Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis

We derive a family of stochastic master equations describing homodyne measurement of multi-qubit diagonal observables in circuit quantum electrodynamics. In the regime where qubit decay can be neglected, our approach replaces the polaron-like transformation of previous work, which required a lengthy calculation for the physically interesting case of three qubits and two resonator modes. The technique introduced here makes this calculation straightforward and manifestly correct. Using this technique, we are able to show that registers larger than one qubit evolve under a non-Markovian master equation. We perform numerical simulations of the three-qubit, two-mode case from previous work, obtaining an average post-measurement state fidelity of $\sim 94\%$, limited by measurement-induced decoherence and dephasing.Comment: 22 pages, 9 figures. Comments welcom

A Survey on Quantum Computational Finance for Derivatives Pricing and VaR

[Abstract]: We review the state of the art and recent advances in quantum computing applied to derivative pricing and the computation of risk estimators like Value at Risk. After a brief description of the financial derivatives, we first review the main models and numerical techniques employed to assess their value and risk on classical computers. We then describe some of the most popular quantum algorithms for pricing and VaR. Finally, we discuss the main remaining challenges for the quantum algorithms to achieve their potential advantages.Xunta de Galicia; ED431G 2019/01All authors acknowledge the European Project NExt ApplicationS of Quantum Computing (NEASQC), funded by Horizon 2020 Program inside the call H2020-FETFLAG-2020-01 (Grant Agreement 951821). Á. Leitao, A. Manzano and C. Vázquez wish to acknowledge the support received from the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union (European Regional Development Fund- Galicia 2014-2020 Program), by Grant ED431G 2019/01

Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

This paper introduces a fast stochastic surrogate modeling technique for the frequency-domain responses of linear and passive electrical and electromagnetic systems based on polynomial chaos expansion (PCE) and principal component analysis (PCA). A rational PCE model provides high accuracy, whereas the PCA allows compressing the model, leading to a reduced number of coefficients to estimate and thereby improving the overall training efficiency. Furthermore, the PCA compression is shown to provide additional accuracy improvements thanks to its intrinsic regularization properties. The effectiveness of the proposed method is illustrated by means of several application examples