Related papers: Fault-ignorant Quantum Search
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in terms of the superoperator perspective,…
Simulating open quantum systems on quantum computers presents a fundamental challenge: open quantum dynamics are intrinsically nonunitary, whereas quantum computers operate through unitary evolution. Conventional approaches overcome this…
The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform.…
Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying non-trivial symmetries emerges under…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
In this article, based on some simple and reasonable assumptions, we derive a Gaussian noise model for quantum amplitude estimation. We provide results from quantum amplitude estimation run on various IBM superconducting quantum computers…
The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
Quantum algorithm can find target item in a database faster than any classical. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster: this is partial search. One can think of…
We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
We consider the problem of finding the minimum element in a list of length $N$ using a noisy comparator. The noise is modelled as follows: given two elements to compare, if the values of the elements differ by at least $\alpha$ by some…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…