Impact of unreliable devices on stability of quantum computations

TL;DR

This work tackles reliability and stability of quantum computations on NISQ devices under non-stationary noise by linking distributional changes in noise to output stability via the Hellinger distance $H$ and deriving a bound on stability $s_{max}$. It validates the framework with both synthetic depolarizing-noise models and real IBM Washington data using Monte Carlo methods to estimate joint noise distributions and their impact on a 5-qubit Bernstein-Vazirani circuit. The results show substantial non-stationarity in noise (reliability metric ranging from $41\%$ to $92\%$) and a conservative bound $s_{max$}$ that remains below observed stability oscillations, illustrating the device’s unreliability for reproducible mean outcomes in the BV benchmark. The methodology is general, modular, and applicable to larger-scale quantum systems, offering a principled approach to quantify reliability and guide calibration and error-mitigation strategies in the fault-tolerant transition.

Abstract

Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk and other sources of noise. This raises concerns regarding the stability of results when using NISQ devices since strategies for mitigating errors generally require well-characterized and stationary error models. Here, we quantify the reliability of NISQ devices by assessing the necessary conditions for generating stable results within a given tolerance. We use similarity metrics derived from device characterization data to derive and validate bounds on the stability of a 5-qubit implementation of the Bernstein-Vazirani algorithm. Simulation experiments conducted with noise data from IBM Washington, spanning January 2022 to April 2023, revealed that the reliability metric fluctuated between 41% and 92%. This variation significantly surpasses the maximum allowable threshold of 2.2% needed for stable outcomes. Consequently, the device proved unreliable for consistently reproducing the statistical mean in the context of the Bernstein-Vazirani circuit.

Figures (12)

• Figure 1: Daily estimates of the state preparation and measurement (SPAM) fidelity for two register elements in a superconducting device collected from 1-Jan-2022 to 30-Apr-2023. Day of the year is indexed starting with 1 and index 365 corresponds to Dec 31.
• Figure 2: A quantum circuit implementation of the Bernstein-Vazirani algorithm that employs 5 qubits, denoted $q_0$ to $q_4$. The first four qubits are used to compute the 4-bit secret string, while the fifth qubit serves as an ancilla and initially resides in the $\ket{-}$ superposition state. The symbol $H$ denotes the Hadamard gate while the oracle unitary ($U_r$) implements the secret string ($r$). The depolarizing noise channel is denoted by $\mathcal{E}_\text{x}(\cdot)$. A quantum measurement operation is represented by the meter box symbol at the circuit's end.
• Figure 3: Plot of the ratio of $s$ to the predicted upper bound $s_\text{max}$ for a circuit simulation with time-varying noise (with length of the secret string varying as 4, 8, and 12).
• Figure 4: Experimental heatmap for correlation between the 16 noise parameters defined in Table \ref{['tab:noiseParameters']} as observed in Apr-2023.
• Figure 5: Schematic layout of the $127$-qubit washington device produced by IBM. Circles denote register elements and edges denote connectivity of 2-qubit operations. The register elements $0$, $1$, $2$, $3$, and $4$ in Fig. \ref{['fig:bv_ckt_b']} are mapped to the physical qubits $4$, $3$, $2$, $1$, and $0$, respectively, in the diagram above. The CNOT gates used in the circuit connect the physical qubits $(0,1)$ and $(2,1)$, in the diagram above, where the first number represents the control qubit and the second one represents the target qubit.