With the advent of scalable quantum computing questioning the security of contemporary cryp- tosystems - such as RSA - there has been a concerted e↵ort to develop and standardise quantum secure cryptographic methods. The post-quantum cryptography (PQC) standardisation pro- cedure has produced a clear front runner in lattice based cryptography, for which many of the proposed schemes have security assurances given by the shortest vector problem (SVP). Whilst these schemes appear to be resistant to the method of quantum attack that have necessitated their development, it behooves cryptography researchers to ensure that they are not susceptible to attacks via alternative quantum systems.
The quadratic unconstrained binary optimisation (QUBO) form of SVP provides a convenient framework on which to base quantum algorithms for SVP. This thesis extends the framework with further encoding methods to those already proposed, in addition to providing a greater depth of analysis of complexity requirements for algorithms based within this framework.
There is a striking resemblence between the QUBO formulation of SVP and Ising models, suggesting that coherent Ising machines (CIM) are an ideal quantum device on which to imple- ment QUBO algorithms for SVP. Numerical simulations of such algorithms are presented here, alongside analysis of the e cacy in solving SVP.
Boson sampling promises to deliver a quantum computational system that inherently provides quantum supremacy in its functioning. However, the applications of such a device have long been in question. Two approaches for sampling lattice vectors via boson sampling are provided: a Fock-state boson sampling approach and a trainable Gaussian boson sampler (GBS). In the GBS setting a heuristic for examining where one might expect to observe a quantum advantage in the use of the systems is presented, and used to predict for which lattice problems this would provide such an advantage.