Quantum computing with limited resources: challenges and algorithms
File(s)
Author(s)
Wang, Samson
Type
Thesis
Abstract
In this thesis we present new results studying the landscape of quantum computing applications where resources are limited. In the first part we study the limitations of near-term devices in the presence of noise. We demonstrate that noise can impede the resolvability of expectation values generated from different states. This phenomenon occurs exponentially quickly in the circuit depth. This has particular relevance for variational quantum algorithms and presents a barrier in reliably training such algorithms when they pass beyond a certain size. We then study a general class of error mitigation techniques and find that asymptotically they cannot remove such scalability barriers without investing an exponential number of classical or quantum resources. We also show that for fixed problem size, certain error mitigation schemes can actually worsen resolvability. In the second part of this thesis we work in a regime where we assume we have enough resources to implement error correction (and can broadly disregard the effects of noise), but the number of logical qubits is still limited. We present a simple framework for constructing quantum algorithms that sample properties of matrix functions which only uses one ancillary qubit and avoids the use of any quantum oracles. We present concrete applications for linear systems and estimating properties of ground states and Gibbs states.
Version
Open Access
Date Issued
2023-09
Date Awarded
2024-02
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Berta, Mario
Kim, Myungshik
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)