The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry
By Waheeda Saib, Research Scientist at IBM Quantum, IBM Research-Africa in Johannesburg, South Africa
Perhaps one of the most well-known near-term quantum algorithms is the variational quantum eigensolver (VQE). This algorithm begins with a quantum circuit, called an ansatz, that is parametrized, meaning the results of its gates rely on an inputted variable. We take this ansatz and attempt to bring it closer to the correct answer through repeated classical optimization, updating the parameters after each run until the circuit represents an optimal solution.
The VQE algorithm is important especially for finding the ground-state energy in chemistry problems and may even begin to offer speedups on near-term quantum hardware — that is, hardware limited by qubit number, qubit connectivity, gate errors, and decoherence. Given these noisy processors, how do we know the best ansatz to start with?
In our study, presented at the technical paper track at IEEE QCE 2021 and published in IEEE Xplore, we focused on how noise can influence which ansatz family is best for a quantum chemistry problem. We began with twelve different ansatzes with each circuit employing four qubits. We applied each of these ansatzes to the VQE algorithm to find the ground state energy of the hydrogen molecule, and ran the algorithm on both the ideal and noisy qasm simulators in Qiskit. We ranked the performance of each ansatz using two metrics: 1. A metric called expressibility, which is a measure designed to understand the capability of parametrized quantum circuits under ideal conditions and 2. By comparing the difference between the actual and computed ground state energy of hydrogen.
Our simulations demonstrated that the intensity of the noise has a significant effect on which ansatz results in a solution closest to the classically known answer. This demonstrates that an ansatz selected under ideal quantum conditions is not necessarily the best ansatz when performing the problem on noisy quantum simulators or actual quantum hardware. Conversely, deciding on an ansatz informed by noisy quantum simulations or actual quantum device runs leads to a more accurate decision on the optimal ansatz to choose.
Not only does the amount of noise play a role in ansatz selection, but changing the noise model has an impact on ansatz performance as well. Interestingly, we note that the ranking of the optimal ansatz for a chemistry problem does not remain constant for the different IBM quantum device simulators. To decide on the optimal ansatz to use in practice, one should avoid simulations performed in the absence of noise, or on different noise models, since circuit performance is coupled to the noise model of the quantum device used. In short, we found that the performance of the VQE algorithm is closely coupled to the specific hardware with respect to the noise levels and quantum architecture.
We finally analyzed how the expressibility measure plays into ansatz selection in the presence of noise. “Expressibility is a measure of a parameterized quantum circuit’s ability to generate states from the Hilbert space,” and you can read more about it here. We performed an analysis of how expressibility correlates with the performance of circuits applied to VQE for finding the ground state energy of hydrogen. Our study revealed that expressibility unfortunately did not correlate with the performance of the corresponding circuits for a quantum chemistry problem. Additionally, we discovered that expressibility changes significantly simply by changing the parameter sampling methodology for a given circuit. This indicates, that expressibility may not be a suitable measure for selecting optimal ansatz within VQE for chemistry applications when using noisy simulations or hardware.
Given the impact of ansatz selection on a VQE algorithm’s performance, it’s important that researchers continue to design quantum algorithms with a hardware-aware mindset. Thinking about algorithms, circuits, and hardware together could help mitigate noise and enable optimal VQE performance.
For more stories like these, subscribe to the Qiskit blog!
