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Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim and Lloyd for solving systems of linear equations. The utility of {classical} linear…
Variational algorithms have received significant attention in recent years due to their potential to solve practical problems using noisy intermediate-scale quantum (NISQ) devices. A fundamental step of these algorithms is the evaluation of…
Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of…
We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the…
The concept of quantum nondemolition (QND) measurement is extended to coherent oscillations in an individual two-state system. Such a measurement enables direct observation of intrinsic spectrum of these oscillations avoiding the…
Conventional strategies of quantum metrology are built upon POVMs, thereby possessing several general features, including the demolition of the state to be measured, the need of performing a number of measurements, and the degradation of…
Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial…
We discuss the characterization and properties of quantum non-demolition (QND) measurements on qubit systems. We introduce figures of merit which can be applied to systems of any Hilbert space dimension thus providing universal criteria for…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…
In recent years, variational quantum algorithms have garnered significant attention as a candidate approach for near-term quantum advantage using noisy intermediate-scale quantum (NISQ) devices. In this article we introduce kernel descent,…
Accurate quantum tomography is a vital tool in both fundamental and applied quantum science. It is a task that involves processing a noisy measurement record in order to construct a reliable estimate of an unknown quantum state, and is…
Many applications of quantum simulation require to prepare and then characterize quantum states by performing an efficient partial tomography to estimate observables corresponding to $k$-body reduced density matrices ($k$-RDMs). For…
This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagonalization (SQD) as near-term alternatives…
The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such process involves the coupling of a single system of interest, called signal, with a single probe system, so that the…