Related papers: LWE with Quantum Amplitudes: Algorithm, Hardness, …
The estimation of the amplitude of a sine wave from the sequence of its quantized samples is a typical problem in instrumentation and measurement. A standard approach for its solution makes use of a least squares estimator (LSE) that,…
We demonstrate that the problem of amplitude estimation, a core subroutine used in many quantum algorithms, can be mapped directly to a problem in signal processing called direction of arrival (DOA) estimation. The DOA task is to determine…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Amplitude Estimation (AE) is a critical subroutine in many quantum algorithms, allowing for a quadratic speedup in various applications like those involving estimating statistics of various functions as in financial Monte Carlo simulations.…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
We provide more sample-efficient versions of some basic routines in quantum data analysis, along with simpler proofs. Particularly, we give a quantum "Threshold Search" algorithm that requires only $O((\log^2 m)/\epsilon^2)$ samples of a…
We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…
We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes…
Variational Quantum Algorithms (VQAs) are a leading approach for near-term quantum computing but face major optimization challenges from noise, barren plateaus, and complex energy landscapes. We benchmarked more than fifty metaheuristic…
In this work, we provide the first QFT-free algorithm for Quantum Amplitude Estimation (QAE) that is asymptotically optimal while maintaining the leading numerical performance. QAE algorithms appear as a subroutine in many applications for…
Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
We present a quantum algorithm for estimating the amplitude content of user-specified sequency bands in quantum-encoded signals. The method employs a sequency-ordered Quantum Walsh-Hadamard Transform (QWHT), a comparator-based oracle that…
We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…
Discrete Gaussian Sampling on lattices is a fundamental problem in lattice-based cryptography. It appears both in basic cryptographic primitives such as digital signatures and as an important cryptanalysis building block for solving hard…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…