Evaluating the noise resilience of variational quantum algorithms

Abstract

We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We first use a variational quantum eigensolver to find the ground state of a Hamiltonian in presence of noise, and adopt two quality measures in addition to the energy, namely fidelity and concurrence. We then extend the task to the one of constructing, with a layered quantum circuit ansatz, a set of general random target states. We determine the optimal circuit depth for different types and levels of noise, and observe that the variational algorithms mitigate the effects of noise by adapting the optimized parameters. We find that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise. For such overparameterised circuits different sets of parameters can result in the same final state in the noiseless case, which we denote as parameter degeneracy. Numerically, we show that this degeneracy can be lifted in the presence of noise, with some states being significantly more resilient to noise than others. We also show that the average deviation from the target state is linear in the noise level, as long as this is small compared to a circuit-dependent threshold. In this region the deviation is well described by a stochastic model. Above the threshold, the optimisation can converge to states with largely different physical properties from the true target state, so that for practical applications it is critical to ensure that noise levels are below this threshold.

The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry

“…Recent studies exploring the effect of noise on variational quantum algorithms, employed different noise models, types of noise and noise levels to assess the VQE performance using the hardware efficient ansatz [11], [12]. These studies only explore two specific hardware efficient circuit layouts with different parameterized gates and circuit layers, while the effect of noise is not as well studied for quantum chemistry.…”

“…This finding demonstrates, that noise affects the expressibility of different parameterized circuit families in different way. This observation is especially relevant since studies such as [11], [12] base the decision of the ansatz to use on the classically simulated results of a set of circuits studied in the expressibility paper [8], without delving in the robustness of this measure in real noisy setting.…”

Towards Cosmological Simulations of Dark Matter on Quantum Computers

“…Different types of noise affect a quantum calculation, for which noise-resilient techniques are being developed (Fontana et al 2020). We do not consider full hardware and measurement noise, but investigate the effect of adding random Gaussian errors to the variational parameters (λ ← λ + δλ) after each timestep to examine how errors may propagate during the nonlinear time evolution.…”

Universal noise-precision relations in variational quantum algorithms

“…As numerical simulations of noisy quantum computers on classical computers are heavy and limited to small scale problems, analytic estimations of the impact of the noise are urgent for obtaining knowledge about intermediate scale problems with potential quantum advantage. In fact, this issue has been actively studied in recent years, and some analytic results have been obtained, for example, on the noise resilience of the optimization results [27,28], noise-induced barren plateaus [29], noise-induced breaking of symmetries [30], effects of the noise on the convergence property of the optimizations in VQAs [31].…”