Superposed Quantum Error Mitigation

Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary states. We demonstrate, numerically and on the IBM Quantum Platform, that parallel applications of the same operation lead to significant noise mitigation when arbitrary noise processes are considered. We first design probabilistic implementations of our scheme that are plug and play, independent of the noise characteristic and require no postprocessing. We then enhance the success probability (up to deterministic) using adaptive corrections. We provide an analysis of our protocol performance and demonstrate that unit fidelity can be achieved asymptotically. Our approaches are suitable to both standard gate-based and measurement-based computational models.

Figure 1

Illustration of the strategy for enhancing the fidelity of noisy gate-based (a) and measurement-based (b) computations. The protocol steps from one to six (described in the main text) are highlighted. The input (auxiliary) state follows the superposed green (orange) paths depending on the state of the control.

Figure 2

Postselection probability $P$ and infidelity ratio $\mathcal{R}$ in different scenarios. Full and dashed lines are characterized by ${\omega }_1<1$ and ${\omega }_1=1$, respectively. In (a)–(c), the probabilistic scheme is considered, $U=\text{cNOT}$ followed by dephasing noise. In panel (c) we set $p_{\mathrm{ne}}=0.9$ [dotted, red line in (b)] and show $\mathcal{R}$ for varying ${\omega }_1$. In (d), the deterministic protocol is applied to a $T$ gate affected by dephasing. In (e), the detrimental contribution of noise from the cSWAP is investigated for ${\omega }_1=1$. We consider the MB implementation of the probabilistic protocol for $U=[\text{cNOT}(T\otimes T){]}^{N_{\mathrm{L}}}$, and depolarizing noise with error probabilities $1-p_{\mathrm{ne}}$ affecting each qubit of the resource state (including the ones implementing the cSWAPs). In (f), SQEM is demonstrated on the quantum computer “ibm_perth,” with $|{\psi }_{\mathrm{in}}⟩=|{\varphi }_0⟩=|+⟩$ and $U=\mathbb{1}$. Dots correspond to real device data (error bars are negligible compared to the size of the dots), while the lines represent the expected simulated behavior obtained by modeling each cNOT within the two cSWAP gates as a perfect operation followed by a depolarizing channel with noise parameters extracted from experimental data (see main text).