Related papers: An elementary derivation of the Deutsch-Jozsa algo…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
A bare description of the seminal quantum algorithm devised by Deutsch could mean more than an introduction to quantum computing. It could contribute to opening the field to interdisciplinary research.
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
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 consider a family of unstructured problems, for which we propose a method for constructing analog, continuous-time quantum algorithms that are more efficient than their classical counterparts. In this family of problems, which we refer…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
We implemented the refined Deutsch-Jozsa algorithm on a 3-bit nuclear magnetic resonance quantum computer, which is the meaningful test of quantum parallelism because qubits are entangled. All of the balanced and constant functions were…
We present a generalized Deutsch-Jozsa (DJ) quantum algorithm that not only determines both the global type of an unknown Boolean function (constant or balanced) but also determines explicit output values of the function in a single oracle…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. \emph{Basic Quantum Algorithms} revisits the earliest quantum algorithms. The journey began in 1985 with Deutsch…
Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations…
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…
The present work points out that the Deutsch-Jozsa algorithm was the first formal description of a quantum decider. In particular, it is studied here the class of languages whose indicator functions allow the Deutsch-Jozsa algorithm to…
An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…