Related papers: Amplitude amplification and estimation require inv…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Quantum simulation with adiabatic annealing can provide insight into difficult problems that are impossible to study with classical computers. However, it deteriorates when the systems scale up due to the shrinkage of the excitation gap and…
We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics.…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…
A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use…
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Boosting is a general method to convert a weak learner (which generates hypotheses that are just slightly better than random) into a strong learner (which generates hypotheses that are much better than random). Recently, Arunachalam and…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
Quantum amplitude amplification algorithm is an important and basic technique in quantum computing. In this paper, our goal is to study distributed quantum amplitude amplification algorithms, and the main contributions are: (1) A…
A recent work of Schmidhuber et al (QIP, SODA, & Phys. Rev. X 2025) exhibited a quantum algorithm for the noisy planted $k$XOR problem running quartically faster than all known classical algorithms. In this work, we design a new classical…
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…
Quantum annealing is a powerful alternative model for quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive proof of a quantum speedup…
Grover's algorithm is a well-known contribution to quantum computing. It searches one value within an unordered sequence faster than any classical algorithm. A fundamental part of this algorithm is the so-called oracle, a quantum circuit…
We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization…
The glued-trees problem is the only example known to date for which quantum annealing provides an exponential speedup, albeit by partly using excited state evolution, in an oracular setting. How robust is this speedup to noise on the…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…