Quantum Algorithm for Efficient Kalman Filter Computation
The proposed quantum algorithm exponentially accelerates the computation of the Kalman filter compared to traditional classical methods, reducing the time complexity from O(n^3) to O(κpoly log(n/ϵ) log(1/ϵ')).
Quantum Algorithms for Solving Geometric 3SUM-Hard Problems and Beyond
This paper presents quantum algorithms that can solve various geometric 3SUM-hard problems, such as finding a triangle with area at most q, finding a unit disk that covers at least q points, and determining interval containment, in O(n^(1+o(1))) time, where n is the input size.
Efficient Quantum Ground-State Algorithms using Neural Schrödinger Forging
A hybrid quantum-classical algorithm is proposed that leverages generative neural networks to efficiently identify the most relevant bitstrings in the Schmidt decomposition, enabling scalable ground-state computations without the need for exponential summation.
Estimating Truncation Errors in Quantum Bosonic Systems Using Sampling Algorithms
Markov Chain Monte Carlo methods can be used to efficiently estimate the digitization errors in a wide class of bosonic quantum systems, even for large system sizes beyond the reach of exact diagonalization techniques.
Deterministic Quantum Search Algorithm for Complete Bipartite Graphs
A deterministic quantum search algorithm is presented for complete bipartite graphs, which generalizes Grover's search algorithm and enables efficient search on structured graphs.
A Comprehensive Review of Quantum Machine Learning: From Noisy Intermediate-Scale Quantum (NISQ) to Fault-Tolerant Quantum Computation
Quantum machine learning, which involves running machine learning algorithms on quantum devices, has significant potential but faces challenges in the current Noisy Intermediate-Scale Quantum (NISQ) era. This review provides a comprehensive overview of the various concepts and techniques that have emerged in the field, including Variational Quantum Algorithms (VQA), Quantum Neural Tangent Kernel (QNTK), and the issue of barren plateaus. It also explores the potential of Fault-Tolerant Quantum Computation (FTQC) algorithms and their applications in quantum machine learning.
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