Abstract
Hybrid classical-quantum protocols for quantum simulations on NISQ platforms. The project focuses on hybrid classical-quantum protocols devised for quantum simulations, and it is structured to navigate through two different but intertwined dimensions: i) numerical algorithms and related methodological issues, ii) physical description and control of many body Hamiltonians, while keeping in mind and exploiting available quantum devices. In particular, we plan to utilize the quantum annealer technology of D-Wave and the Rydberg atom platform developed by Pasqal.
Results achieved
: • Development of hybrid protocols for some relevant Physical Models, such as: 1a. Random spin models; 1b. Long range spin Hamiltonians; 1c. Finite group lattice gauge theories. • Applications of hybrid protocols to Numerical Methods, such as: 2a. Bayesian inference or machine learning approaches for VQA; 2b. Interpolation techniques for smoothness of parameters in optimization schemes; 2c. Quantum annealing or Rydberg atom platform for projective QMC techniques. • Hybrid protocols for Quantum control and dynamics, such as: 3a. Adiabaticity in QAOA/VQA protocols in quantum Ising Hamiltonians as in quantum annealers and Rydberg atom platforms; 3b. Hybrid protocols for the evaluation of time-dependent observables and correlations in simple few-body systems; 3c. TDDFT framework for quantum spin models beyond regimes accessible via unbiased algorithms. ACHIEVED RESULTS: Throughout the project, the three participating units maintained active and continuous scientific exchanges, ensuring strong coordination across the different research lines. The collaboration was structured around a set of common scientific objectives: the development and assessment of hybrid classical–quantum algorithms for near-term quantum devices, the study of optimization problems and many-body quantum dynamics, and the integration of classical numerical methods, machine-learning techniques, and quantum computing protocols. A central feature of the project was the complementary expertise of the three units. UniBO, SISSA, and UniCAM jointly contributed to the broader goal of understanding the potential and limitations of NISQ-era quantum technologies for optimization, simulation, and the study of complex quantum systems. Common activities included the analysis of variational quantum algorithms, the use of quantum-inspired and classical numerical benchmarks, the investigation of noisy quantum dynamics, and the exploration of efficient strategies for probing ground states, spectral gaps, and non-equilibrium behavior. Taken together, exchanges among the units strengthened the integration of classical computational tools, machine-learning-based approaches, and digital or analog quantum algorithms for near-term platforms. Overall, the project promoted a coherent research effort across the three units. While each unit pursued specific directions, their activities converged on common themes: the design of improved quantum optimization protocols, the characterization of many-body quantum systems, the evaluation of algorithmic performance under realistic noise, and the development of theoretical and numerical tools to guide future experiments. The main contributions of the individual units are briefly summarized below. UNIBO The University of Bologna unit focused primarily on hybrid classical–quantum computational methods for NISQ platforms. Its activity included the study of QAOA for complex optimization problems on noisy quantum hardware, with both numerical simulations and experimental implementations. In particular, an analog version of QAOA was implemented on Pasqal’s neutral-atom quantum processing unit to address NP-hard graph optimization problems. The unit also analyzed the performance of quantum natural gradient optimization methods on different noisy hardware platforms, including Rydberg-atom devices and superconducting quantum circuits. UNIBO further investigated the computational cost of probing many-body quantum systems and their real-time dynamics. A relevant test case was the one-dimensional ℤ₂ Schwinger model following a non-equilibrium quench, studied through noisy simulations and experiments on IBM quantum hardware. In parallel, the unit explored the use of classical shadows, showing that shallow classical shadows can be effectively applied to relatively large systems and general circuit connectivities. Finally, UNIBO extended its work to classical–quantum probabilistic cellular automata and quantum cellular automata as tools for graph-based optimization, with particular attention to the Maximum Independent Set problem. Tensor-network simulations were used to estimate the scaling of convergence times, suggesting that quantum cellular automata dynamics may offer an efficient alternative to adiabatic and variational quantum optimization methods. SISSA The SISSA unit contributed to the project through theoretical and algorithmic studies of digital quantum optimization and quantum dynamics. A major contribution was the analysis of the digital controllability of transverse-field Ising chains, aimed at assessing QAOA as a digital optimization protocol. The results showed that QAOA can reach the exact ground state with a number of layers scaling quadratically with system size, independently of the annealing gap. This highlights an important distinction between digital protocols and analog quantum annealing. SISSA also investigated frustrated Ising models and MaxCut problems on weighted 3-regular graphs, including hard instances with small spectral gaps. Using approaches inspired by optimal control, such as CRAB-based digitized quantum annealing, Fourier and Chebyshev schedule parametrizations, and structured QAOA parameterizations, the unit developed smooth digital schedules capable of achieving high-quality solutions. These results support the broader project goal of identifying efficient alternatives to standard linear-schedule quantum annealing. In addition, SISSA extended the project scope to dissipative quantum dynamics. In particular, it studied measurement-induced dissipation in the Su–Schrieffer–Heeger model, showing that suitably designed dissipation patterns can preserve characteristic signatures of topological edge modes, despite modifications of the system’s entanglement structure. UNICAM The UniCAM unit contributed mainly through machine-learning-based and Quantum Monte Carlo approaches to strongly correlated and disordered quantum systems. It developed and implemented hybrid classical–quantum algorithms based on machine-learning techniques for estimating ground-state energies in strongly correlated systems, contributing to the project’s broader effort to combine classical learning methods with quantum computing platforms. UniCAM also predicted a spin-glass quantum phase transition in systems of Rydberg atoms arranged in amorphous arrays, providing theoretical guidance for future experiments on disordered quantum simulators. In addition, the unit implemented a projective Quantum Monte Carlo algorithm for estimating energy gaps in quantum many-body systems. This method was used to predict the scaling of the spectral gap in the Sherrington–Kirkpatrick model, offering insights into the possible efficiency of adiabatic quantum computing strategies for complex optimization problems. Taken together, the activities of the three units produced a coordinated set of results on quantum optimization, quantum simulation, many-body dynamics, and machine-learning-assisted computational methods. The project strengthened the interaction between complementary theoretical and numerical approaches and provided useful guidance for future developments in NISQ algorithms, quantum simulation experiments, and hybrid classical–quantum strategies for complex systems.Dettagli del progetto
Responsabile scientifico: Elisa Ercolessi
Strutture Unibo coinvolte:
Dipartimento di Fisica e Astronomia "Augusto Righi"
Coordinatore:
ALMA MATER STUDIORUM - Università di Bologna(Italy)
Contributo totale di progetto: Euro (EUR) 209.210,00
Contributo totale Unibo: Euro (EUR) 75.616,00
Durata del progetto in mesi: 24
Data di inizio
28/09/2023
Data di fine:
28/02/2026
