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arXiv · 2409.07332

Quantum state preparation via piecewise QSVT

Oliver O'Brien·Christoph Sünderhauf
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Abstract

Efficient state preparation is essential for implementing efficient quantum algorithms. Whilst several techniques for low-cost state preparation exist, this work facilitates further classes of states, whose amplitudes are well approximated by piecewise polynomials. We show how such states can be efficiently prepared using a piecewise Quantum Singular Value Transformation along with a new piecewise linear diagonal block encoding. We illustrate this with the explicit examples of $x^\alpha|x\rangle$ and $\log x|x\rangle$. Further, our technique reduces the cost of window boosted Quantum Phase Estimation by efficiently preparing the B-spline window state. We demonstrate this window state requires 50 times fewer Toffolis to prepare than the state-of-the-art Kaiser window state, and we show that the B-spline window replicates the Kaiser window's exponential reduction in tail probability for QPE.

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Oliver O'Brien, Christoph Sünderhauf. 2024-09-11. Quantum state preparation via piecewise QSVT. https://doi.org/10.22331/q-2025-07-03-1786

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