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.
Optimal Polynomial Based Quantum Eigenstate Fil- tering with Application to Solving Quantum Linear Systems
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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).
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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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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Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
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.