Related papers: Speedup in quantum computation is associated with …
Central to the power of quantum computing is the concept of quantum parallelism: quantum systems can explore and process multiple computational paths simultaneously. In this paper, we discuss the elusive nature of quantum parallelism,…
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speed-ups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speed-up over…
We develop a framework for identifying nonclassical speedups in systems with polarization, likewise spin degrees of freedom. By confining the dynamics to the manifold of angular momentum coherent states, which act as the classical reference…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
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…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
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…
The quantum speed limit indicates the maximal evolution speed of the quantum system. In this work, we determine speed limits on the informational measures, namely the von Neumann entropy, maximal information, and coherence of quantum…
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.…
The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…
Despite their importance as subfields of mathematics and engineering, signal and image processing have not received much attention in the field of quantum computation. Cross-correlations are instrumental to all the aforementioned fields. In…
Large quantum computers promise to solve some critical problems not solvable otherwise. However, modern quantum technologies suffer various imperfections such as control errors and qubit decoherence, inhibiting their potential utility. The…