相关论文: Fast quantum algorithms for numerical integrals an…

Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be…

Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…

Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…

Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…

We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…

A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are…

Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…

Spectral methods are a leading approach for tensor PCA with a ``spiked" Gaussian tensor. The methods use the spectrum of a linear operator in a vector space with exponentially high dimension and in Ref. 1 it was shown that quantum…

Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…

In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…

Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…

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…

Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum…

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…

By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover…

Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…