Equation of motion approach to black-box quantization: taming the multi-mode Jaynes-Cummings model

An accurate modeling of a Josephson junction that is embedded in an arbitrary environment is of crucial importance for qubit design. We present a formalism to obtain a Lindblad master equation that describes the evolution of the system. As the qubit degrees of freedom oscillate with a well-defined frequency $\omega_q$, the environment only has to be modeled close to this frequency. Different from alternative approaches, we show that this goal can be achieved by modeling the environment with only few degrees of freedom. We treat the example of a transmon qubit coupled to a stripline resonator. We derive the parameters of a dissipative single-mode Jaynes-Cummings model starting from first principles. We show that the leading contribution of the off-resonant modes is a correlated decay process involving both the qubit and the resonator mode. In particular, our results show that the effect of the off-resonant modes in the multi-mode Jaynes-Cummings model is perturbative in $1/ \omega_q$.Comment: 10 pages, 3 figure

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

Stoquasticity in circuit QED

We analyze whether circuit-QED Hamiltonians are stoquastic focusing on systems of coupled flux qubits: we show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. Despite this, we corroborate the recent finding [arXiv:1903.06139] that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits. We find that if the capacitive coupling is sufficiently small, this non-stoquasticity of the effective qubit Hamiltonian can be avoided if we perform a canonical transformation prior to projecting onto an effective qubit Hamiltonian. Our results shed light on the power of circuit-QED Hamiltonians for the use of quantum adiabatic computation and the subtlety of finding a representation which cures the sign problem in these system

Homological Quantum Rotor Codes: Logical Qubits from Torsion

We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which encode logical oscillators. Unlike for qubits or oscillators, homological quantum rotor codes allow one to encode both logical rotors and logical qudits, depending on the homology of the underlying chain complex. In particular, such a code based on the chain complex obtained from tessellating the real projective plane or a M\"{o}bius strip encodes a qubit. We discuss the distance scaling for such codes which can be more subtle than in the qubit case due to the concept of logical operator spreading by continuous stabilizer phase-shifts. We give constructions of homological quantum rotor codes based on 2D and 3D manifolds as well as products of chain complexes. Superconducting devices being composed of islands with integer Cooper pair charges could form a natural hardware platform for realizing these codes: we show that the $0$-$\pi$-qubit as well as Kitaev's current-mirror qubit -- also known as the M\"{o}bius strip qubit -- are indeed small examples of such codes and discuss possible extensions.Comment: 47 pages, 10 figures, 2 table

3D geothermal modelling of the Mount Amiata hydrothermal system in Italy

In this paper we build a subsurface model that helps in visualizing and understanding the structural framework, geology and their interactions with the Mt. Amiata geothermal system. Modelling in 3D provides the possibility to interpolate the geometry of structures and is an effective way of understanding geological features. The 3D modelling approach appears to be crucial for further progress in the reconstruction of the assessment of the geothermal model of Mt. Amiata. Furthermore, this model is used as the basis of a 3D numerical thermo-fluid-dynamic model of the existing reservoir(s). The integration between borehole data and numerical modelling results allows reconstructing the temperature distribution in the subsoil of the Mt. Amiata area. Keywords

Microwave-activated gates between a fluxonium and a transmon qubit

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100 MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 99% can be obtained with gate times between 100 and 300 ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate

The integration of 3D modeling and simulation to determine the energy potential of low-temperature geothermal systems in the Pisa (Italy) sedimentary plain

Shallow, low-temperature geothermal resources can significantly reduce the environmental impact of heating and cooling. Based on a replicable standard workflow for three-dimensional (3D) geothermal modeling, an approach to the assessment of geothermal energy potential is proposed and applied to the young sedimentary basin of Pisa (north Tuscany, Italy), starting from the development of a geothermal geodatabase, with collated geological, stratigraphic, hydrogeological, geophysical and thermal data. The contents of the spatial database are integrated and processed using software for geological and geothermal modeling. The models are calibrated using borehole data. Model outputs are visualized as three-dimensional reconstructions of the subsoil units, their volumes and depths, the hydrogeological framework, and the distribution of subsoil temperatures and geothermal properties. The resulting deep knowledge of subsoil geology would facilitate the deployment of geothermal heat pump technology, site selection for well doublets (for open-loop systems), or vertical heat exchangers (for closed-loop systems). The reconstructed geological-hydrogeological models and the geothermal numerical simulations performed help to define the limits of sustainable utilization of an area's geothermal potential

Direct healthcare costs of non-metastatic castration-resistant prostate cancer in Italy

Objectives: The management of non-metastatic castration-resistant prostate cancer (nmCRPC) is rapidly evolving; however, little is known about the direct healthcare costs of nmCRPC. We aimed to estimate the cost-of-illness (COI) of nmCRPC from the Italian National Health Service perspective. Methods: Structured, individual qualitative interviews were carried out with clinical experts to identify what healthcare resources are consumed in clinical practice. To collect quantitative estimates of healthcare resource consumption, a structured expert elicitation was performed with clinical experts using a modified version of a previously validated interactive Excel-based tool, EXPLICIT (EXPert eLICItation Tool). For each parameter, experts were asked to provide the lowest, highest, and most likely value. Deterministic and probabilistic sensitivity analyses (PSA) were carried out to test the robustness of the results. Results: Ten clinical experts were interviewed, and six of them participated in the expert elicitation exercise. According to the most likely estimate, the yearly cost per nmCRPC patient is €4,710 (range, €2,243 to €8,243). Diagnostic imaging (i.e., number/type of PET scans performed) had the highest impact on cost. The PSA showed a 50 percent chance for the yearly cost per nmCRPC patient to be within €5,048 using a triangular distribution for parameters, and similar results were found using a beta-PERT distribution. Conclusions: This study estimated the direct healthcare costs of nmCRPC in Italy based on a mixed-methods approach. Delaying metastases may be a reasonable goal also from an economic standpoint. These findings can inform decision-making abou

Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit

We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron confined in a two-dimensional plane and under the effect of strong magnetic field and of a periodic potential. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction. We also propose realistic design parameters for an experimental realization and we describe possible protocols to perform logical one- and two-qubit gates, state preparation and readout