arXiv subjects

Guglielmo Lami

Publications and source records attributed to Guglielmo Lami.

25 records · Page 2Linked to original sources

arXiv2024

Variational ground-state quantum adiabatic theorem

We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement variational manifolds and target Hamiltonians with classical ground states. Despite the presence of highly entangled intermediate states along the exact quantum annealing path, the variational evolution converges to the target ground state. We demonstrate this approach with several examples that align with our theoretical analysis.

quant-ph↗

arXiv2024

Retrieving non-stabilizerness with Neural Networks

Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic) states. Despite their significance, quantifying and characterizing these states pose formidable challenges. Here, we introduce a novel approach leveraging Convolutional Neural Networks (CNNs) to classify quantum states based on their magic content. Without relying on a complete knowledge of the state, we utilize partial information acquired from measurement snapshots to train the CNN in distinguishing between stabilizer and nonstabilizer states. Importantly, our methodology circumvents the limitations of full state tomography, offering a practical solution for real-world quantum experiments. In addition, we unveil a theoretical connection between Stabilizer Rényi Entropies (SREs) and the expectation value of Pauli matrices for pure quantum states. Our findings pave the way for experimental applications, providing a robust and accessible tool for deciphering the intricate landscape of quantum resources.

quant-ph↗

arXiv2024

Learning the stabilizer group of a Matrix Product State

We present a novel classical algorithm designed to learn the stabilizer group -- namely the group of Pauli strings for which a state is a $\pm 1$ eigenvector -- of a given Matrix Product State (MPS). The algorithm is based on a clever and theoretically grounded biased sampling in the Pauli (or Bell) basis. Its output is a set of independent stabilizer generators whose total number is directly associated with the stabilizer nullity, notably a well-established nonstabilizer monotone. We benchmark our method on $T$-doped states randomly scrambled via Clifford unitary dynamics, demonstrating very accurate estimates up to highly-entangled MPS with bond dimension $χ\sim 10^3$. Our method, thanks to a very favourable scaling $\mathcal{O}(χ^3)$, represents the first effective approach to obtain a genuine magic monotone for MPS, enabling systematic investigations of quantum many-body physics out-of-equilibrium.

quant-ph↗

arXiv2023

Continuously Monitored Quantum Systems beyond Lindblad Dynamics

The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.

quant-ph↗

arXiv2023

Quantum Magic via Perfect Pauli Sampling of Matrix Product States

We introduce a novel breakthrough approach to evaluate the nonstabilizerness of an $N$-qubits Matrix Product State (MPS) with bond dimension $χ$. In particular, we consider the recently introduced Stabilizer Rényi Entropies (SREs). We show that the exponentially hard evaluation of the SREs can be achieved by means of a simple perfect sampling of the many-body wave function over the Pauli string configurations. The sampling is achieved with a novel MPS technique, which enables to compute each sample in an efficient way with a computational cost $O(Nχ^3)$. We benchmark our method over randomly generated magic states, as well as in the ground-state of the quantum Ising chain. Exploiting the extremely favourable scaling, we easily have access to the non-equilibrium dynamics of the SREs after a quantum quench.

quant-ph↗

arXiv2023

Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

quant-ph↗

arXiv2022

Matrix Product States with Backflow correlations

By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new structure provides enough resources to ensure that states in dimension larger or equal than one obey an area law for entanglement. It can be efficiently manipulated to address the ground-state search problem by means of an optimization scheme which mixes tensor-network and variational Monte-Carlo algorithms. We benchmark the new ansatz against spin models both in one and two dimensions, demonstrating high accuracy and precision. We finally employ our approach to study the challenging $S=1/2$ two dimensional $J_1 - J_2$ model, demonstrating that it is competitive with the state of the art methods in 2D.

cond-mat.str-el↗