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Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of - notoriously quite fragile - GHZ…

This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric introduction to the NMR of an ensemble of indistinguishable spins, and then show how this…

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…

This paper describes recent progress using nuclear magnetic resonance (NMR) as a platform for implementing quantum information processing (QIP) tasks. The basic ideas of NMR QIP are detailed, examining the successes and limitations of…

We describe a nuclear magnetic resonance (NMR) experiment which implements an efficient one-to-two qubit phase-covariant cloning machine(QPCCM). In the experiment we have achieved remarkably high fidelities of cloning, 0.848 and 0.844…

Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin…

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic…

Multiple penalized least squares (MPLS) models are a flexible approach to find adaptive least squares solutions required to be simultaneously sparse and smooth. This is particularly important when addressing real-life inverse problems where…

Magnetic resonance spectroscopy is universally regarded as one of the most important tools in chemical and bio-medical research. However, sensitivity limitations typically restrict imaging resolution to length scales greater than 10 \mu m.…

The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is…

The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum…

Nuclear magnetic resonance (NMR) is a powerful tool for applications ranging from chemical analysis to quantum information processing. Achieving optical initialization and detection of molecular nuclear spins promises new opportunities -…

Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…

We employ so-called quantum kernel estimation to exploit complex quantum dynamics of solid-state nuclear magnetic resonance for machine learning. We propose to map an input to a feature space by input-dependent Hamiltonian evolution, and…

The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. A particular application is to obtain ground…

Quantum phase estimation (QPE) is one of the core algorithms for quantum computing. It has been extensively studied and applied in a variety of quantum applications such as the Shor's factoring algorithm, quantum sampling algorithms and the…

We discuss methods of quantum state tomography for solid-state systems with a large nuclear spin $I=3/2$ in nanometer-scale semiconductors devices based on a quantum well. Due to quadrupolar interactions, the Zeeman levels of these…

Nuclear magnetic resonance (NMR) spectroscopy exploits the magnetic properties of atomic nuclei to discover the structure, reaction state and chemical environment of molecules. We propose a probabilistic generative model and inference…

Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe…

While the recent demonstration of accurate computations of classically intractable simulations on noisy quantum processors brings quantum advantage closer, there is still the challenge of demonstrating it for practical problems. Here we…