Information Scrambling in Computationally Complex Quantum Circuits (2101.08870v1)

Abstract: Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish the two mechanisms associated with quantum scrambling, operator spreading and operator entanglement, and experimentally observe their respective signatures. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

• The paper demonstrates that operator entanglement, unlike operator spreading, significantly complicates classical simulations of quantum circuits.
• It employs a 53-qubit processor with Clifford and non-Clifford gates to measure out-of-time-order correlators (OTOCs) and validate theoretical models.
• The study’s findings advance our understanding of many-body quantum dynamics and set the stage for enhancing quantum processor performance.

Information Scrambling in Quantum Circuits

The paper "Information Scrambling in Computationally Complex Quantum Circuits" explores the intricate dynamics of quantum information scrambling using a 53-qubit quantum processor. This paper investigates the mechanisms of quantum scrambling—specifically operator spreading and operator entanglement—and delineates their distinct experimental signatures via the measurement of out-of-time-order correlators (OTOCs).

Quantum Scrambling Dynamics

Quantum scrambling is a process through which a quantum system disperses localized information into its many-body degrees of freedom. It is a pivotal mechanism underlying the thermalization of isolated quantum systems and is described in terms of two main mechanisms: operator spreading and operator entanglement. Operator spreading describes how initial operators change by increasing the number of affected qubits, while operator entanglement reflects the increase in the number of terms needed to describe the time-evolved operator on a quantum system.

The team's experimental design on the 53-qubit quantum processor distinguishes these two mechanisms, wherein operator spreading was found manageable via classical simulations, but operator entanglement posed significant computational challenges due to its exponential scaling with circuit size. This difficulty highlights operator entanglement as a key contributor to the classical simulation complexity of quantum observables.

Experimental Methodology and Findings

The experimental configuration involved 53 superconducting qubits arranged in a two-dimensional layout. OTOCs were measured by applying the same quantum circuit $\hat{U}$ and its inverse $\hat{U}^\dagger$, interspersed with a "butterfly operator". Two types of gates were utilized in these circuits: classical Clifford gates and non-Clifford gates, which facilitated differential impacts on spreading and entanglement.

• Operator Spreading was experimentally identified through the decay of average OTOCs and matched with predictions from a classical population dynamics model. This was confirmed across various configurations involving different types of quantum gates, notably $\sqrt{\text{iSWAP}}$ and iSWAP gates.
• Operator Entanglement was measured through the fluctuation in OTOCs and was more challenging to simulate classically. Its impact was particularly severe on OTOC simulation costs, establishing entanglement as the computational bottleneck when simulating quantum scrambling.

The research further elaborateed on the implementation of various error-mitigation techniques in their quantum circuits, which are critical for accurate recovery of coherent signals amidst noise. This step was crucial to isolate genuine scrambling dynamics from decoherence and gate infidelity effects.

Implications and Future Potential

The outcomes of this research are manifold. The capacity to characterize quantum scrambling and elucidate the mechanisms behind operator spreading and entanglement provide a solid foundation for resolving perplexing physical phenomena, including black hole information paradoxes, high-temperature superconductivity, and many-body localization. Practically, this work contributes to the ongoing enhancement of quantum processors, paving the way for achieving and recognizing quantum supremacy.

Looking forward, a key area of expansion lies in applying these techniques to more complex quantum dynamics, including modeling behavior in quantum gravity and unconventional quantum phases. The improvement of quantum processor fidelity and reduction of computational error are paramount as these avenues are explored.

In summary, this paper showcases a comprehensive exploration of quantum scrambling within a large quantum system, revealing both theoretical insights and tangible implications for the advancement of quantum computation and related fields.