⚛️ quantum physics

Many-Body Localization Induced by Correlated Disorder in Interacting Superconducting Qubits

This paper demonstrates that the Many-Body Localization phase transition in interacting superconducting transmon qubit networks remains robust against correlated disorder, establishing a framework for controlling localization properties through engineered hardware parameters and validating findings via block entanglement entropy variance and a local memory parameter.

Original authors: Thiago R. Girão Souza, Andreia Saguia, Alan C. Santos, Marcelo S. Sarandy

Published 2026-08-10

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CC BY 4.0

Original authors: Thiago R. Girão Souza, Andreia Saguia, Alan C. Santos, Marcelo S. Sarandy

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Great Quantum Memory Game

Imagine a crowded room where everyone is chatting. If you whisper a secret to the person next to you, that secret quickly spreads. Within moments, the whole room knows the story, and no one can remember who started it or what the original whisper sounded like. In the world of quantum physics, this is called "thermalization." It's the rule that isolated quantum systems follow: they scramble their information until they forget their past and settle into a chaotic, uniform state. This is usually explained by a rulebook called the Eigenstate Thermalization Hypothesis (ETH), which suggests that local parts of a system eventually act like their own tiny heat baths, erasing any memory of how they began.

But what if the room was designed so that secrets couldn't spread? What if the walls were made of a special material that trapped information in place? This is the phenomenon of "Many-Body Localization" (MBL). Instead of the whole room learning the secret, the person who heard it keeps it forever, and the chaos never takes over. Scientists are incredibly interested in this because if we can build quantum computers that stay in this "localized" state, they might be able to hold onto delicate information without it getting scrambled by noise or chaos. Usually, researchers study this by shaking the system with completely random, unpredictable noise. But in the real world, nothing is perfectly random; things are often connected, or "correlated." This paper asks a big question: If the noise is correlated—like a pattern rather than pure chaos—does the quantum memory still hold, or does the system finally give in and forget everything?

The Paper's Discovery: Correlated Chaos Doesn't Break the Memory

In this study, the authors, Thiago R. Girão Souza and their team, decided to test this idea using a very specific type of quantum hardware: superconducting circuits made of "transmon qubits." Think of these qubits as tiny, artificial atoms on a chip that can be tuned to act like a chain of interacting magnets. The researchers wanted to see what happens when these qubits are subjected to "correlated disorder." In plain English, this means the "noise" or randomness affecting the qubits isn't just a bunch of unrelated static; it's a pattern where the disturbance on one qubit is linked to the disturbance on its neighbors, much like how a ripple in a pond affects the water in a connected area.

The team first showed how to build this specific type of correlated noise right into the hardware. By tweaking the physical parts of the circuit—like the size of the capacitors and the magnetic fields applied to each qubit—they could engineer a situation where the randomness naturally became correlated. They then simulated the behavior of these qubit chains to see if the "memory" of the system would survive this correlated chaos.

Their main finding is surprisingly reassuring for anyone trying to build quantum computers. They discovered that the "Many-Body Localization" phase is incredibly robust. Even when the disorder is correlated and the qubits interact in complex, non-local ways, the system still manages to lock up its information. The quantum memory doesn't break just because the noise has a pattern. The researchers found that the transition point—the moment the system switches from remembering everything to forgetting everything—stays almost exactly the same as it does for purely random disorder.

To prove this, they used two different "detective tools." The first tool looked at "entanglement," which is a fancy way of measuring how much the qubits are sharing information with each other. In a chaotic system, this sharing spreads out like a flood (volume-law), but in a localized system, it stays contained (area-law). They found that even with correlated noise, the system still showed the signs of being localized. The second tool was a "memory parameter." They started the system with a specific pattern (like having the first half of the qubits "on" and the second half "off") and watched to see if that pattern survived over time. In the localized phase, the pattern stayed intact, like a frozen snapshot. In the chaotic phase, the pattern melted away into a uniform blur.

The simulations, which ran on systems with up to 16 qubits, showed that the "memory" held strong against the correlated disorder. The critical point where the system flips from remembering to forgetting occurred at a disorder strength of about $\Delta\phi \approx 2.17$ when looking at the middle of the energy spectrum, and around $\Delta\phi \approx 1.82$ when looking at the long-term memory dynamics. These numbers suggest that the "correlated" nature of the noise doesn't make the system more fragile; in fact, the localized phase is just as stable as if the noise were completely random.

This is a big deal because it means that the unavoidable imperfections and correlations in real-world quantum hardware might not be the enemies we thought they were. The paper suggests that we don't need to worry that these complex, connected patterns of disorder will ruin our ability to keep quantum information safe. Instead, the transmon platforms seem naturally equipped to handle this kind of "messy" reality, keeping the quantum memory alive even when the world around it is correlated and complex. The authors conclude that this robustness provides a solid framework for designing better quantum processors, showing that we can tune these devices to stay in the "remembering" zone, even with the messy, correlated noise that comes with the territory.

Technical Summary: Many-Body Localization Induced by Correlated Disorder in Interacting Superconducting Qubits

Problem Statement
Many-Body Localization (MBL) represents a failure of quantum thermalization, where strong disorder prevents a system from acting as its own thermal bath. While extensively studied in theoretical spin chains and realized in synthetic platforms like ultracold atoms and trapped ions, the transition has primarily been analyzed under assumptions of purely random disorder and local couplings. Realistic superconducting circuits, particularly transmon qubit architectures, inherently possess complex configurations involving network-mediated non-local interactions and unavoidable correlated disorder. These correlations arise from the physical dependence of qubit frequencies and coupling strengths on shared fabrication parameters and external fluxes. The central problem addressed is whether the MBL phase transition remains robust in the presence of these intrinsic correlations and non-local interactions, and how to systematically characterize this transition in hardware-constrained environments.

Methodology
The authors investigate the quantum dynamics of a linear chain of $N$ transmon qubits. The system is modeled by a Hamiltonian describing two-level systems with site-dependent energies ( $\omega_n$ ) and both nearest-neighbor and non-local capacitive couplings ( $g_{nm}$ ).

Engineering Correlated Disorder: The authors demonstrate that correlated disorder emerges naturally when external magnetic fluxes ( $\phi_n$ ) fluctuate. By tuning physical hardware parameters—specifically Josephson energies ( $E_J$ ), shunting capacitances ( $C_S$ ), and coupling capacitances ( $C_{n,n+1}$ )—they map these physical elements to effective spin couplings and fields. They show that even uncorrelated flux fluctuations ( $\delta\phi$ ) induce correlations between the local qubit energy and the interaction strength due to the functional dependence of $\omega_n$ and $g_{nm}$ on the flux.
Entanglement Analysis: To characterize the MBL transition, the authors analyze the block entanglement of energy eigenstates in the middle of the spectrum. They utilize the 2nd-order Rényi entropy ( $S_2$ ) of a half-system partition, averaged over disorder realizations. The variance of this entropy, $\text{Var}(S_2)$ , is used to locate the critical point, as it is expected to peak at the transition. This metric is chosen for its experimental feasibility via randomized measurements, avoiding full state tomography.
Dynamical Analysis: Independently, the authors introduce a local memory parameter, $\langle M(t) \rangle$ , based on the time-evolution of site occupation numbers. Starting from a domain-wall initial state ( $|e\rangle^{\otimes L/2}|g\rangle^{\otimes L/2}$ ), they measure the deviation of the density profile from its initial state. In the localized phase, memory is retained ( $\langle M \rangle \to 1$ ), whereas in the ergodic phase, the system thermalizes ( $\langle M \rangle \to 0$ ). The critical point is identified by the peak in the numerical derivative of the long-time averaged memory parameter with respect to disorder strength.

Key Results

Robustness of MBL: The study confirms that the MBL phase transition is robust against the correlated disorder patterns inherent to transmon devices. The critical behavior observed in the presence of correlations closely mirrors that of the uncorrelated disorder case.
Critical Point Identification:
- Entanglement Variance: For system sizes up to $L=14$ , the variance of the block Rényi entropy exhibits a pronounced maximum at a disorder strength of $(\Delta\phi)_{\text{max}} \approx 2.17$ . This peak scales with system size, signaling the critical point.
- Memory Parameter: The dynamical analysis yields a consistent critical point. The derivative of the long-time memory parameter peaks at $\Delta\phi^* \approx 1.82$ for $L=16$ . While slightly lower than the entropy-based precursor (likely due to the specific initial state being easier to localize than mid-spectrum eigenstates), the results confirm the existence of a sharp transition.
Hardware Engineering: The authors provide a concrete mapping showing how to control the degree of correlated disorder by adjusting the junction asymmetry parameter ( $\alpha$ ) and the reference external flux ( $\phi_0$ ). This allows for the systematic engineering of disorder patterns in quantum hardware.

Significance and Claims
The paper claims to provide a framework for understanding localization in complex quantum network topologies, specifically addressing the realistic conditions of superconducting transmon processors. The primary significance lies in demonstrating that the MBL phenomenon is not fragile to the non-local interactions and correlated disorder that are intrinsic to current quantum hardware designs. This robustness suggests that the localized phase, which is essential for suppressing quantum chaos and preserving quantum information in practical processors, can be reliably tuned and maintained even in the presence of these complex correlations. Furthermore, the introduction of the local memory parameter offers a practical, experimentally accessible diagnostic tool for NISQ-era devices, requiring only single-qubit readouts rather than complex multi-qubit tomography. The work bridges the gap between idealized theoretical models of MBL and the physical realities of superconducting circuit implementations.

The Great Quantum Memory Game

The Paper's Discovery: Correlated Chaos Doesn't Break the Memory

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