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.
Quantum Linear System Solver Based on Time-Optimal Adiabatic Quan- tum Computing and Quantum Approximate Op- timization Algorithm
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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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Constrained Optimal Polynomials for Quantum Linear System Solvers
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.
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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).