Related papers: Discrimination of unitary transformations in the D…
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
Deutsch-Jozsa algorithm has been implemented via a quantum adiabatic evolution by S. Das et al. [Phys. Rev. A 65, 062310 (2002)]. This adiabatic algorithm gives rise to a quadratic speed up over classical algorithms. We show that a modified…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
This work demonstrates that the Deutsch algorithm can be effectively modelled using a two-level harmonic oscillator within the second quantization formalism. By adopting this framework, evolution operators are derived. We present a…
Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary…
We study possible advantages of randomized and quantum computing over deterministic computing for scalar initial-value problems for ordinary differential equations of order k. For systems of equations of the first order this question has…
The query model has generated considerable interest in both classical and quantum computing communities. Typically, quantum advantages are demonstrated by showcasing a quantum algorithm with a better query complexity compared to its…
We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are…
We study the query complexity of quantum learning problems in which the oracles form a group $G$ of unitary matrices. In the simplest case, one wishes to identify the oracle, and we find a description of the optimal success probability of a…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work,…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both…
We present an idealized quantum continuous variable analog of the Deutsch-Jozsa algorithm which can be implemented on a perfect continuous variable quantum computer. Using the Fourier transformation and XOR gate appropriate for continuous…
Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum…
Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than…
In this article, we present an introduction to quantum computing (QC) tailored for computing professionals such as programmers, machine learning engineers, and data scientists. Our approach abstracts away the physics underlying QC, which…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…