Gabriel Matos

• Doctor of Philosophy
• Research Scientist at Quantinuum

Building upon recent progress in Lindblad engineering for quantum Gibbs state preparation algorithms, we propose a simplified protocol that is shown to be efficient under the eigenstate thermalization hypothesis (ETH). The ETH reduces circuit overhead of the Lindblad simulation algorithm and ensures a fast convergence toward the target Gibbs state....

We present the first implementation of text-level quantum natural language processing, a field where quantum computing and AI have found a fruitful intersection. We focus on the QDisCoCirc model, which is underpinned by a compositional approach to rendering AI interpretable: the behaviour of the whole can be understood in terms of the behaviour of...

Progress in the realisation of reliable large-scale quantum computers has motivated research into the design of quantum machine learning models. We present Quixer: a novel quantum transformer model which utilises the Linear Combination of Unitaries and Quantum Singular Value Transform primitives as building blocks. Quixer operates by preparing a su...

We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional lattice – with and without decoupled angles – is able to prepare all fermionic Gaussian states respecting the symmet...

We study the dependence of the Laughlin states on the geometry of the sphere and the plane, for one-parameter Mabuchi geodesic families of curved metrics with Hamiltonian S1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...

We study variational quantum algorithms from the perspective of free fermions. Using Lie theoretical techniques, we characterize the space of states that the Quantum Approximate Optimization Algorithm (QAOA) is able to prepare at arbitrary circuit depth on a one-dimensional lattice with and without decoupled angles. We show that this is the set of...

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-12 chain. Here, we quantitatively analyze this behavior by establishing the relation between system size and...

We study the change of the Laughlin states under large deformations of the geometry of the sphere and the plane, associated with Mabuchi geodesics on the space of metrics with Hamiltonian $S^1$-symmetry. For geodesics associated with the square of the symmetry generator, as the geodesic time goes to infinity, the geometry of the sphere becomes that...

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-$\frac{1}{2}$ chain. Here, we quantitatively analyse this behaviour by establishing the relation between syst...

Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as the quantum approximate optimization algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quant...

Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as Quantum Approximate Optimization Algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quantifyi...

We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that every norm closed Lie module of a continuous nest algebra is decomposable. The continuity of the nest cannot be l...

We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that every norm closed Lie module of a continuous nest algebra is decomposable. The continuity of the nest cannot be l...