[Paper Review] Observation of strong and weak thermalization in a superconducting quantum processor

Fusheng Chen, Zheng‐Hang Sun+23 more|arXiv (Cornell University)|Feb 17, 2021

Quantum many-body systems53 references41 citations

TL;DR

This study experimentally demonstrates strong and weak thermalization in a 12-qubit superconducting quantum processor by preparing different initial states in a non-integrable 1D Ising-like Hamiltonian. Using time-resolved measurements of local observables, entanglement entropy, and concurrence, the authors show that strong thermalization leads to convergence of local observables to thermal values, while weak thermalization exhibits persistent oscillations requiring time averaging. The results establish entanglement dynamics as a key diagnostic for thermalization regimes.

ABSTRACT

We experimentally study the ergodic dynamics of a 1D array of 12 superconducting qubits with a transverse field, and identify the regimes of strong and weak thermalization with different initial states. We observe convergence of the local observable to its thermal expectation value in the strong-thermalizaion regime. For weak thermalization, the dynamics of local observable exhibits an oscillation around the thermal value, which can only be attained by the time average. We also demonstrate that the entanglement entropy and concurrence can characterize the regimes of strong and weak thermalization. Our work provides an essential step towards a generic understanding of thermalization in quantum systems.

Motivation & Objective

• To experimentally observe and distinguish strong and weak thermalization in a non-integrable quantum many-body system.
• To investigate how initial state preparation affects thermalization dynamics in a superconducting qubit array.
• To evaluate the role of entanglement entropy and concurrence as indicators of thermalization regimes.
• To assess the robustness of thermalization signatures against decoherence in a realistic quantum processor.
• To establish a connection between initial state effective temperature and the emergence of thermal equilibrium.

Proposed method

• Realized a 1D array of 12 superconducting transmon qubits with tunable nearest-neighbor coupling and local transverse fields via microwave drives.
• Engineered a non-integrable Hamiltonian by adding a transverse field term to a XX+YY spin model, enabling ergodic dynamics.
• Prepared initial states in the parametric space (θ₀, φ₀) corresponding to different effective inverse temperatures β.
• Performed time-resolved quantum state tomography to measure local observables 〈σᶻ(t)〉, entanglement entropy (EE), and concurrence.
• Used numerical simulations with and without decoherence (via Lindblad master equation) to compare with experimental data.
• Calibrated dynamical phases to ensure identical initial states across qubits, enabling reproducible non-equilibrium quench dynamics.

Experimental results

Research questions

• RQ1 Can strong and weak thermalization be experimentally observed in a superconducting quantum processor?
• RQ2 How do different initial states, characterized by their effective inverse temperature, influence the convergence of local observables to thermal values?
• RQ3 Can entanglement entropy and concurrence serve as reliable indicators to distinguish between strong and weak thermalization regimes?
• RQ4 To what extent are thermalization signatures robust against decoherence in a realistic superconducting platform?
• RQ5 Does the observed dynamics in weak thermalization correspond to thermal entanglement in the long-time limit?

Key findings

• The local observable 〈σᶻ(t)〉 converges to its thermal expectation value in the strong-thermalization regime, with initial state |π, 0⟩ showing no oscillations.
• In the weak-thermalization regime, the local observable 〈σᶻ(t)〉 exhibits persistent oscillations around the thermal value, only reaching it under time averaging.
• The entanglement entropy (EE) of single-qubit subsystems clearly distinguishes strong from weak thermalization, with higher and more stable EE in the strong regime.
• The concurrence of nearest-neighbor qubits shows a finite value in the weak-thermalization regime, consistent with thermal entanglement at Jβ ≈ −1.034.
• Numerical simulations including decoherence (T₁ ≈ 23.6 µs, T₂ ≈ 3.82 µs) show good agreement with experimental data for both EE and concurrence.
• The time-averaged entanglement entropy matches experimental data best when decoherence is included in the simulation, confirming its critical role in realistic dynamics.