Relaxation and Thermalization

Yun Li

Tabea Herrmann, Felix Fritzsch, Arnd Bäcker

Isolated quantum systems typically approach thermal equilibrium as described by the Eigenstate Thermalization Hypothesis (ETH). Going beyond this involves either higher order correlators (full thermalization) or the formation of state designs, i.e., the approach of moments of state ensembles after a projective measurement towards thermal equilibrium (deep thermalization). We compare these two extensions of ETH using extensive numerical studies within a paradigmatic model for chaotic many-body quantum dynamics. For this we find exponential relaxation for both extensions: For deep thermalization all moments relax with the same rate, which approximately equals the relaxation rate of the autocorrelation function captured by ETH. In contrast, higher order correlation functions in full thermalization approach equilibrium faster. This means that at higher orders full thermalization is faster than deep thermalization.

Enhyeok Jang, Seungwoo Choi, Youngmin Kim +2 more

One of the predominant causes of program distortion in the real quantum computing system may be attributed to the probability deviation caused by thermal relaxation. We introduce Barber (Balancing reAdout Results using Bit-invErted ciRcuits), a method designed to counteract the asymmetric thermal relaxation deviation and improve the reliability of near-term quantum programs. Barber collaborates with a bit-inverted quantum circuit, where the excited quantum state of qubits is assigned to the |0〉 and the unexcited state to the |1〉. In doing so, bit-inverted quantum circuits can experience thermal relaxation in the opposite direction compared to standard quantum circuits. Barber can effectively suppress the thermal relaxation deviation in program's readout results by selectively merging distributions from the standard and bit-inverted circuits.

Kevin Dusling, Thomas Epelbaum, François Gelis +1 more

Jin-Fu Chen, Kshiti Sneh Rai, Patrick Emonts +5 more

Understanding and optimizing the relaxation dynamics of many-body systems is essential both for foundational studies in quantum thermodynamics and for applications such as quantum simulation and quantum computing. Efficient preparation of thermal states of a many-body Hamiltonian is governed by the spectral properties of the associated Lindbladian, in particular its spectral gap, which determines the slowest relaxation rate. In this work, we develop a systematic framework for constructing Lindbladians that prepare thermal states. Our approach reveals a simple relation between the relaxation dynamics at finite and infinite temperatures. The framework is scalable to larger system sizes when implemented using tensor-network methods. We find that efficient thermalization requires that the relaxation dynamics respect the symmetries of the thermal state, which reduces the number of free parameters. By applying gradient-based optimization to the Lindbladians, we enhance the spectral gap and thereby boost thermalization. When applied to both classical and quantum spin models, our method demonstrates a substantial enhancement of the spectral gap. For larger system sizes, our approach provides a variational upper bound and enables a certified lower bound on the minimum relaxation rate.

V. M. Akulin, N. V. Karlov