achieving over 99.99% fidelity and near-ideal scaling on up to 96 GPUs.
Alternative adiabatic dynamics implementable via discrete gates on quantum computers yield optimal QLSP algorithms and improved randomized Trotter bounds.
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Quantum algorithm for solving high-dimensional linear stochastic differential equations via amplitude encoding of the noise term
Quantum algorithms achieve polylog(N) complexity for high-dimensional linear SDEs by amplitude-encoding the solution and noise via Dyson series or Euler-Maruyama approximations plus quantum linear systems solvers.
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Distributed Variational Quantum Linear Solver
D-VQLS with FWHT Pauli decomposition and 1% thresholding reduces circuit evaluations by 256x for 10-qubit tridiagonal systems while achieving over 99.99% fidelity and near-ideal scaling on up to 96 GPUs.
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Alternative adiabatic quantum dynamics with algorithmic applications
Alternative adiabatic dynamics implementable via discrete gates on quantum computers yield optimal QLSP algorithms and improved randomized Trotter bounds.