Disorder-free Localization Enables Benchmarking Near-term Simulators Via Finite Rényi Entropy Signals in Stark Fields

The challenge of controlling complex quantum systems motivates research into many-body localization, a phenomenon where interactions prevent energy spreading and maintain quantum information. Han-Ze Li, Yi-Rui Zhang, Yu-Jun Zhao, and Xuyang Huang from Shanghai University, along with Jian-Xin Zhong, now demonstrate a crucial aspect of this control, revealing how systems exhibiting many-body localization retain a degree of inherent complexity. Their work focuses on a specific model subjected to a strong electric field, and the results show that this system, despite being localized, does not fully conform to simple, easily simulated quantum rules, a property termed ‘nonstabilizerness’. This discovery establishes nonstabilizerness as a measurable indicator of how effectively a system breaks from predictable behaviour, offering a practical tool for assessing and improving the design of quantum simulators and advancing our understanding of complex quantum dynamics.

The team explores how this property influences the localization and dynamics of interacting quantum systems subjected to a strong, quasiperiodic potential. They analyse the system’s spectral properties and spatial distribution of energy states to characterise the degree of localization. Numerical simulations reveal how varying system parameters, such as the strength of the potential and the interactions between particles, affect the system’s behaviour. By quantifying nonstabilizerness through theoretical analysis and computation, the researchers establish a direct link between this property and the transition to a many-body localized phase, advancing our understanding of complex quantum states and strongly interacting disordered systems.

A significant challenge in quantum computation lies in harnessing nationally costly non-Clifford resources. Researchers demonstrate that in a transverse-field Ising chain exhibiting disorder-free Stark many-body localization, the stabilizer Rényi entropy grows slowly to a finite value, even deep within the strong Stark-field regime, and is sensitive to the initial state. As the Stark field increases, long-time magic and entanglement consistently signal a shift from free-flowing dynamics to constrained, localized behaviour. These results establish nonstabilizerness as a practical measure of ergodicity breaking and constrained localization, with direct relevance to benchmarking and designing near-term quantum simulators.

Entanglement Growth and Non-Stabilizerness in Tilted Ising Models

This research investigates the interplay between entanglement growth and the emergence of non-stabilizerness in a transverse-field Ising model subjected to a linear potential. The goal is to understand the limits of quantum computation and the behaviour of complex quantum systems. The researchers utilise a standard model in condensed matter physics, the transverse-field Ising model, and introduce a linear potential to drive interesting dynamics. The focus on non-stabilizerness is crucial, as most interesting quantum systems are not easily described by stabilizer states, and understanding how systems deviate from this restricted class is essential for advancing quantum technologies.

Trapped ions are used as the experimental platform due to their high coherence times and precise control over interactions. The model is mapped onto the trapped ion system by utilising the Mølmer-Sørensen mechanism to create interactions and implementing single-qubit gates with detuned laser pulses. A second-order Strang splitting algorithm approximates the time evolution of the system. The researchers employ a diverse set of initial states, including fully polarized, superposition, and random product states, to probe typical behaviour. Key observables include the half-chain Rényi-2 entanglement entropy and the Second Renyi Entropy, which quantifies non-stabilizerness.

The proposal employs a randomized measurement scheme, applying random Clifford unitaries before measurement to reduce the measurement overhead. Kernel estimators and bootstrap resampling are used to estimate quantities and statistical uncertainties. The researchers carefully consider the trade-off between the number of Clifford unitaries and the number of measurements to optimise resource allocation. This comprehensive design, coupled with the use of random initial states and a randomized measurement scheme, represents a significant strength, and the inclusion of a mixed-state correction in the non-stabilizerness estimator ensures accuracy.

This experiment will provide valuable insights into the dynamics of complex quantum systems and the limits of quantum computation. The results could shed light on the behaviour of strongly correlated quantum systems and validate theoretical models of quantum dynamics. In summary, this is a highly ambitious and well-designed research proposal that addresses a fundamental question in quantum physics and utilises state-of-the-art experimental techniques.

Non-stabilizerness and Stark Many-body Localization Correlation

This research establishes a clear link between the emergence of non-stabilizerness, a measure of quantum complexity, and the phenomenon of disorder-free Stark many-body localization. By investigating a tilted transverse-field Ising chain, scientists demonstrate that even when particle transport is suppressed and dynamics are constrained, the system generates genuine non-Clifford computational resources, indicated by a slow growth of the stabilizer Rényi entropy. This challenges the notion that constrained localization necessarily implies trivial quantum behaviour. The team identified a crossover from behaviour resembling thermal equilibrium to the localized regime of Stark many-body localization, and uncovered a strong correlation between the growth of non-stabilizerness and entanglement within this localized state, dependent on the initial conditions.

Supporting this experimental work, the researchers developed a theoretical framework, based on a Schrieffer-Wolff approach, which explains the slow growth of non-stabilizerness through factorially suppressed long-range couplings. They also proposed a practical trapped-ion digital simulation protocol to measure both entanglement and non-stabilizerness using the same data. The authors acknowledge that their analysis focuses on a specific model and that exploring the interplay between non-stabilizerness and the quantum Mpemba effect in more complex systems represents a promising avenue for future research. They anticipate that these investigations can be directly implemented on existing digital quantum processors, furthering our understanding of quantum many-body phenomena.