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Paper 1
Flagging the Clifford hierarchy:~Fault-tolerant logical $\fracπ{2^l}$ rotations via measuring circuit gauge operators of non-Cliffords
Shival Dasu, Ben Criger
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.24573
- arXiv
- 2603.24573
We provide a recursively defined sequence of flag circuits which will detect logical errors induced by non-fault-tolerant $R_{\overline{Z}}(\fracπ{2^l})$ gates on CSS codes with a fault distance of two. As applications, we give a family of circuits with $O(l)$ gates and ancillae which implement fault-tolerant logical $R_{Z}(\fracπ{2^l})$ or $R_{ZZ}(\fracπ{2^l})$ gates on any $[[k + 2, k, 2]]$ iceberg code and fault-tolerant circuits of size $O(l)$ for preparing $|\fracπ{2^l}\rangle$ resource states in the $[[7,1,3]]$ code, which can be used to perform fault-tolerant $R_{\overline{Z}}(\fracπ{2^l})$ rotations via gate teleportation, allowing for implementations of these gates that bypass the high overheads of gate synthesis when $l$ is small relative to the precision required. We show how the circuits above can be generalized to $π( x_0.x_{1}x_{2}\ldots x_{l}) = \sum_{j}^{l} π\frac{x_j}{2^j}$ rotations with identical overheads in $l$, which could be useful in quantum simulations where time is digitized in binary. Finally, we illustrate two approaches to increase the fault-distance of our construction. We show how to increase the fault distance of a Cliffordized version of the T gate circuit to $3$ in the Steane code and how to increase the fault-distance of the $\fracπ{2}$ iceberg circuit to $4$ through concatenation in two-level iceberg codes. This yields a targeted logical $R_{\overline{Z}}(\fracπ{2})$ gate with fault distance $4$ on any row of logical qubits in an $[[(k_2+2)(k_1+2), k_1k_2, 4]]$ code.
Open paperPaper 2
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.
Open paper