Enabling large-scale digital quantum simulations with superconducting qubits

TL;DR

The thesis addresses the challenge of performing large-scale digital quantum simulations on noisy superconducting hardware by integrating hardware innovations (qudit transmons and qudit gate synthesis), algorithmic advances (informationally complete POVMs, parallelized subspace expansion, and quantum dynamics techniques), and rigorous error mitigation (noise learning, PEC, ZNE, TEM, and gauge-consistent methods). It develops a comprehensive stack-wide approach that leverages higher-dimensional transmon states for more efficient circuit synthesis, enables efficient extraction of observables via IC measurements and dual-frame processing, and demonstrates error-mitigated quantum simulations on IBM hardware up to tens of qubits and, in TEM cases, over 90 qubits. The work shows that self-consistent noise characterization removes bias due to gauge freedom and can massively reduce sampling overhead, enabling credible ground-state and dynamical simulations (including dual-unitary Floquet models) that approach classically intractable regimes. Collectively, the contributions push digital quantum simulation forward toward practical quantum advantage on near-term devices and provide a blueprint for future fault-tolerant integration. The findings underscore the value of quantum-centric supercomputing, where quantum and classical resources are tightly coupled to extend the reach of quantum computations in the pre-fault-tolerant era and guide design choices for next-generation hardware and software stacks.

Abstract

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.

Figures (46)

• Figure 1: Schematic of a four-qubit quantum circuit. Qubits are initialized in the all-zero state $\ket{0\dots 0}$. A series of single- and two-qubit gates apply a unitary transformation to the state. Finally, a measurement yields a classical bitstring sampled according to the Born rule from the final state.
• Figure 2: Classical simulations of quantum circuits scale exponentially with the circuit size (dashed line). For error-corrected quantum computers (blue) this is polynomial, but comes at the cost of a large resource overhead, represented as a y-axis offset. Error-mitigated quantum computers (red/green) also scale exponentially in general. It is an open question whether the basis of this exponential can be reduced to a point where this beats classical methods to provide a quantum advantage (shaded region).
• Figure 3: The Bloch sphere represents all single-qubit quantum states through a vector $\vec{r}$ as introduced in Eq. \ref{['eq:bloch_sphere_rep']}. The $+1$ ($-1$) Pauli eigenstates of the $Z$, $X$, and $Y$ operatos are labeled $\ket{0}$ ($\ket{1}$), $\ket{+}$ ($\ket{-}$), and $\ket{i}$ ($\ket{-i}$), respectively. The blue arrow shows a pure state as an example.
• Figure 4: Schematic of a 5-qubit matrix product state (MPS) that approximates the state vector through a chain of tensors connected through bonds with dimension $\chi$.
• Figure 5: Schematic of low-lying energy spectra of a harmonic LC circuit (left) and the transmon circuit (right). The non-linear circuit element of the Josephson junction creates an anharmonic spectrum that allows for selected driving of transitions.