A quantum algorithm estimates the static structure factor via Bloch-basis density operator block encoding and amplified Hadamard test, plus adaptive binary search for the infrared fitting window, to mitigate finite-size errors with ilde{O}(N_b N_k)^3 cost and ilde{O}(N_b N_k) qubits.
On the optimal order of integration in Hermite spaces with finite smoothness
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abstract
We study the numerical approximation of integrals over $\mathbb{R}^s$ with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of functions. The decay rate of the associated sequence is specified by a single integer parameter which determines the smoothness classes and the inner product can be expressed via $L_2$ norms of the derivatives of the function. We map higher order digital nets from the unit cube to a suitable subcube of $\mathbb{R}^s$ via a linear transformation and show that such rules achieve, apart from powers of $\log N$, the optimal rate of convergence of the integration error.
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quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Fault tolerant computation of the static structure factor and finite size effects
A quantum algorithm estimates the static structure factor via Bloch-basis density operator block encoding and amplified Hadamard test, plus adaptive binary search for the infrared fitting window, to mitigate finite-size errors with ilde{O}(N_b N_k)^3 cost and ilde{O}(N_b N_k) qubits.