The search is on for near term applicable quantum algorithms. The financial sector is one field where improvements to computationally challenging tasks could be highly beneficial. We have explored...Show moreThe search is on for near term applicable quantum algorithms. The financial sector is one field where improvements to computationally challenging tasks could be highly beneficial. We have explored the use of quantum machine learning for one such task, the generation of synthetic financial data. Building on the current classical state of the art, we have implemented a Wasserstein generative adversarial network with gradient penalty for the generation of synthetic time series. We have expanded this classical framework using a parametrised quantum generator circuit. By using Pauli string expectation values, we can generate multi-dimensional continuous samples. This approach has allowed for the generation of small scale synthetic time series samples, based on the S&P 500 index, that show characteristic signs of the same temporal properties present in real financial data.Show less
Quantum mechanics either violates realism (non-determinism) or locality. This follows from Bell’s theorem by showing the measurement statistics of the EPR-experiment can never be fully reproduced...Show moreQuantum mechanics either violates realism (non-determinism) or locality. This follows from Bell’s theorem by showing the measurement statistics of the EPR-experiment can never be fully reproduced by any local hidden variable model (LHV-model). Research has been done in the last couple of decades into the degree to which LHV-models can reproduce measurement statistics approximating the EPR’s statistics. Specifically of interest is finding which amplitudes can be reproduced by LHV-models with an exact correlation. Our analysis and the literature take into consideration: a density matrix separability criterion on the two-electron singlet state, constructs by Kaszlikowski and Zukowski, and the Grothendieck constant. Further, open question arise and new approaches to the locality of quantum states are given.Show less
