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Paper 1
Iteratively decoded magic state distillation
Kwok Ho Wan
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.17992
- arXiv
- 2410.17992
We present numerical simulation results for the 7-to-1 and 15-to-1 state distillation circuits, constructed using transversal CNOTs acting on multiple surface code patches. The distillation circuits are decoded iteratively using the method outlined in [arXiv:2407.20976]. We show that, with a re-configurable qubit architecture, we can perform fast magic state distillation in $\sim\mathcal{O}(1)$ code cycles. We confirm that both circuits suppress an injected input error rate $p$ to $\mathcal{O}(p^3)$ in the presence of additional circuit-level noise. We also outline how ZX-calculus and Pauli webs can be used to benchmark stabiliser proxies for these distillation circuits.
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Quantum Monte Carlo Integration for Simulation-Based Optimisation
Jingjing Cui, Philippe J. S. de Brouwer, Steven Herbert, Philip Intallura, Cahit Kargi, Georgios Korpas, Alexandre Krajenbrink, William Shoosmith, Ifan Williams, Ban Zheng
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.03926
- arXiv
- 2410.03926
We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of all systematic errors arising in the formulation of quantum Monte Carlo integration in order to better understand the resources required to encode various distributions such as a Gaussian, and to evaluate statistical quantities such as the Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) of an asset. Finally, we study the applicability of quantum Monte Carlo integration for fundamental financial use cases in terms of simulation-based optimisations, notably Mean-Conditional-Value-at-Risk (Mean-CVaR) and (risky) Mean-Variance (Mean-Var) optimisation problems. In particular, we study the Mean-Var optimisation problem in the presence of noise on a quantum device, and benchmark a quantum error mitigation method that applies to quantum amplitude estimation -- a key subroutine of quantum Monte Carlo integration -- showcasing the utility of such an approach.
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