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

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Authors: Thiago R. Girão Souza, Andreia Saguia, Alan C. Santos, Marcelo S. Sarandy — arXiv:2608.07149v1 [quant-ph], 07 Aug 2026

Overview

Research area: Quantum many-body physics and superconducting quantum hardware — specifically many-body localization (MBL) in networks of coupled transmon qubits, and how the disorder that is unavoidable in real devices (correlated disorder) affects the localization transition.

Technical level: Intermediate to Advanced. The paper assumes familiarity with the Eigenstate Thermalization Hypothesis, entanglement entropy scaling laws, and transmon circuit quantization, though the physical motivation and the dynamical memory diagnostic are accessible to a broader audience.

Scope (one sentence): The paper maps the physical hardware parameters of a transmon array onto a disordered spin model and numerically shows that MBL criticality survives the correlated disorder intrinsic to such devices, using both entanglement-entropy statistics and a new, experimentally cheap local memory parameter.

What This Paper Is About

Most theoretical studies of many-body localization assume purely random disorder and short-range couplings. In real superconducting transmon devices, disorder is created by detuning qubit frequencies with local magnetic fluxes — but because both each qubit's frequency and its coupling to neighbours depend on those same fluxes, the disorder in the fields and the disorder in the couplings are inevitably correlated. The paper asks whether the MBL transition survives this realistic correlation, and whether it can be diagnosed with observables that are actually measurable on today's hardware.

Key Contributions

1. A hardware-to-model mapping. The authors show explicitly how to tune shunting capacitances, Josephson energies, local external fluxes, and qubit-qubit coupling capacitances to control and quantify the degree of correlated disorder in the resulting effective spin model, defining a dimensionless disorder strength Δ(φ₀) = δ(φ₀)/J(φ₀) from experimentally accessible parameters.

2. A quantitative measure of the correlation. They derive the covariance between a qubit's frequency and its coupling to a neighbour, σ_nm ≈ A_nm(φ₀)⟨(δφ_m)²⟩, and identify the coefficient A_nm(φ₀) as an amplifier of correlated disorder that can be tuned via the junction asymmetry α and the reference flux φ₀.

3. Proof that MBL criticality is robust to correlated disorder. Using the variance of the half-system block entanglement (2nd-order Rényi entropy) across disorder realizations, they locate the transition and show it is consistent with the uncorrelated-disorder case.

4. A new, measurement-efficient dynamical order parameter. They introduce a disorder-averaged local memory parameter built only from single-qubit occupation numbers, whose long-time behaviour and derivative with respect to disorder locate the critical point consistently with the entanglement analysis.

Main Findings

• Strong coupling is deliberately engineered. The devices are considered in a regime of strong capacitive coupling, C_{n,n+1} = C_C = 0.2 C_{S,n}, in contrast with conventional transmons that operate at C_{n,n+1} ≪ C_{S,n}. Entering this regime is what produces non-negligible non-local interaction terms and hence network-mediated couplings.

• Correlated disorder is tunable, not just tolerated. Because ω_m and g_nm are both functions of the local flux φ_m, small random flux fluctuations δφ_m produce correlated fluctuations in fields and couplings. Choosing the junction asymmetry α and the reference flux φ₀ allows devices with a high degree of correlation to be designed; the covariance is evaluated over 3,000 realizations for a 7-qubit system with C_{S,n} = 100 fF, C_{n,n+1} = 0.2 C_{S,n}, and E_{J,n} = 2 × 10⁻²³ J.

• The flux knob produces mostly on-site disorder. In the supplementary analysis (10 qubits, 500 realizations, φ_n random in [0, 0.5]), the mean qubit frequency varies strongly and nonlinearly with φ₀ with a minimum near φ₀ ≃ 0.5, while nearest-neighbour and next-nearest-neighbour couplings vary only moderately, and their ratio stays approximately constant. The dimensionless disorder Δ(φ₀) is strongly enhanced near φ₀ ≃ 0.5 and reaches values well beyond unity.

• Entanglement shows the expected volume-law to area-law crossover. For system sizes L ∈ {8, 10, 12, 14}, ten eigenstates from the middle of the spectrum, and 10³ disorder realizations, the mean Rényi entropy ⟨S₂⟩ grows with L at low disorder (ergodic, volume-law) and saturates to a size-independent value at large disorder (localized, area-law).

• The entanglement variance locates the critical point. The variance Var(S₂) peaks at (Δφ)_max ≈ 2.17 for L = 14, which the authors describe as consistent with the uncorrelated disorder case. The von Neumann entropy analysis in the supplement gives a peak at (Δφ)_max ≈ 2.41 for L = 14.

• The memory parameter reproduces the transition with local measurements only. For L ∈ {8, 10, 12, 14, 16} and an initial state with the first L/2 qubits fully excited, the disorder-averaged late-time memory ⟨M⟩ shows a scale-invariant crossing near Δφ ≃ 2 at τ_L ≃ 864 (t ≃ 320 ns, with g_nn/(2π) ≈ 0.43 GHz). The derivative d⟨M⟩/dΔφ sharpens with L, peaking at Δφ* ≃ 1.82 with χ_∞^max ≃ 0.57 for L = 16 (the Fig. 3 caption states ≃ 0.58).

• The two diagnostics agree. Since the mid-spectrum eigenstates used in the entropy analysis are the hardest to localize, the lower Δφ* ≃ 1.82 from the memory parameter is described as an estimate fully consistent with the entanglement-entropy diagnostics. Dynamics used 1,000 disorder realizations for L ≤ 14 and 500 for L = 16.

Methodology in Plain English

The authors start from a circuit-level description of a chain of transmon qubits, each defined by a Josephson energy, a shunting capacitance, and a local flux, coupled to neighbours through small capacitors. In the strong-coupling regime they work in, the array is well described by an effective spin-1/2 model in which each qubit's excitation energy and each pairwise hopping amplitude both depend on the applied fluxes.

Because the same random flux controls both quantities, the disorder in energies and the disorder in couplings are tied together. The authors quantify this with a covariance formula derived by expanding frequency and coupling to first order in small flux fluctuations, assuming flux lines are statistically independent so that ⟨δφ_m δφ_n⟩ = 0. The prefactor of this covariance acts as a knob: by choosing junction asymmetry and reference flux, one can amplify or suppress the correlation. They also define a dimensionless disorder strength by dividing half the accessible frequency range by the mean nearest-neighbour coupling.

To test whether this correlated disorder destroys MBL, they exactly diagonalize the Hamiltonian for chains of up to L = 14 and look at entanglement between two contiguous halves of the chain, quantified by the 2nd-order Rényi entropy S₂ = −log₂ Tr(ρ_A²). The choice of Rényi entropy is deliberate: it can be estimated experimentally with randomized measurements rather than full state tomography. The critical point is identified not from the mean entropy but from its variance across disorder realizations, which peaks sharply near the transition in finite systems.

As a complementary and more experimentally friendly probe, they simulate the time evolution of a state with half the qubits excited and track the total distance D(t) between the instantaneous and initial density profiles. Normalizing by the value D_erg = 2ν(1−ν)L expected for a fully thermalized, uniform profile gives a memory parameter ⟨M(t)⟩ = 1 − ⟨D(t)⟩/D_erg, which tends to 0 in the ergodic phase and stays near 1 in the localized phase. Measuring it requires only single-qubit population readout.

Why This Matters

Impact on research. The paper moves MBL studies from idealized random spin chains to the disorder that actually exists in transmon hardware, and shows the transition is not washed out. It also provides a diagnostic — the local memory parameter — that avoids the experimentally prohibitive task of resolving highly excited energy eigenstates or performing full tomography, making the MBL transition testable on existing devices.

Real-world applications (as motivated or implied by the paper):

• Multi-qubit processor design: the authors note potential implications for designing processors where localization suppresses the onset of quantum chaos and the loss of quantum information.
• Disorder engineering as a resource: the flux-controlled architecture is presented as a route to tunable disorder landscapes, where diagonal and weak correlated off-diagonal disorder are generated by the same control mechanism.
• NISQ-era benchmarking: the memory parameter requires only single-qubit local population measurements via standard projective or dispersive readout, drastically reducing measurement overhead compared with entanglement-based metrics.
• Entanglement metrology: the use of Rényi entropy via randomized measurements connects the analysis to techniques already demonstrated in trapped-ion and superconducting-qubit platforms.

Industry relevance. Superconducting transmon architectures are the leading platform for gate-based quantum computing, and their operation already relies on frequency detuning that creates a localized regime. Understanding how correlated disorder, junction asymmetry, and capacitive participation ratio affect localization gives hardware designers a quantitative handle on a regime they currently enter by necessity rather than by design.

Future Directions

1. Experimental demonstration. The paper is a theory and exact-diagonalization study using experimentally feasible parameters; no experimental data are reported. The randomized-measurement protocol for S₂ and the single-qubit readout for ⟨M⟩ are both proposed as directly implementable, so a device-level test is the natural next step.

2. Scaling beyond L = 16. Exact diagonalization limits the entanglement analysis to L ≤ 14 and the dynamics to L = 16. Whether the variance maximum and the derivative peak converge to a common critical Δφ in the thermodynamic limit is not established here, and would require tensor-network or other large-scale methods.

3. Beyond the linear chain and the two-level approximation. The study treats a chain with nearest- and next-nearest-neighbour capacitive couplings in the two-level (qubit) subspace. How the conclusions change for two-dimensional networks, longer-range couplers, or with leakage to transmon higher levels is not addressed.

4. Full characterization of the coupling disorder. The authors note that flux-induced variations of the couplings remain substantially smaller than those of the qubit frequencies over the operating range, so the dominant effect is on-site disorder. A systematic study of the regime where off-diagonal correlated disorder is comparably strong remains open.

Target Audience

This paper is most useful to researchers working on many-body localization and thermalization in interacting quantum systems, to superconducting-qubit experimentalists interested in disorder engineering and hardware-level noise, and to quantum-architecture designers who need practical, low-overhead diagnostics of localization on near-term processors. Graduate students with a background in quantum many-body physics or circuit QED will find the hardware-to-Hamiltonian mapping in the appendices particularly instructive.

Authors’ abstract

The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.