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 Variational Quantum Eigensolver: a review of methods and best practices

“…Finally, appropriate mitigation of quantum noise is likely required for VQE. Variational algorithms have been shown to exhibit at least some degree of ability to learn the biases created by quantum noise [37,74,75]. However, further methods, such as symmetry verification and extrapolation based methods, despite coming at a significant computational cost, could be required to achieve the target accuracy with VQE.…”

“…Conversely, it was suggested in the early days of VQE that variational algorithms possess inherent noise resilience since the optimization can effectively adapt to the noise [37]. This resilience has helped VQE to be more successful than other algorithms on the current generation of quantum devices, and has been numerically demonstrated in small qubit simulations [74]. However, it remains unclear whether this resilience from noise can be retained in larger quantum experiments, where one is confronted with a more complex ansatz, with more noise coming from the difficulty of controlling large numbers of qubits with precision.…”

“…Second, parallelization could result in higher noise levels. We note two possible sources of additional noise: (1) if parallelization is done on multi-threaded quantum computers, there is higher chance of cross-talk between qubits; (2) variational algorithms are considered to be somewhat noise resilient as they can learn the systematic biases of a given hardware [37,74] -if the algorithm is run on multiple quantum computers these noise resilient effects may disappear, as systematic biases on one set of qubits, which differs on another, may no longer be learned through the variational process.…”

“…Finally, the extent to which VQE is resilient to quantum noise, and its ability to be mitigated in a tractable manner, remains unclear. Variational algorithms have the advantage of exhibiting some ability to learn away certain types of systematic noise [74,75]. While it was also shown that the cost of several error mitigation methods may largely outweigh the benefits [76], the question of the impact of quantum noise on VQE results and the predictability of these errors should be studied in much further depth than has been done so far.…”

Recompilation-enhanced simulation of electron-phonon dynamics on IBM Quantum computers

“…Important example of this include studying the conditions required for optimal energy transfer [53] and fitting values to unknown system parameters based on experimental data [54]. Notably, solving such problems can be done in the presence of noise [55,8], making it an appealing application for nearterm quantum computers. Thus, using real quantum hardware to solve optimisation problems involving electron-phonon systems would represent an interesting extension of the results presented in this work.…”