Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

Abstract

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. In this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.

Figures (2)

• Figure 1: Magnitude of the density matrix elements in the $\mathfrak{q}$-basis for the TFIM with four spins, averaged over the pink noise ensemble with (a) global dephasing noise and (b) local dephasing noise. The symmetry representation decomposes the Hilbert space into three sectors: $j=\{0, 1, 2\}$. Panel (a) demonstrates that symmetry-preserving noise causes decoherence exclusively in the SPS. In contrast, in panel (b), local dephasing leads to specific transitions out of the SPS, constrained by symmetry. The averaged faulty quantum state is block diagonal in the symmetry representation. Each calculation is averaged over an ensemble of 20,000 noise trajectories. The simulation time is $T \approx 2\tau$, where $\tau$ is the noise correlation length. The correlation length was found by fitting an exponential curve to the autocorrelation function $C(t)=\mathcal{F}^{-1}_t[S(\omega)]$.
• Figure 2: Magnitude of the density matrix elements in the $\mathfrak{q}$-basis for the $[[4,2,2]]$ code, averaged over the pink noise ensemble with (a) $X$ noise and (b) multiaxis noise. Panel (a) demonstrates that the model preserving the $X$ parity causes decoherence within the symmetric subspace and transitions flipping the Z parity. In contrast, in panel (b), the model breaks both symmetries, which leads to transitions out of the symmetric subspace into the other three eigenspaces.