Quantum Resources Exhibit Universal Rise-Peak-Fall Dynamics in Random Circuits

Quantum resources, such as coherence and entanglement, underpin many promising quantum technologies, but understanding how these fragile properties evolve in complex systems remains a significant challenge. Sreemayee Aditya, Xhek Turkeshi, and Piotr Sierant, working at the Institut f ̈ur Theoretische Physik and the Barcelona Supercomputing Center, investigate the growth and spread of these resources within a chain of qubits subjected to random, yet structured, quantum operations. Their research reveals a universal pattern in systems capable of generating quantum resources, where the amount of resource initially rises, reaches a peak, and then decays as the system becomes increasingly disordered. Importantly, the team also demonstrates that even circuits lacking resource-generating capabilities can still spread existing quantum resources, effectively acting as a conduit for quantum information, and establishes a fundamental understanding of how these resources behave in realistic quantum systems.

Resource Decay Across Subsystem Sizes

This supplemental material provides a detailed analysis of how quantum resources decay as the size of a quantum subsystem changes, offering a complementary perspective to the main research. The study employs exponential fitting and threshold-based characterization to analyze resource decay, confirming consistent results with both approaches. Researchers quantified nonstabilizerness, coherence, and non-Gaussianity, revealing clear quantitative results including numerical values for decay constants that demonstrate the rate at which these resources diminish.

Tracking Quantum Resource Spread in Chains

Scientists investigated the spread of quantum resources, nonstabilizerness, coherence, and fermionic non-Gaussianity, within local quantum circuits. They tracked these properties in one-dimensional qubit and qutrit chains, revealing how these resources deviate from classically simulable states. The team developed a method based on discrete Wigner functions and mana, a Wigner-function-based quantifier of nonstabilizerness, applied to qutrit chains, enabling the calculation of mana which increases with the negativity of the Wigner quasi-probability distribution. Experiments began with resource-free product states and evolved them using local two-qutrit Haar-random gates, allowing researchers to observe the initial buildup and subsequent spread of quantum resources. Analysis revealed a characteristic rise-peak-decay behavior for resource-generating gates, with peak times scaling logarithmically with subsystem size. Complementary experiments initialized the chains with localized resourceful clusters, revealing ballistic spreading of the local resource content, demonstrating a unified phenomenology for the spatiotemporal dynamics of these quantum resources.

Quantum Resource Dynamics in Qubit Chains

Scientists have achieved a detailed understanding of how quantum resources, nonstabilizerness, coherence, and fermionic non-Gaussianity, behave within one-dimensional quantum systems. Experiments demonstrate that when circuits utilize resource-generating gates and begin with a low-resource initial state, the resource content exhibits a universal rise-peak-fall behavior, with the peak time scaling logarithmically with subsystem size. Data shows that the resource eventually decays as the subsystem approaches a maximally mixed state, demonstrating a natural limit to resource accumulation. In a complementary setup, the team investigated circuits with gates that do not create the resource but entangle neighboring qubits, confirming ballistic spreading of the resource initially confined to a small region of the system. By shifting the position of the subsystem, scientists observed the resource spreading at a constant rate, confirming ballistic propagation.

Resource Dynamics and Ballistic Spreading in Chains

This research investigates the dynamics of quantum resources, nonstabilizerness, coherence, and fermionic non-Gaussianity, within one-dimensional qubit chains evolving under random circuits. The team demonstrates that resource-generating gates induce a characteristic rise-peak-decay pattern in local resource content, with the peak time scaling logarithmically with subsystem size, suggesting a rapid emergence of nonclassical features within local regions of the system. Complementary simulations reveal ballistic spreading of resources when the system begins with a localized resourceful cluster and evolves under gates that do not generate additional resources. Importantly, the researchers observed a unified phenomenology governing the spatiotemporal dynamics of all three investigated resources, indicating that locality and unitarity, rather than specific details of the dynamics or resource theory, are primary factors in resource spreading. The authors acknowledge limitations in their current models, particularly the use of random circuits as a simplification of more complex quantum systems. Future work should focus on developing analytical frameworks to explain the observed phenomena, potentially by connecting nonstabilizerness to the hydrodynamic modes of many-body dynamics, and extending the research to fully ergodic Floquet drives and genuinely chaotic Hamiltonian evolutions.