Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
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A recipe for initial points in variational compression of quantum time-evolution operators that provably converges to near-optimal O(N t polylog(N t/ε)) gate complexity for local translationally invariant Hamiltonians.
The paper presents a zero-padding method to make QFT block-encodings match open-boundary Toeplitz truncations of fractional Laplacians instead of periodic circulant surrogates.
A quantum algorithm for genuine Navier-Stokes equations is developed using Schrödinger-Navier-Stokes reformulation, Hamilton-Jacobi equations, and tensor-network Carleman embedding, with classical emulation shown for moderate-Reynolds Kolmogorov flows.
Quadratic bosonic Hamiltonian simulation is BQP-complete for a broad class that includes classical oscillator networks and continuous-time quantum walks, but becomes PostBQP-hard when extended to more general quadratic interactions.
A quantum algorithm for rovibrational Hamiltonian simulation on fault-tolerant quantum computers using hybrid DVR and Walsh-Hadamard QROM, claiming exponential resource savings over prior quantum and classical methods.
Quantum trajectory algorithm achieves additive O(T + log(1/ε)) query complexity for simulating dissipative Lindbladians.
Variational compression of Trotterized circuits preserves reaction rate coefficients in nonadiabatic dynamics simulations while reducing circuit depth.
citing papers explorer
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Quantum Koopman Algorithms
Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
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Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression
A recipe for initial points in variational compression of quantum time-evolution operators that provably converges to near-optimal O(N t polylog(N t/ε)) gate complexity for local translationally invariant Hamiltonians.
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Boundary-Aware QFT Block-Encoding of Fractional Laplacians
The paper presents a zero-padding method to make QFT block-encodings match open-boundary Toeplitz truncations of fractional Laplacians instead of periodic circulant surrogates.
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Schr\"odinger-Navier-Stokes Equation for the Quantum Simulation of Navier-Stokes Flows
A quantum algorithm for genuine Navier-Stokes equations is developed using Schrödinger-Navier-Stokes reformulation, Hamilton-Jacobi equations, and tensor-network Carleman embedding, with classical emulation shown for moderate-Reynolds Kolmogorov flows.
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Complexity of Quadratic Bosonic Hamiltonian Simulation: $\mathsf{BQP}$-Completeness and $\mathsf{PostBQP}$-Hardness
Quadratic bosonic Hamiltonian simulation is BQP-complete for a broad class that includes classical oscillator networks and continuous-time quantum walks, but becomes PostBQP-hard when extended to more general quadratic interactions.
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Simulating high-accuracy nuclear motion Hamiltonians using discrete variable representation and Walsh-Hadamard QROM on fault-tolerant quantum computers
A quantum algorithm for rovibrational Hamiltonian simulation on fault-tolerant quantum computers using hybrid DVR and Walsh-Hadamard QROM, claiming exponential resource savings over prior quantum and classical methods.
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Quantum algorithms based on quantum trajectories
Quantum trajectory algorithm achieves additive O(T + log(1/ε)) query complexity for simulating dissipative Lindbladians.
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Variationally Compressing Quantum Circuits to Approximate Nonadiabatic Molecular Quantum Dynamics
Variational compression of Trotterized circuits preserves reaction rate coefficients in nonadiabatic dynamics simulations while reducing circuit depth.