Related papers: Quantum Verification of Matrix Products
This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable…
Existing numerical optimizers deployed in quantum compilers use expensive $\mathcal{O}(4^n)$ matrix-matrix operations. Inspired by recent advances in quantum machine learning (QML), QFactor-Sample replaces matrix-matrix operations with…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
In this paper we provide the quantum version of the Convex Non-negative Matrix Factorization algorithm (Convex-NMF) by using the D-wave quantum annealer. More precisely, we use D-wave 2000Q to find the low rank approximation of a fixed…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
Quantum gates and measurements on quantum hardware are inevitably subject to hardware imperfections that lead to quantum errors. Mitigating such unavoidable errors is crucial to explore the power of quantum hardware better. In this paper,…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values…
Accurate and robust quantum process tomography (QPT) is crucial for verifying quantum gates and diagnosing implementation faults in experiments aimed at building universal quantum computers. However, the reliability of QPT protocols is…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
Post-processing is a significant step in quantum key distribution(QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error…
Quantum computing has proven to be capable of accelerating many algorithms by performing tasks that classical computers cannot. Currently, Noisy Intermediate Scale Quantum (NISQ) machines struggle from scalability and noise issues to render…
Given an algorithm that outputs the correct answer with bounded error, say $1/3$, it is sometimes desirable to reduce this error to some arbitrarily small $\varepsilon$ -- e.g., if one wants to call the algorithm many times as a subroutine.…
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…