Related papers: Quantum Logspace Algorithm for Powering Matrices w…
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 show that quantum algorithms of time $T$ and space $S\ge \log T$ with unitary operations and intermediate measurements can be simulated by quantum algorithms of time $T \cdot \mathrm{poly} (S)$ and space $ {O}(S\cdot \log T)$ with…
In the classical RAM, we have the following useful property. If we have an algorithm that uses $M$ memory cells throughout its execution, and in addition is sparse, in the sense that, at any point in time, only $m$ out of $M$ cells will be…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09, arXiv:0811.3171] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems, which are often encountered in the industry (portfolio optimization, fleet optimization, charging stations, etc.). It was developed within the framework…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Given the success of deep learning in classical machine learning, quantum algorithms for traditional neural network architectures may provide one of the most promising settings for quantum machine learning. Considering a fully-connected…
Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
Polynomial--time constant--space quantum Turing machines (QTMs) and logarithmic--space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakary\i lmaz 2014, arXiv:1411.7647). In this…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
This paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness $c$ and soundness $s$, either with or without a witness (corresponding…
Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation, as qubits are an especially precious and limited resource.…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…