Novel Ansätze for Stochastic Coupled Cluster

This thesis presents the development of two new types of algorithms in the framework of Coupled Cluster Monte Carlo (CCMC). First, the CCMC paradigm is expanded to multireference coupled cluster (MRCC). The multireference CCMC (mr-CCMC) approach takes advantage of Monte Carlo methods’ ca- pacity to treat any cluster expansion with little additional algorithmic difficulty to encode a MRCC wavefunction based on a fully arbitrary reference space and cluster truncation level. The technique is shown to be highly accurate even in regimes where single-reference CC methods fail, while only incurring a linear increase in memory requirements. The mr-CCMC approach is further expanded to build upon a Configuration Interaction Quantum Monte Carlo (CIQMC) reference wavefunction for more rapid convergence. Two approximations to the mr-CCMC method are also defined by allowing partial relaxation of the reference wavefunction in the presence of contributions from the external space. These are shown to reduce noise and generally increase stability relative to the original method, at the cost of slightly increased energy errors. Secondly, stochastic versions of the unitary coupled cluster (UCC) method and its disen- tangled variant are developed. These methods are shown to agree with their deterministic counterparts and can be easily extended beyond the single and double excitations trunca- tion commonly employed deterministically. The new Unitary Coupled Cluster Monte Carlo (UCCMC) algorithm is then used as a classical pre-processing step to decrease the complex- ity of wavefunction parametrisations for the Variational Quantum Eigensolver (VQE). The method is successful in significantly reducing the quantum resources required for VQE while maintaining accuracy, opening a potential route to allow larger quantum chemical problems to be treated on near-term noisy intermediate-scale quantum (NISQ) devices. Finally, the new developements in this work are combined to obtain a unitary stochastic representation of a MRCC wavefunction. Both UCCMC and the disentangled approximation are amenable to extension to a multireference treatment. While the disentangled form becomes intractable for moderate system sizes, multireference UCCMC shows promising results in stereotypical multi-configurational test cases.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2022

Author dc:creator

• Filip, Maria-Andreea

Advisor dc:contributor.advisor

• Thom, Alex

• Chemistry
• Theoretical chemistry
• Electronic structure theory
• Coupled cluster
• Monte Carlo algorithms
• Quantum computing

Licence

• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0002-9551-0235

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/342486