Faster, shallower, more accurate method for quantum computational chemistry

Christopher K. Long, Kieran Dalton, David R. M. Arvidsson-Shukur, and Normann Mertig

Date & time: 17 June 2022 13:40–14:00 CEST

Location: Linnæus University, Växjö, Sweden

Conference: Quantum Information and Probability: from Foundations to Engineering (QIP22)  [1]

I presented work from Layering and subpool exploration for adaptive variational quantum eigensolvers: Reducing circuit depth, runtime, and susceptibility to noise  [2].

Download slide deck: PPTX¹, PDF¹

Abstract

From Ref.  [3]:

We propose a new algorithm, the sub-pool algorithm, for dynamically constructing ansätze for variational quantum eigensolvers (VQE) in the context of quantum computational chemistry. VQEs are a class of quantum-classical hybrid algorithms that use the variational principle to obtain an upper bound to the lowest eigenvalue of a Hermitian matrix, $H$, such as a Hamiltonian. VQEs consist of a parameterised quantum circuit $U(\theta )$ called the ansatz with a fixed input state $|\psi ⟩$ that is optimised with respect to $⟨\psi |U^{†}(\theta )HU(\theta )|\psi ⟩$. Previous approaches for dynamic ansätze construction, such as ADAPT-VQE and QEB-ADAPT-VQE, iteratively append parameterised unitaries (elements) from a set of unitaries (the pool $\mathcal{P}$) to the ansätze. The elements are selected based on the evaluation of some loss function for all elements in the pool. Our sub-pool algorithm produces shallower ansätze with lower CNOT depth using less loss function evaluations per appended element, $N$, than previous known methods. This is achieved by searching the pool in sub-pools, with maximum cardinality $C$, of all the elements non-commuting with the current best element. Doing so identifies elements that will not block the addition of a better element. We show that $\Omega (C)\le N\le \mathcal{O}(|\mathcal{P}|)$ for our sub-pool algorithm in comparison to $N=\Theta (|\mathcal{P}|)$ with previous methods. The algorithm is outlined as a sequence of interchangeable procedures for which several procedures are numerically compared: demonstrating an advantage in the number of Hamiltonian evaluations for molecules with 12 basis orbitals; and displaying comparable rates of convergence with previous methods as a function of the number of elements.

References

[1]

https://www.lnu.se/en/meet-linnaeus-university/current/events/2022/qip22, 2022, Internet Archive: https://web.archive.org/web/20220613173439/https://lnu.se/en/meet-linnaeus-university/current/events/2022/qip22/. ↩

[2]

Christopher K. Long, Kieran Dalton, Crispin H. W. Barnes, David R. M. Arvidsson-Shukur, and Normann Mertig. Layering and subpool exploration for adaptive variational quantum eigensolvers: Reducing circuit depth, runtime, and susceptibility to noise, Phys. Rev. A 109, 042413 (2024), DOI: 10.1103/PhysRevA.109.042413. ↩

[3]

Quantum Information and Probability: from Foundations to Engineering (QIP22) Abstracts and Posters (2022), Internet Archive: https://web.archive.org/web/20230606012900/https://lnu.se/contentassets/437bc2d832dc40689250e3279ad29f0e/abstracts_posters_qip22.pdf. ↩

Footnotes

1. Licence of this file: CC BY 4.0 and Third-party all rights reserved; see its entry on the licences page for what each licence covers and the copyright holders. ↩ ↩²