Finding Angles for Quantum Signal Processing with Machine Precision

Abstract

We describe an algorithm for finding angle sequences in quantum signal processing, with a novel component we call halving based on a new algebraic uniqueness theorem, and another we call capitalization. We present both theoretical and experimental results that demonstrate the performance of the new algorithm. In particular, these two algorithmic ideas allow us to find sequences of more than 3000 angles within 5 minutes for important applications such as Hamiltonian simulation, all in standard double precision arithmetic. This is native to almost all hardware.

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• Quantum Algorithms for Estimating Physical Quantities using Block-Encodings
• Hybridized Methods for Quantum Simulation in the Interaction Picture
• Realization of quantum signal processing on a noisy quantum computer
• Efficient quantum amplitude encoding of polynomial functions
• Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions
• Stable factorization for phase factors of quantum signal processing
• On efficient quantum block encoding of pseudo-differential operators
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Infinite quantum signal processing
• Modular quantum signal processing in many variables
• Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation
• On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Improving quantum linear system solvers via a gradient descent perspective