Observation of disorder-free localization and efficient disorder averaging on a quantum processor (2410.06557v1)

Abstract: One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

• The paper demonstrates that translationally invariant quantum systems can exhibit localization without explicit disorder.
• It leverages quantum parallelism with ancillas to efficiently average over disorder realizations and sample rare event dynamics.
• Experiments in 1D and 2D lattices reveal dimension-invariant behavior, providing insights for error resilience in quantum technologies.

Observation of Disorder-Free Localization and Efficient Disorder Averaging on a Quantum Processor

The paper presents a pioneering paper on disorder-free localization (DFL) in quantum many-body systems using a superconducting quantum processor. Localization is conventionally associated with the presence of disorder in a system, leading to the breakdown of ergodicity and a transition to non-equilibrium states, which remain isolated in some regions of Hilbert space. The key contribution of the research lies in observing localization phenomena in systems that are translationally invariant, thereby devoid of any explicit disorder.

Summary of the Research

The authors implement a novel approach leveraging quantum parallelism to efficiently sample over all disorder realizations, facilitating the paper of rare events which are typically computationally intensive in classical simulations. They explore the dynamics governed by a Trotterized Hamiltonian featuring local terms and translationally invariant initial conditions, observing that energy excitations remain localized in both one-dimensional (1D) and two-dimensional (2D) systems.

The Hamiltonian under investigation is described as:

$$\hat{H}_{\textrm{LGT}} = \sum_{j} J \hat{\sigma}^{Z}_j \hat{Z}_{j,j+1} \hat{\sigma}^{Z}_{j+1} + h \hat{X}_{j,j+1} + \mu \hat{\sigma}^{X}_j$$

where the coefficients $J, h,$ and $\mu$ control the system dynamics through Ising interactions and local symmetry operations, with the interactions exhibiting extensive local symmetries.

Key Results

1. Disorder-Free Localization (DFL): The results indicate that translationally invariant states can exhibit localization without the need for explicit disorder. This is achieved through a variety of initial state preparations that inherently embed a symmetry-based disorder component into the dynamics.
2. Efficient Averages over Disorder: By exploiting quantum entanglement and ancillary qubits, the research demonstrates an efficient averaging over disorder realizations. This averaging is facilitated by initializing ancillas to represent a superposition of all possible disorder configurations, effectively leading to a disorder average.
3. Dimension-Invariant Behavior: The paper confirms DFL in both 1D and 2D lattices, showcasing the robustness of localization phenomena in higher dimensions, which is notably challenging to achieve in classical systems where localization often diminishes with dimensional extension.
4. Entropic Measurements: The paper utilizes second Rényi entropy to assess entanglement growth. The superposition state shows rapid growth to a volume-law entanglement, signaling distinct behaviors compared to conventional many-body localized (MBL) phases which typically demonstrate logarithmic entanglement growth.

Implications and Future Directions

The implications of this work are multifaceted. The observed DFL suggests that quantum systems can maintain localization without the necessity of disorder, potentially revolutionizing our understanding of materials where imperfections are often a given. This new phase of matter, governed by symmetry rather than disorder, could have substantial implications for quantum technologies, particularly in error resilience and the design of quantum materials with predictable localization properties.

The paper also opens doors to further studies on the nature of DFL in strongly interacting systems, particularly regarding stability against perturbations and its interplay with other exotic phases. Investigating larger systems or different lattice topologies could reveal new insights into the universality and limits of DFL behaviors.

Future applications may explore new quantum simulation propositions where disorder averaging is crucial or consider disorder-induced phenomena that go beyond the current capabilities of classical computational techniques.

In conclusion, this paper paves the way to a deeper understanding and utilization of quantum many-body systems under novel symmetry-based conditions, driving forward the frontier of quantum computing capabilities and foundational physics research.