Robustness of the quantum Mpemba effect against state-preparation errors

TL;DR

The paper investigates how initial-state preparation errors affect two forms of quantum Mpemba-like effects: open-system accelerated thermalisation under GKSL dynamics and closed-system accelerated symmetry restoration in a $U(1)$-symmetric random unitary circuit. The open-system approach relies on preparing a state with zero overlap with the slowest decaying Liouvillian mode, yielding an exponential speed-up with relaxation governed by $\tau_2 = 1/\mathrm{Re}(l_2)$; however, this speed-up is exponentially quenched by even modest preparation errors $\varepsilon$. In contrast, the closed-system RUC mechanism is robust to state-preparation noise, with small errors having little effect and larger errors potentially enhancing thermalisation by increasing overlaps with high-dimension charge sectors, indicating a noise-assisted regime. Overall, robustness to state-preparation errors depends strongly on the QME mechanism, highlighting the need for model-specific error analyses to assess practical feasibility in NISQ devices.

Abstract

The quantum Mpemba effect (QME) is a phenomenon observed in many-body systems where initial systems configurations farther from equilibrium can be observed to equilibrate faster than configurations that are closer to it. By considering noise induced error in the initial system state preparation, we analyse the robustness of various models exhibiting the QME. We demonstrate that exponentially accelerated thermalisation in open system dynamics modelled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation is highly sensitive to noise induced deviations in the initial state, making this approach to accelerated thermalisation difficult to achieve. In contrast, we demonstrate that accelerated restoration of symmetry in $U(1)$ symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, we show that this can in fact induce a higher rate of symmetry restoration and a stronger QME.

Figures (8)

• Figure 1: Schematic of two layers of a $U(1)$ symmetric RUC applied to a chain of $N$ spin-1/2 particles, with periodic boundary conditions. $U_T$ represents one complete layer of the circuit, with $U_{ij}$ representing a $U(1)$ symmetric unitary acting on spins $i$ and $j$.
• Figure 2: Hilbert-Schmidt distance $\Delta$ as a function of time $t$ for the Dicke model with $N=40$ spins. Original state is a random pure state presented in comparison with corresponding orthogonalised states with preparation error $\varepsilon$.
• Figure 3: Time of thermalisation $t_{eq}$ as a function of state preparation error $\varepsilon$, with differing thermalisation boundaries $\eta$ for the Dicke model with $N=40$ spins.
• Figure 4: Relative speed-up as a function of error $\varepsilon$ for the Dicke model with (a) varying number of spins $N$ and (b) varying initial states of $N=20$ spins.
• Figure 5: Hilbert-Schmidt distance $\Delta$ as a function of time $t$ for a SHO coupled to a thermal bath with occupation of up to the $N=20$th level. Original state is a random pure state presented in comparison with corresponding diagonalised state.