---
tags: VQE, NISQ, Noise, Numerical
sort-date: 2022-06-17
description: "Quantum Information and Probability: from Foundations to Engineering (QIP22) | 17 June 2022 13:40–14:00 CEST | Linnæus University, Växjö, Sweden"
---

[[/index|Christopher K. Long]]<a href="https://orcid.org/0009-0001-3230-942X"><font color="#a6ce39"><i class='fa-brands fa-orcid'></i></font></a>,
Kieran Dalton<a href="https://orcid.org/0009-0006-2416-356X"><font color="#a6ce39"><i class='fa-brands fa-orcid'></i></font></a>,
David R. M. Arvidsson-Shukur<a href="https://orcid.org/0000-0002-0185-0352"><font color="#a6ce39"><i class='fa-brands fa-orcid'></i></font></a>,
and Normann Mertig<a href="https://orcid.org/0000-0003-3025-7141"><font color="#a6ce39"><i class='fa-brands fa-orcid'></i></font></a>

**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)](https://www.lnu.se/en/meet-linnaeus-university/current/events/2022/qip22) [@qip22]

I presented work from [[/Articles/Layering and subpool exploration for adaptive variational quantum eigensolvers: Reducing circuit depth, runtime, and susceptibility to noise]] [@PhysRevA.109.042413].

Download slide deck: [[PowerPoints/Faster, shallower, more accurate method for quantum computational chemistry.pptx|PPTX]], [[PDFs/Faster, shallower, more accurate method for quantum computational chemistry.pdf|PDF]]

# Abstract

From Ref. [@qip22_abstracts]:

> 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 $\ket{\psi}$ that is optimised with respect to $\bra{\psi}U^\dagger(\theta)HU(\theta)\ket{\psi}$. 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.