Uncovering and Circumventing Noise in Quantum Algorithms via Metastability

TL;DR

Near-term quantum devices suffer from noise that obscures quantum advantage. The authors exploit metastability in open quantum systems to design noise-resilient digital and analog algorithms, using a computable resilience metric $\lambda_M$ and an efficiently upper-bounded bound $\tilde{\lambda}_M$ that does not require full circuit simulation. They develop a GKLS-based framework, apply it to variational quantum algorithms and adiabatic state preparation, and validate the concepts with experiments on IBM superconducting devices and D-Wave annealers, including a supplemental analysis of hardware-efficient ansatzes. The results show that aligning algorithmic symmetries with the metastable noise can yield intrinsic resilience without extra encoding, potentially enabling deeper circuits on NISQ hardware, and they extend the analysis to non-unital noise regimes observed in annealers. Overall, the work provides a practical, cross-platform noise-aware paradigm for robust quantum computation and motivates further study of metastability in quantum devices.

Abstract

The presence of noise is the primary challenge in realizing fault-tolerant quantum computers. In this work, we introduce and experimentally validate a novel strategy to circumvent noise by exploiting the phenomenon of metastability, where a dynamical system exhibits long-lived intermediate states. We demonstrate that if quantum hardware noise exhibits metastability, both digital and analog algorithms can be designed in a noise-aware fashion to achieve intrinsic resilience. We develop a general theoretical framework and introduce an efficiently computable noise resilience metric that avoids the need for full classical simulation of the quantum algorithm. We illustrate the use of our framework with applications to variational quantum algorithms and analog adiabatic state preparation. Crucially, we provide experimental evidence supporting the presence of metastable noise in gate-model quantum processors as well as quantum annealing devices. Thus, we establish that the intrinsic nature of noise in near-term quantum hardware can be leveraged to inform practical implementation strategies, enabling the preparation of final noisy states that more closely approximate the ideal ones.

Figures (5)

• Figure 1: Schematic illustration contrasting a noise-sensitive algorithm, whose final output approaches a fully mixed state, with a metastability-based algorithm, whose output remains close to the ideal target state. For different algorithms that give the same final state $\rho_f^I$, leveraging metastability allows selecting the one that, under noise conditions, prepares a final state $\rho_f^N$ that is closer to the desired one.
• Figure 2: (a) Ansatz used in the numerical simulations. (b) Absolute value of the cost-function derivative with respect to $\theta_{1,1}$. (c) Distance between the cost-function value obtained from the circuit output and the one relative to the fully mixed state. All the points are averages over $10^{4}$ random circuit initializations. Noise parameters are fixed to $q_x = q_z=0.5$, $q_y = 0$, taking $n=8$. A significantly slower decay is found for the noise-adapted ansatz.
• Figure 3: Difference between the observable expectation values evaluated on the circuits implemented on the $\texttt{ibm\_fez}$ device and the one theoretically evaluated on the fully mixed state. Each point has been averaged on $100$ random circuit initializations, while each sample is estimated using $10000$ shots. The number of the considered device lines used for building both circuits is $n=12$. The green line represents the ideal average distance, which coincides for both circuits.
• Figure 4: Fidelity evolution over time for the Adiabatic State Preparation example. (a) Noiseless case. (b) Noisy case. The total evolution time is fixed at $T=100$, and the system size is $n=5$.
• Figure 5: (a) Annealing schedules implemented in the D-Wave devices. The forward protocol is shown in red, while the reverse protocol is in blue. (b–d) Relative errors between the experimentally measured average energy and the theoretically expected value for the Advantage_system4.1, Advantage_system6.4, and Advantage2_system1.5 machines, respectively. Each experimental point is computed taking $1000$ samples. Statistical uncertainties were found to be negligible.