Universally Robust Control of Open Quantum Systems

Abstract

Mitigating noise-induced decoherence is the central challenge in controlling open quantum systems. While existing robust protocols often require precise noise models, we introduce a universal framework for noise-agnostic quantum control that achieves high-fidelity operations without prior environmental noise characterization. This framework capitalizes on the dynamical modification of the system-environment coupling through control drives, an effect rigorously encoded in the dynamical equation. Since the derived noise sensitivity metric remains independent of the coupling details between the system and the environment, our protocol demonstrates provable robustness against arbitrary Markovian noises. Numerical validation through quantum state transfer and gate operations reveals near-unity fidelity ($>\!99\%$) across diverse noise regimes, achieving orders-of-magnitude error suppression compared to target-only approaches. This framework bridges critical gaps between theoretical control design and experimental constraints, establishing a hardware-agnostic pathway toward fault-tolerant quantum technologies across platforms such as superconducting circuits, trapped ions, and solid-state qubits.

Figures (3)

• Figure 1: Universally robust quantum state transfer in a two-level system. Quantum state transfer from initial state $\hat{\rho}_{-x}$ to target state $\hat{\rho}_{+x}$ under environmental noise. Dash-dotted lines: target-only control ($c=0$); solid lines: universally robust control ($c=10^{-2}$). (a) State infidelity $1-\mathcal{F}_{\rm state}$ versus coupling strength $\lambda$ for specific noise ($\hat{A} = \hat{\sigma}_z$). Inset: Infidelity versus $c$ for $\lambda=0.1$. (b) $1-\mathcal{F}_{\rm state}$ for generic noise ($\hat{A} = \mathbf{n}\cdot\hat{\boldsymbol{\sigma}}$; $\mathbf{n}$: random unit vector). Data averaged over 100 realizations and the error bars indicate the standard deviation. (c) Optimized control fields $u_x(t)$ and $u_y(t)$ for $\hat{A} = \hat{\sigma}_z$ and $\lambda=0.1$. The values of the time-integrated control power, $\bar{u}_{x,y}=\int_{0}^{\tau }u_{x,y}^{2}(t){\rm d}t$, are indicated in the legends. (d) State evolution trajectories on Bloch sphere for $\hat{A} = \hat{\sigma}_z$ and $\lambda=0.1$. The evolution trajectory is color-coded to represent the purity of the state. Initial state: black square. Final states: blue dot (target-only) and green diamond (universally robust control). Parameters: Total control time $\tau=2/\Delta$ and inverse temperature $\beta = 1/\Delta$.
• Figure 2: Universally robust control for single-qubit Hadamard gate. Dash-dotted lines: target-only control ($c=0$); Solid lines: universally robust control ($c=10^{-2}$). (a) Gate infidelity $1-\mathcal{F}_{\rm gate}$ versus coupling strength $\lambda$ for specific noise ($\hat{A} = \hat{\sigma}_z$). Inset: Infidelity versus $c$ for $\lambda=0.1$. (b) $1-\mathcal{F}_{\rm gate}$ for generic noise ($\hat{A} = \mathbf{n}\cdot\hat{\boldsymbol{\sigma}}$; $\mathbf{n}$: random unit vector). Data averaged over 100 realizations and the error bars indicate the standard deviation. (c) Optimized control fields $u_x(t)$ and $u_y(t)$ for $\hat{A} = \hat{\sigma}_z$ and $\lambda=0.1$. The values of the time-integrated control power, $\bar{u}_{x,y}=\int_{0}^{\tau }u_{x,y}^{2}(t){\rm d}t$, are indicated in the legends. (d) State evolution trajectories on Bloch sphere under the Hadamard gate (from the $x$ to the $z$ direction) for $\hat{A} = \hat{\sigma}_z$ and $\lambda=0.1$. The evolution trajectory is color-coded to represent the purity of the state. Initial state: black square. Final states: blue dot (target-only) and green diamond (universally robust control). Parameters: Total control time $\tau=2/\Delta$ and inverse temperature $\beta = 1/\Delta$.
• Figure 3: Universally robust control for two-qubit CZ gate. Dash-dotted lines: target-only control ($c=0$); solid lines: universally robust control ($c=10^{-2}$). (a) Gate infidelity $1-\mathcal{F}_{\rm gate}$ versus coupling strength $\lambda$ for specific noise ($\hat{A}=\hat{\sigma}_y \otimes \hat{\sigma} _0$). Inset: Infidelity versus $c$ for $\lambda=0.1$. (b) $1-\mathcal{F}_{\rm gate}$ versus $\lambda$ for generic noise [$\hat{A}=\sum_{\mu\nu}a_{\mu\nu} \hat{\sigma} _\mu \otimes \hat{\sigma} _\nu$, where the random coefficients $a_{\mu\nu}\sim N(0,1)$ with $\sum_{\mu\nu}a^2_{\mu\nu} = 1$]. Data averaged over 100 realizations and the error bars indicate the standard deviation. (c) Optimized control fields $u _{j}(t)$ ($j=1,2,3,4$) for $\hat{A}=\hat{\sigma} _y \otimes \hat{\sigma} _0$ and $\lambda =0.1$. The values of the time-integrated control power, $\bar{u}_{j}=\int_{0}^{\tau }u_{j}^{2}(t){\rm d}t$, are indicated in the legends. Parameters: Total control time $\tau=2.5/\Delta$ and inverse temperature $\beta = 1/\Delta$.