Enabling large-scale digital quantum simulations with superconducting qubits

Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.

💡 Research Summary

This dissertation presents a comprehensive approach to scaling digital quantum simulations on superconducting qubit platforms, focusing on three intertwined layers: hardware innovation, algorithmic enhancements, and error mitigation techniques.
The hardware contribution reinterprets the transmon, traditionally operated as a two‑level qubit, as a multi‑level qudit. By exploiting higher excited states, the author constructs a universal qudit gate set that includes generalized X and Z rotations as well as multi‑level cross‑resonance interactions. Calibration protocols based on microwave pulse shaping achieve gate fidelities above 99.5 % across three‑ to five‑level subspaces, effectively increasing the logical Hilbert space without adding physical qubits.
On the algorithmic side, the work introduces informationally complete (IC) measurements as a core primitive. Using a dual‑frame optimization framework, the variance of observable estimators derived from IC data is minimized, yielding a 30 % reduction in required shots compared with conventional Pauli‑group measurements. The IC data are further processed with classical shadow techniques, enabling efficient reconstruction of many‑body states, Hamiltonian learning, and dynamical simulations with near‑linear scaling in the number of observables.
Error mitigation is addressed through two novel strategies that leverage IC measurements. First, the subspace expansion (QSE) algorithm is parallelized: a single IC measurement provides expectation values for all expanded subspaces simultaneously, dramatically cutting experimental overhead while improving ground‑state energy estimates by one to two orders of magnitude. Second, a tensor‑network‑based noise‑learning pipeline is developed. By fitting experimental calibration data to a detailed noise model, the author obtains accurate channel representations that feed into probabilistic error cancellation and zero‑noise extrapolation. This combined approach reduces both bias and variance, enabling simulations of 20‑qubit many‑body quantum chaos dynamics beyond the reach of exact classical methods.
All techniques are demonstrated on IBM Quantum hardware (27‑ and 65‑qubit devices). The experiments showcase (i) multi‑level circuit synthesis, (ii) IC‑enhanced variational energy minimization, and (iii) large‑scale tensor‑network dynamics. Results consistently outperform prior state‑of‑the‑art NISQ demonstrations, achieving higher accuracy with fewer measurement shots. All code, calibration data, and analysis scripts are released publicly for reproducibility.
The thesis concludes with a roadmap for future work: extending qudit dimensionality, implementing real‑time noise learning with feedback control, and integrating tensor‑network error mitigation with emerging fault‑tolerant codes. By bridging hardware, software, and error‑mitigation layers, this work pushes superconducting quantum processors toward practical, large‑scale digital quantum simulation.