arXiv subjects

Davide Cugini

Publications and source records attributed to Davide Cugini.

8 recordsLinked to original sources

arXiv2026

Pathwise Random Hamiltonian Simulation

Randomized product formulas such as qDrift offer a resource-efficient alternative to deterministic Trotter--Suzuki decompositions for Hamiltonian simulation, removing their polynomial dependence on the number of Hamiltonian terms. qDrift, however, is intrinsically limited to first order in the evolution time, so its query complexity remains linear in the inverse of the target accuracy, $1/\epsilon$. We introduce Pathwise Random Hamiltonian Simulation (PRHS), which extends qDrift to arbitrary order by subdividing each time step into $M$ correlated slices, each evolving under a term sampled from a quasi-probability distribution that we construct in closed form and prove unique, with a bias decaying factorially in $M$. Optimizing jointly over the number of slices $M$ and the number of independent blocks $N$ interpolates between the standard qDrift protocol at long times and a high-precision regime where the query cost grows slower than any power of $1/\epsilon$, without requiring ancillary qubits. Numerical simulations of five molecular Hamiltonians confirm this advantage, with PRHS achieving accuracies two to four orders of magnitude beyond qDrift at equal query cost.

quant-ph↗

arXiv2026

State convertibility and fluctuation theorems from a dynamical reference: majorization meets martingales

State convertibility represents a fundamental concept used to determine whether a transformation is possible given a specific set of resources. Within the field of Thermodynamics, where physical process are required to preserve a reference state typically in microcanonical or canonical form, this translates into the notions of majorization and thermo-majorization ---criteria that require constructing and comparing state-dependent Lorenz curves. In this work, we firstly unify and extend these notions to an arbitrary and possibly time-dependent reference distribution $g(t)$, introducing the concept of $g(t)$-majorization; we then introduce a dual picture whereby state convertibility is turned into a one-dimensional convex-order problem, which allows us to demonstrate that a transition is admissible if and only if the associated real-valued distributions of relative populations $ k_j(t)/g_j(t)$ are connected by a martingale. Building on it, we then derive an exact fluctuation theorem for a reference-relative entropy production whose average violation certifies, through a $\chi^{2}$-divergence bound, the mismatch between an assumed and the true reference evolution---a model-independent diagnostic that requires no independent characterization of the latter and turns an observed breakdown of the fluctuation relation into a certified lower bound on the reference error.

cond-mat.stat-mech↗

arXiv2026

Resource-Optimal Importance Sampling for Randomized Quantum Algorithms

Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical implementations, the dominant cost of such protocols typically arises from circuit execution and measurement, and depends on hardware-specific resources such as gate counts, circuit depth, runtime, or dissipated energy. We introduce a general framework for applying classical importance sampling to randomized quantum protocols. Given a cost function for running quantum circuits, the proposed approach minimizes a net-cost figure of merit that jointly captures the computational expense per circuit and the estimator variance. We further extend the framework to scenarios where the quantum computation is subject to errors arising either from algorithmic approximations or from physical noise, proving that importance sampling preserves estimator bias despite altering the sampling distribution, and to settings with error-detection schemes, where we characterize the resulting changes in the optimal sampling strategy and achievable net-cost reduction. Representative applications include the Qdrift protocol, dephasing channels, mixed-states simulation, composite observables estimation, classical shadows, and probabilistic error cancellation. Overall, our results establish a principled approach for reducing the computational resources required by randomized quantum protocols through classical sampling optimization.

quant-ph↗

arXiv2025

Spectral Gap Estimation via Adiabatic Preparation

Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the Adiabatic Preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H2 and He2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.

quant-ph↗

arXiv2025

Symmetry-guided quantum state preparation: Branched-Subspaces Adiabatic Preparation (B-SAP)

Quantum state preparation lies at the heart of quantum computation and quantum simulations, enabling the investigation of complex manybody systems across physics, chemistry, and data science. While existing methods such as Variational Quantum Algorithms (VQAs) and Adiabatic Preparation (AP) offer viable pathways, both face substantial limitations. Here we introduce a hybrid algorithm that integrates the conceptual strengths of both VQAs and AP, enhanced via the use of group-theoretic structures and classical post-processing to approximate ground and excited states of many-body Hamiltonian models. We validate our approach by applying it to the one-dimensional XYZ Heisenberg model with periodic boundary conditions, evaluating its performance across a broad range of parameters and system sizes. Our results show accurate preparation of low-energy eigenstates, achieved with circuit depths with polynomial scaling versus system size.

quant-ph↗

arXiv2024

Universal emergence of local Zipf-Mandelbrot law

A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as Zipf-Mandelbrot law (ZM), and plenty of problem-specific explanations for its emergence have been provided in different fields. Yet, an explanation for ZM ubiquity is currently lacking. In this paper we first provide an analytical expression for the cumulants of any ranked sample of i.i.d. random variables once sorted in decreasing order. Then we make use of this result to rigorously demonstrate that, whenever a small fraction of such ranked dataset is considered, it becomes statistically indistinguishable from a ZM law. We finally validate our results against several relevant examples.

physics.soc-ph↗

arXiv2024

Exponential optimization of adiabatic quantum-state preparation

The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for state preparation, whose error decreases exponentially as a function of the preparation time, we derive an explicit analytic expression for the dependence of the characteristic time on the Hamiltonian used in the adiabatic evolution. Exploiting this knowledge, we then design a preconditioning term that modifies the adiabatic preparation, thus reducing its characteristic time and hence giving an exponential advantage in state preparation. We prove the efficiency of our method with extensive numerical experiments on prototypical spin-models, which gives a promising strategy to perform quantum simulations of manybody models via Trotter evolution on near-term quantum processors.

quant-ph↗

arXiv2024

Spectral Gap Superposition States

This work introduces a novel NISQ-friendly procedure for estimating spectral gaps in quantum systems. By leveraging Adiabatic Thermalization, we are able to create the Spectral Gap Superposition state, a newly defined quantum state exhibiting observable fluctuations in time that allow for the accurate estimation of any energy gap. Our method is tested by estimating the energy gap between the ground and the first excited state for the 1D and 2D Ising model, the Hydrogen molecule H2 and Helium molecule He2. Despite limiting our circuit design to have at most 40 Trotter steps, our numerical experiments of both noiseless and noisy devices for the presented systems give relative errors in the order of $10^{-2}$ and $10^{-1}$. Further experiments on the IonQ Aria device lead to spectral gap estimations with a relative error of $10^{-2}$ for a 4-site Ising chain, demonstrating the validity of the procedure for NISQ devices and charting a path towards a new way of calculating energy gaps.

quant-ph↗