Extending Adaptive Methods for Finding an Optimal Circuit Ansatze in VQE Optimization

[camponogaraviera]

Team Name:

Hackeinberg.

Project Description:

Most widely considered hardware-efficient and Chemistry-inspired ansatze, although generic, suffer from either barren plateaus [1] or inconsistency under low-order trotterization steps [2], respectively. To circumvent this drawback, different algorithms for optimization of variational quantum circuits (VQA), the so-called adaptive circuits, have already been proposed in the literature [4]. One example is the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) [3]. In a nutshell, the ADAPT-VQE approach is to grow the ansatz by adding fermionic operators one-at-a-time so to preserve the amount of correlation energy. This approach can also be regarded as a particular optimization procedure for Full Configuration Interaction (FCI) VQE.

In this work, we extended some of the existing methods applied to the hybrid quantum-classical VQE [5] algorithm for the particular case of the ground state of the LiH molecule. We prioritized the minimization of the circuit depth (the longest sequence of gates acting on a qubit register) at the cost of increasing parameter count (the number of parameters to be optimized) given their tradeoff between difficulty in implementation on NISQ devices vs difficulty in optimization on classical computers, respectively. The baseline approach took into consideration the following features for a good ansatz:

1. Coherence friendly: the circuit must be shallow, i.e, have a small number of layers in order to be computed during a time window smaller than the decoherence time.
2. Hardware friendly (qubit routing): gate coupling allowed only between nearest-neighbor qubits to avoid SWAP gates during qubit routing (mapping from the circuit diagram to a hardware topology).
3. Small number of hyperparameters: we seek the minimum amount of angles to be optimized in order to avoid classical optimization overhead (when classical computation becomes too expensive).

In this first stage of the work, our goal was to find a quasi-optimal ansatz by restricting the VQE simulation to single and double order excitations only. For the future, we plan to use a deep reinforcement learning approach to learn an exact circuit ansatz considering higher excitation orders and the Qamuy SDK that was not possible given the short time window.

References

[1] McClean, J.R., Boixo, S., Smelyanskiy, V.N. et al. Barren plateaus in quantum neural network training landscapes. Nat Commun 9, 4812 (2018).

[2] Grimsley, H. R.; Claudino, D.; Economou, S. E.; Barnes, E.; Mayhall, N. J. Is the trotterized uccsd ansatz chemically well-defined? J. Chem. Theory Comput. 2020, 16, 1.

[3] Harper R. Grimsley, Sophia E. Economou, Edwin Barnes, Nicholas J. Mayhall, “An adaptive variational algorithm for exact molecular simulations on a quantum computer”. Nat. Commun. 2019, 10, 3007.

[4] PennyLane dev team, "Adaptive circuits for quantum chemistry". PennyLane, 13 September 2021.

[5] Peruzzo, A., McClean, J., Shadbolt, P. et al. A variational eigenvalue solver on a photonic quantum processor. Nat Commun 5, 4213 (2014).

Presentation:

GitHub.

Source code:

GitHub.

Which challenges/prizes would you like to submit your project for?

• Quantum Chemistry Challenge.
• Science Challenge.