Entanglement-Induced Resilience of Quantum Dynamics

Abstract

Quantum many-body devices suffer from imperfections that destabilize dynamics and limit scalability. We show that the dynamical growth of entanglement can intrinsically protect generic quantum dynamics against coherent and perturbative noise. Through rigorous theoretical analysis of general quantum dynamics and numerical simulations of spin chains and fermionic lattices, we prove that entanglement-entropy growth confines the influence of local Hamiltonian perturbations, thereby suppressing errors in dynamical errors. The degree of protection correlates quantitatively with the entanglement entropy of subsystems on which the perturbations act, and applies broadly to both analog quantum simulators and real-time control protocols. This entanglement-induced resilience is conceptually distinct from quantum error correction or dynamical decoupling: it passively leverages native many-body correlations without additional qubits, measurements, or control overhead. Our results reveal a generic mechanism linking entanglement growth to dynamical stability and provide practical guidelines for designing noise-resilient quantum devices.

Figures (11)

• Figure 1: Entanglement-induced resilience of quantum dynamics. The red shaded band shows the error envelope. Consider a local error Hamiltonian acting on a spin chain, where the error terms involve $k$ near-neighbour qubits and comprise $\text{poly}(k)$ Pauli operators with small coefficients. (a) When the quantum system exhibits weak or no entanglement, the dynamical error may scale linearly with the number of error terms, i.e., $\text{poly}(k)$. (b) In contrast, sufficient entanglement suppresses the dynamical error, leading to a scaling proportional to the square root of the number of error terms, i.e., $\sqrt{\text{poly}(k)}$.
• Figure 2: Error of Analog quantum simulation of 1D QIMF model in typical and atypical cases. The perturbation Hamiltonian is comprised of disorder terms with coefficients $\delta_i\in\mathcal{N}(0,0.01)$ and an imperfection term $\eta=0.01$. (a) Long-time analog simulation error. In typical input state, where the entanglement entropy grows during the system's evolution, our estimate closely matches the average-case performance, scaling with $\norm{H_{\text{pert}}}_F$. Notably, at early times when entanglement has not yet developed sufficiently, the error curve exhibits a slight curvature with a slope higher than the average-case estimate. However, after the entanglement saturates (around $t\approx0.5$), the error slope aligns with the average case, and our bound and the average-case bound run approximately parallel. In contrast, in an atypical input state, where the entanglement entropy remains low throughout the evolution, the error scaling deviates significantly from the average case and approaches the worst-case bound characterized by the spectral norm. (b) One-segment simulation error, $\|(U_0(\delta t)-U(\delta t))\ket{\psi(t)}\|_F$, evaluated for different initial states with $\delta t=0.1$. The corresponding entanglement entropy of two qubits ($S_{1,2},~S_{1,3},~S_{1,4},~S_{1,5}$) is also shown, illustrating how entropy growth correlates with error suppression.
• Figure 3: Error of one-segment analog simulation with Fermi-Hubbard model. The vertical axis represents the corresponding empirical error for each individual segment with segment length $\Delta t=0.1$. The system scale is set as $L=8$ and the noise strength is $\delta=0.01$. The initial state is prepared as (a) $\ket{\uparrow\downarrow}_1\ket{\uparrow\downarrow}_2\ket{\uparrow\downarrow}_3\ket{\uparrow\downarrow}_4$, (b) $\ket{\uparrow\downarrow}_1\ket{\uparrow\downarrow}_2\ket{\uparrow\downarrow}_4\ket{\uparrow\downarrow}_5$, (c) $\ket{\uparrow\downarrow}_1\ket{\uparrow\downarrow}_3\ket{\uparrow\downarrow}_5\ket{\uparrow\downarrow}_7$, (d) $\ket{\uparrow\downarrow}_1\ket{\uparrow\downarrow}_3\ket{\uparrow\downarrow}_4\ket{\uparrow\downarrow}_6$. The entanglement entropy is defined on the subsystem of two sites numbered as $(j,j+1),~(j,j+2),~(j,j+3),~(j,j+4)$, respectively. Entanglement entropy and the simulation error display an inverse relationship: as the entanglement entropy increases to the maximum 4 during the evolution, the simulation error reduces to the Frobenius norm level; when the entanglement entropy drops, the error exhibits sharp spikes.
• Figure 4: The contribution of Hermitian cross terms for both the typical and the atypical cases. The noise terms include both disorder and control imperfections. The Hermitian contribution is defined as ${\bra{\psi(t)} {{H^\dagger}_{\text{pert} j}} H_{\text{pert}j^\prime}+\text{H.C.}\ket{\psi(t)}}/{\norm{{{H^\dagger}_{\text{pert} j}} } \norm{H_{\text{pert}j^\prime}}}$, where $\ket{\psi(t=6)}$ is the evolved state for typical and atypical cases and $H_{\text{pert}j^\prime}$ is a Pauli string component in the perturbation Hamiltonian. These observables track whether the error behaves close to the Frobenius norm (typical) or drifts toward spectral‑norm (atypical) scaling.
• Figure 5: Subsystem entanglement and gate error. (a) Schematic partition of a quantum-control circuit for a target single-qubit gate into subsystem $A$ (the target qubit plus nearby qubits directly coupled to the control fields) and subsystem $B$ (the remaining register qubits). (b) Quantum-dot system driven with robust control pulses for a single-qubit gate. The optimal driving waveform for implement time $T=180$ns and target gates $X_\pi,X_{\pi/2},X_{2\pi}$, respectively. (c) Dependence of effective gate error on the entanglement entropy (higher temperature of purified Gibbs state, higher entanglement entropy) of the initial states with corresponding waveforms. We consider a 2D lattice in which 4 spectator qubits couple to the target (so $|A| = 5$ and $S_{\text{max}} = \log(2^5) = 5$). States are sampled as Gibbs states with temperatures $T$ chosen as $T\in\left\{\frac{1}{t}|t\in\{0.008,0.016,\dots,0.48\}\right\}$ (equivalently $T$ spanning $\approx 2.08 ~\text{to}~125$). As the entanglement entropy $S(A)$ approaches its maximum, the error bound rapidly decreases, indicating that greater preexisting entanglement between $A$ and $B$ suppresses the influence of gate imperfections.

Theorems & Definitions (9)

• Lemma 1
• Lemma 2
• Corollary 1: Bound on the difference between evolved states with time-dependent Hamiltonians
• Lemma 3: Entanglement-induced circuit resilience
• proof
• Corollary 2: 1-order approximation
• Corollary 3: 2-order approximation
• Lemma 4
• proof