Analyzing Chaotic Behavior in Quantum Circuits

The recent results from the collaboration between IBM Quantum, Algorithmiq and Prof. John Goold's group at Trinity College Dublin is a good example of how we can work together towards the goal of quantum advantage and continue to show that we are in what I call as the era of quantum utility where a quantum computer can be used to explore interesting science beyond exact circuit simulations. They are investigating a special case of many body dynamics using a class of maximally chaotic circuits known as dual-unitary circuits — that are composed of gates that are unitary in space and time. The team executes these circuits on our Eagle processor (ibm_strasbourg), leveraging advances in Pauli noise learning, parametric updates for fast circuit compilation, and the tensor network error mitigation (TEM) methods developed by Algorithmiq and implemented entirely in classical post-processing. They leverage the fact that at the dual-unitary point there are analytical solutions for certain correlation functions and then they perturb the circuits away from this point where both analytical solutions and brute force simulation on classical computers are not possible. In this parameter space they compare their results to approximate classical simulations known as tensor network methods in both the Heisenberg and Schrödinger picture. This in it self is both a powerful benchmarking tool for quantum computers as it can be use to show that error mitigation is working at scale, and second it continues to expand the methodology of how we search for advantage. The team was able to execute circuit volumes up to 91 qubits and roughly 4100 two-qubit gates (see figure) and show really good agreement with the exact solution (see figure) and when they perturb away from the point with and analytical solution the results continued to agree with the Heisenberg while the Schrödinger picture failed to reproduce the results (see figure). This gives us trust in our quantum computers are working in what we call the utility scale and as a field we are developing new methods to perturb our circuits beyond exact verification and still have confidence in the accuracy. Furthermore, this result also add to an increasing body of work that demonstrates the use of classical HPC to extend the reach of current quantum computers, an architecture we call quantum-centric supercomputing. The preprint can be found here https://lnkd.in/ermzhdH3 and Algorithmiq have added there TEM method to our Qiskit Function Catalog https://lnkd.in/eWCNrsuY

QUANTUM SYSTEM AT THE EDGE OF CHAOS: A PATH TOWARD STABLE QUANTUM COMPUTATION Quantum physics rarely offers moments where theory, engineering, and the raw behavior of many‑body systems collide to reveal a new dynamical regime. Yet that is exactly what the 78‑qubit Chuang‑tzu 2.0 processor has uncovered: a quantum system pushed to the brink of chaos can be held in a long‑lived, tunable prethermal state—an island of order suspended inside non‑equilibrium turbulence. This discovery goes far beyond Floquet physics. Periodic driving has already given us time crystals and engineered topological phases, but non‑periodic driving—especially with structured randomness—has long been synonymous with rapid heating and the loss of quantum information. Instead, this experiment shows that temporal randomness can be engineered to suppress heating, stabilize dynamics, and preserve coherence far longer than expected. Random multipolar driving, neither periodic nor chaotic, acts as a hidden temporal scaffold that shapes how energy flows through the system. Applied to a two‑dimensional Bose–Hubbard model across 78 qubits and 137 couplers, this protocol prevents the system from collapsing into chaos. Instead, it enters a robust prethermal plateau where imbalance decays slowly, entanglement grows in a controlled way, and the heating rate becomes tunable—matching universal algebraic scaling predicted for multipolar drives. This is not a subtle correction; it is a macroscopic reshaping of the system’s dynamical landscape. The geometry of entanglement is equally striking. Different subsystems show distinct behaviors—some oscillate coherently, others settle into plateaus—revealing a highly non‑uniform spread of correlations across the lattice. It is the first time such fine‑grained entanglement dynamics have been observed in a large, non‑periodically driven quantum simulator. Classical tensor‑network methods like GMPS and PEPS cannot keep pace once heating accelerates, confirming that these dynamics lie firmly beyond classical reach. Quantum systems at the brink of chaos are not doomed to disorder. With the right temporal geometry, they can be shaped, stabilized, and made computationally powerful. This work demonstrates that the boundary between coherence and chaos is not a hard limit but a navigable frontier—and that the future of quantum computation may lie precisely in mastering this edge. # https://lnkd.in/eJBkGts5

Out-of-Time-Ordered Correlators (OTOCs) are essential tools for understanding the behavior of complex quantum systems, especially those exhibiting chaotic dynamics. They help scientists study how information spreads and becomes hidden within these systems over time, a process known as information scrambling. What Are OTOCs? OTOCs are mathematical expressions that involve operators applied at different times in a sequence that isn't straightforward. This unique arrangement makes them particularly sensitive to the chaotic nature of a system. In systems where chaos is present, OTOCs tend to grow rapidly, indicating quick information scrambling. In contrast, in more orderly systems, this growth is slower, reflecting more predictable behavior. OTOCs and Black Holes: The black hole information paradox is a puzzle in physics that questions whether information that falls into a black hole is lost forever, which would conflict with the principles of quantum mechanics. Recent research suggests that OTOCs can provide insights into this paradox by analyzing the chaotic behavior of black holes. For example, studies have shown that as a black hole evaporates, certain measures of chaos increase, suggesting that information, while highly scrambled, may not be lost but rather becomes extremely difficult to retrieve. Quantum Fisher Information (QFI): QFI is a concept that measures how sensitive a quantum state is to changes in a particular parameter, such as time. In chaotic systems, QFI can be used to estimate how the system evolves over time. Higher QFI means greater sensitivity, allowing for more precise tracking of time evolution. Studies have found that in chaotic quantum systems, QFI decreases over time for small parts of the system but can remain significant for larger parts, indicating that while local observations become less informative, global observations can still effectively monitor the system's evolution. Implications for Black Hole Evaporation: By combining the insights from OTOCs, measures of chaos, and QFI, researchers can better understand the black hole information paradox. The increase in chaos during black hole evaporation suggests enhanced information scrambling. However, the persistence of QFI in larger subsystems implies that, despite this scrambling, information about the initial state may still be recoverable, aligning with the principles of quantum mechanics. This perspective offers a potential resolution to the paradox, proposing that information is not destroyed but becomes highly scrambled and distributed, making it challenging to retrieve without access to the entire system. 🔹️🔹️For a deeper exploration of topics like this, follow STEMONEF-COMMUNITY and STEMONEF COMMUNITY SUPPORT. We’ll dive further into the complexities and modern insights surrounding these topics and more in future posts!

Quantum complexity phase transitions in monitored random circuits https://lnkd.in/drKBMcrV Recently, the dynamics of #quantumsystems that involve both unitary evolution and quantum #measurements have attracted attention due to the exotic phenomenon of #measurementinducedphasetransitions. The latter refers to a sudden change in a property of a state of n qubits, such as its entanglement entropy, depending on the rate at which individual qubits are measured. At the same time, #quantumcomplexity emerged as a key quantity for the identification of complex behaviour in #quantummanybodydynamics. In this work, we investigate the dynamics of the quantum state complexity in #monitoredrandomcircuits, where n qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We find that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows at least #linearly in time until saturating to a value eΩ(n). Above, the complexity does not exceed poly(n). In our proof, we make use of #percolation theory to find paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. We lower bound the exact #statecomplexity in the former regime using recently developed techniques from algebraic geometry. Our results combine quantum complexity growth, phase transitions, and computation with measurements to help understand the behavior of monitored random circuits and to make progress towards determining the computational power of measurements in many-body systems. Warm thanks to Ryotaro Suzuki, Jonas Haferkamp and Philippe Faist for this wonderful collaboration. I am happy to see this out in the Quantum - the open journal for quantum science. And thanks to our funders, in particular the Deutsche Forschungsgemeinschaft (DFG) - German Research Foundation.