Explicit quantum-circuit simulation of nonlinear 1D fluid via second-order Carleman-linearized Boltzmann equation and QSVD Taylor ODE solver, with logarithmic scaling analysis.
Optimal Polynomial Based Quantum Eigenstate Fil- tering with Application to Solving Quantum Linear Systems
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Constrained Uniform Polynomial (CUP) and Constrained Adaptive Polynomial (CAP) solvers achieve lower error than standard QSVT and Chebyshev methods in noise-limited regimes by optimizing accuracy versus block-encoding normalization under uniform or moment-based spectral models.
The paper gives a QLSS with query complexity (1+O(ε))κ ln(2√2/ε) using one kernel reflection when ||x|| is known, or O(κ log(1/ε)) overall, with explicit bound 56κ + 1.05κ ln(1/ε).
New analytic and Monte Carlo-assisted method tightens energy-based boson truncation bounds, reducing volume dependence in (1+1)D scalar and (2+1)D U(1) gauge theories.
The authors convert classical software bug detection into quantum optimization instances and test QAOA, Grover, and QSVT on small examples for potential polynomial speedup.
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A shortcut to an optimal quantum linear system solver
The paper gives a QLSS with query complexity (1+O(ε))κ ln(2√2/ε) using one kernel reflection when ||x|| is known, or O(κ log(1/ε)) overall, with explicit bound 56κ + 1.05κ ln(1/ε).
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Towards Classical Software Verification using Quantum Computers
The authors convert classical software bug detection into quantum optimization instances and test QAOA, Grover, and QSVT on small examples for potential polynomial speedup.