False Positives of Observable Evaluation induced by Misapplying of Quantum Readout Error Mitigation with Initialization Error Neglected

Abstract

Quantum readout error mitigation is essential for noisy intermediate-scale quantum devices to achieve reliable data. The conventional approaches, conflating initialization errors with measurement errors, not only suppress the influence of measurement errors, but also strengthen that of initialization errors, which is a systematic bias. Here, we demonstrate this exponentially growing bias leads to significant implications. It causes severe fidelity overestimation and gives out false positive results on large-scale entangled state characterizing. Similarly, the results from algorithms like the variational quantum eigensolver and time evolution also deviate negatively, and cover up other errors in the quantum circuit. These findings highlight the critical need for rigorous benchmarking and careful management of initialization errors. Consequently, we establish an upper bound for the tolerable initialization error rate to ensure effective error mitigation at a given system scale.

Figures (5)

• Figure 1: Fidelity overestimation of large-scale entangled states. (a) The fidelity overestimation of different entangling states, including the linear graph state, the star-liked graph state, the fully-connected graph state, the linear GHZ state, and the squared-grid graph state. The data of square graph with its average and its standard deviation is calculated by random sampling methods, and the others are exact solutions by dynamic programming. We also calculate a state which is consisted by $n/2$ pairs of two-qubit graph state (the $2$-cluster). Despite its slower growth, the fake fidelity $\tilde{\mathcal{F}}$ of the $2$-cluster still increases exponentially. Here, only SPAM error is considered ($\tilde{\rho}_i$) and the initialization error rate is set to be $q=0.01$. The overestimation of the $10$-qubit linear graph state (labeled by blue dots) and the $10$-qubit linear GHZ state (labeled by green crosses) are illustrated with depolarization error of controlled-Z (CZ) gates in (b) and with controlled-rotation error in (c), respectively.
• Figure 2: VQE simulation results for hydrogen chain. (a) $4$-qubit UCCSD circuit demonstration. Optimized ground state energy error with the initialization error rate (b) $q=0.001$ and (c) $q=0.06$ for H$_{2}$ (4 qubits) to H$_{10}$ (20 qubits).
• Figure 3: Time evolution errors under initialization error and conventional QREM. Lower subplot shows Trotter error at initialization error $q=0.06$. Upper subplot displays time evolution errors with respect to $N_s$ for varying qubit number $n$.
• Figure 4: The QREM induced error as a function of qubit number and initialization error. Different lines delineate the upper bound on initialization error for a given system size. Only when system parameters fall below these lines can the error in the resulting outcome be rigorously bounded.
• Figure S1: Topology structures, state representations, and state transitions of several typical entangling state.