Presented By: Dissertation Defense - Department of Mathematics
Dissertation Defense: Exploration of Quantum-Inspired Deep Learning Architectures for Fundamental Applications in Scientific Computing
Oliver Knitter
Abstract:
Neural-network quantum states (NQS) is an exciting area of quantum-inspired machine learning, wherein in a fully classical neural network is used to efficiently learn the optimal state vector for a quantum unsupervised learning problem, bypassing the need to model the full exponentially large state space. In theory, NQS architectures are broadly applicable, and have been demonstrated successfully on several fundamental applications. We seek to further explore the practical utility of NQS as a black box solver for various applications in the scientific computing domain. We first present NQS as an explicit avenue for de-quantizing variational quantum eigensolvers, demonstrating with the variational quantum linear solver (VQLS). We then explore the utility of VQLS and its de-quantization, VNLS, as black box solvers for a Newton-based linear complementarity solver, used to model the time evolution of a rudimentary soil system. We introduce a new retentive network (RetNet) autoregressive NQS ansatz to solve electronic ground state calculations in computational quantum chemistry, and we finish with a scaling law analysis of the RetNet architecture and its immediate autoregressive predecessors as applied to electronic structure calculations.
Hybrid Defense:
5822 East Hall
https://umich.zoom.us/j/92606555957
Neural-network quantum states (NQS) is an exciting area of quantum-inspired machine learning, wherein in a fully classical neural network is used to efficiently learn the optimal state vector for a quantum unsupervised learning problem, bypassing the need to model the full exponentially large state space. In theory, NQS architectures are broadly applicable, and have been demonstrated successfully on several fundamental applications. We seek to further explore the practical utility of NQS as a black box solver for various applications in the scientific computing domain. We first present NQS as an explicit avenue for de-quantizing variational quantum eigensolvers, demonstrating with the variational quantum linear solver (VQLS). We then explore the utility of VQLS and its de-quantization, VNLS, as black box solvers for a Newton-based linear complementarity solver, used to model the time evolution of a rudimentary soil system. We introduce a new retentive network (RetNet) autoregressive NQS ansatz to solve electronic ground state calculations in computational quantum chemistry, and we finish with a scaling law analysis of the RetNet architecture and its immediate autoregressive predecessors as applied to electronic structure calculations.
Hybrid Defense:
5822 East Hall
https://umich.zoom.us/j/92606555957
Co-Sponsored By
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