Related papers: Quantum Computer Can Not Speed Up Iterated Applica…
Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
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 computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
An unstructured search for one item out of N can be performed quantum mechanically in time of order square root of N whereas classically this requires of order N steps. This raises the question of whether square root speedup persists in…
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's…
As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…
The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…
We prove the following conjecture, raised by Aaronson and Ambainis in 2008: Let $f:\{-1,1\}^n \rightarrow [-1,1]$ be a multilinear polynomial of degree $d$. Then there exists a variable $x_i$ whose influence on $f$ is at least…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…
Despite numerous advances in the field and a seemingly ever-increasing amount of investment, we are still some years away from seeing a production quantum computer in action. However, it is possible to make some educated guesses about the…