Related papers: Fourier Spectrum of Noisy Quantum Algorithms
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
Decoded Quantum Interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on…
Combining tensor network techniques with quantum autoregressive moving average models, we quantify the effects of time-correlated noise on quantum algorithms and predict their performance at scale. As a paradigmatic test case, we examine…
The effects of noise are one of the most important factors to consider when it comes to quantum computing in the noisy intermediate-scale quantum computing (NISQ) era that we are currently in. Therefore, it is important not only to gain…
Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in…
The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy,…
Classical verification of quantum learning allows classical clients to reliably leverage quantum computing advantages by interacting with untrusted quantum servers. Yet, current quantum devices available in practice suffers from a variety…
Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set…
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
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.…
Quantum noise is known to strongly affect quantum computation, thus potentially limiting the performance of currently available quantum processing units. Even learning models based on variational quantum algorithms, which were designed to…
The speed-up provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speed-up are not yet completely understood…
Quantum computers are inherently affected by noise. While in the long-term error correction codes will account for noise at the cost of increasing physical qubits, in the near-term the performance of any quantum algorithm should be tested…
Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…
Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…
In the race towards quantum computing, the potential benefits of quantum neural networks (QNNs) have become increasingly apparent. However, Noisy Intermediate-Scale Quantum (NISQ) processors are prone to errors, which poses a significant…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in…
Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that…