[Paper Review] Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations

Simon Kochsiek, Federico Carollo+1 more|arXiv (Cornell University)|Apr 11, 2022

Quantum Information and Cryptography37 references49 citations

TL;DR

This paper demonstrates that global spin rotations—simple unitary transformations parameterized by two angles—can exponentially accelerate the relaxation of dissipative quantum spin systems to their stationary state, achieving a quantum Mpemba effect. By rotating the initial state to minimize overlap with the slowest-decaying dynamical mode, the system bypasses the spectral gap bottleneck, enabling faster dissipative preparation of quantum states in trapped-ion and ultracold-atom platforms.

ABSTRACT

We consider open quantum systems whose dynamics is governed by a time-independent Markovian Lindblad Master equation. Such systems approach their stationary state on a timescale that is determined by the spectral gap of the generator of the Master equation dynamics. In the recent paper [Carollo et al., Phys. Rev. Lett. 127, 060401 (2021)] it was shown that under certain circumstances it is possible to exponentially accelerate the approach to stationarity by performing a unitary transformation of the initial state. This phenomenon can be regarded as the quantum version of the so-called Mpemba effect. The transformation of the initial state removes its overlap with the dynamical mode of the open system dynamics that possesses the slowest decay rate and thus determines the spectral gap. While this transformation can be exactly constructed in some cases, it is in practice challenging to implement. Here we show that even far simpler transformations constructed by a global unitary spin rotation allow to exponentially speed up relaxation. We demonstrate this using simple dissipative quantum spin systems, which are relevant for current quantum simulation and computation platforms based on trapped atoms and ions.

Motivation & Objective

• To investigate whether simple global unitary transformations can accelerate relaxation in open quantum systems toward stationarity.
• To explore the feasibility of achieving the quantum Mpemba effect using experimentally accessible operations like global spin rotations.
• To identify parameter regimes where such acceleration occurs robustly in spin chains with power-law interactions.
• To provide a practical alternative to complex, analytically constructed unitaries for speeding up dissipative dynamics.
• To enable faster preparation of entangled and correlated states in quantum simulation and computation platforms.

Proposed method

• The study models driven-dissipative spin chains with power-law interactions and single-spin decay using a Markovian Lindblad Master equation.
• The relaxation dynamics is analyzed via the spectral gap of the dynamical generator, with the slowest-decaying mode dictating the timescale.
• Global unitary spin rotations are applied to the initial state, parameterized by polar and azimuthal angles (θ, φ), to reduce overlap with the slowest-decaying eigenmode.
• The effectiveness of each rotation is quantified by computing the overlap of the transformed state with the second-eigenmode (λ₂), which determines the spectral gap.
• Numerical simulations are performed across various interaction strengths and ranges to map the region of the unit sphere where exponential acceleration occurs.
• The method is validated by comparing results with the ideal unitary transformation from prior work, showing robustness even when analytical construction fails.

Experimental results

Research questions

• RQ1 Can global spin rotations induce exponential acceleration in the approach to stationarity in dissipative quantum spin systems?
• RQ2 What fraction of the rotation sphere (θ, φ) leads to a measurable quantum Mpemba effect in realistic spin chains?
• RQ3 How does the performance of global rotations compare to the analytically constructed ideal unitary in accelerating relaxation?
• RQ4 Is the quantum Mpemba effect robust across different interaction strengths and ranges in power-law interacting spin chains?
• RQ5 Can this approach be practically implemented in current quantum simulation platforms like trapped ions and ultracold atoms?

Key findings

• Global spin rotations with only two parameters (θ, φ) can induce exponential acceleration in relaxation dynamics, achieving the quantum Mpemba effect.
• A significant portion of the rotation sphere—spanning multiple angles—leads to accelerated relaxation, indicating robustness across parameter regimes.
• The method works even in cases where the ideal unitary from prior work cannot be analytically constructed, enhancing practical applicability.
• The acceleration arises from reducing the overlap of the initial state with the slowest-decaying mode (λ₂), thereby shifting the effective spectral gap to λ₃.
• The results are robust across different interaction strengths and ranges, with acceleration observed in both 2-, 3-, and 4-spin systems.
• The approach enables faster dissipative preparation of quantum states, with direct relevance to quantum computation and simulation in trapped-ion and ultracold-atom platforms.