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Best Nursing Schools in Kansas City in 2020 (On-Campus & Online)
Kansas City straddles both Missouri and Kansas, providing a rich history of art, music, and education to the communities of each state. As a central location for higher learning, there are also numerous nursing schools in Kansas City, Missouri that serve the communities in various healthcare settings. Students have options from BSN programs to nurse practitioner schools in Kansas city. Whether prospective students are seeking to earn their LPN certificate or a BSN degree Kansas City has multiple schools to choose from that will train them to be the next generation of compassionate, professional nurses in an occupation that is expected to grow another 18% in the next decade. Browse the schools below to find one that meets your needs.
Schools were ranked according to cost for the nursing program and the NCLEX-RN pass rate of the individual school. Institutions that offered multiple nursing programs ranked higher than those that only offered LPN or ADN degrees.
Best Nursing Schools in the Kansas City Area
1. University of Missouri-Kansas City
UMKC is one of the best accredited nursing schools in Kansas city. As one of the four campuses in the University of Missouri System, UMKC, is also campus to a fully accredited medical school. The UMKC nursing program is among the tops programs in the country with graduates that practice nursing to the full extent of the education they receive and advance research and translating it into practice. With the on-campus medical school students are provided with many on-site clinical experiences in caring for patients. UMKC offers RN to BSN programs, BSN, MSN, DNP as well as Ph.D. programs in nursing.
Tuition: $7,846
Graduation Rate: 52.2%
Teacher to Student Ratio: 15:1
NCLEX Pass Rate: 90.8%
2. St. Luke's College of Health Sciences
Associated with St. Luke's Health System in Kansas City, St. Luke's College of Health Sciences offers a long-standing program of successfully training nurses. With over 115 years of graduates, St. Luke's offers quality education and training in compassionately caring for people of their communities. Students can earn their BSN in 4 semesters and begin a rewarding, high paying career upon graduation.
Graduation Rate: 100%
NCLEX Pass Rate: 90%
3. Baker University
As one of the top nursing schools in Kansas City, MO, Baker University prepares students with critical thinking skills and expert knowledge that will guide them through their practical application. A diploma from Baker gives graduates a 99% guarantee for job placement upon graduation. Baker University offers rigorous educational curricula combined with early clinical experiences and more hours with hands-on practice with patients in various settings.
4. Avila University
A private university sponsored by the sister of St. Joseph of Carondelet, Avila University stands as one of the oldest nursing schools in the state of Missouri. Avila has remained as one of the top ten nursing schools in Missouri for many years as students graduate prepared to lead as nursing professionals in the community. Students receive a promise to receive internships and research opportunities while they earn their BSN at Avila, giving them a stronger resume upon graduation.
NCLEX Pass Rate: 97.37%
5. Research College of Nursing
With a very high graduation rate, students at the Research College of Nursing are guaranteed to receive a personalized education in nursing. With a dedication to professionalism, education in safe and quality caregiving and excellent nursing education, graduates are among the leaders in healthcare. Research offers a BSN and MSN program with three different graduate tracks to choose from to better meet the needs of the students.
Graduation Rate: 98%
6. Rockhurst University
As a private, Jesuit university, Rockhurst was founded over 100 years ago and has a solid foundation as an institute for higher learning. In 2020 Rockhurst University and St. Luke's College of Health Sciences will merge to become one premier 4-year BSN program for nursing. Students will have access to the best faculty and clinical experiences from St. Luke's at the Rockhurst campus. This merge of two top nursing schools in Kansas will have a profound impact on the quality of nursing education for the Midwest.
7. William Jewell College
Learning how to think critically is at the core of education at William Jewell College. Graduates are taught to be problem solvers and see insights that others may miss. As a nursing professional these are skills that separate a good nurse from a leader in the healthcare community. The nursing program at William Jewell provides students with analytical and ethical decision-making skills necessary or nurses in today's world. They offer four nursing tracks: a traditional BSN 3-year plan and a 4-year plan, a Transfer Nursing (Spring and Fall entry points), and an Accelerated Track Nursing 12-month track (May start) or 16-month track (January start).
NCLEX Pass Rate (first-time): 93% Accelerated Track, 100% 4-year BSN
8. Metropolitan Community College
As one of the multiple colleges included in the Community College System of Missouri, Metropolitan Community College offers students an LPN or ADN program to begin their careers in nursing. Currently, nursing is one of the top ten careers to be employed in with the need for qualified nurses increasing every year. Graduates can either begin their career upon graduation or use their degree as a springboard to earn their BSN at a university.
Graduation Rate: Information Not Available
9. Johnson County Community College
Located in Kansas, Johnson County Community College is just a short 20-minute drive from Kansas City and provides another affordable opportunity for students to earn their RN degree. Unlike many other Community Colleges, JCCC offers small class sizes for nursing students and hands-on experiences that adequately prepare graduates to enter the health care field as RNs.
10. Concorde Career College
A truly innovative college that prepares students in less time to enter the healthcare community as health care professionals. Concorde Career College focuses on educating and training students for their particular degree in less time than traditional colleges. With a student-centered approach to teaching and clinical experiences, Concorde has prepared numerous students to work in the healthcare field.
11. Kansas City Kansas Community College
Kansas City Kansas Community College offers a two-year RN degree for students that complete the courses and pass the NCLEX-RN. Students are given opportunities to practice and show clinical competence and professional accountability. With two parts of the program, students will learn about nursing intervention and nursing outcome classifications.
12. Donnelly College
Donelly College is one of the few minority-serving institutions as a private Catholic institution for higher learning. The mission of Donnelly College is to continue the mission of Jesus Christ by making the love of God tangible in our world, the nursing program is no exception and offers that education to those who might otherwise not have that opportunity for higher learning. Whether students are seeking an LPN certificate or an RN degree, Donnelly has a program for both.
Graduation Rate: 9%
13. Ottawa University
One of the top private Christian Universities in the US, Ottawa University is a Baptist liberal arts institution founded in 1865. Ottawa is supportive of training nurses to be supported and empowered. Nursing is a collaborative effort with other healthcare professionals, graduates will learn how to work as a team member in this effort.
NCLEX Pass Rate: Not Currently Available
All the schools listed are accredited and in good standing. Most RNs earn an average of $70,000 per year in the Kansas City area. For those seeking a rewarding career with a high job placement rate and opportunities to grow, nursing is a great option. Browse the online nursing schools in Kansas City and apply them to a program that fits your needs today!
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Lifetime experience of Vis Special Bike center is secure choice for your unique cycling exploration of island Vis. All year round, we provide complete cycling service, like different kind of rental bikes, e-bikes, thematic trails and tours, local guides, transfers, accommodation as well as service on the spot, maps, etc.
Meeting our cycling friendly employees will give you a chance to get loads of helpful local info's and recommendations about the island and cycling trails possibilities. We will be happy to share our inside knowledge about Islands highlights like famous beaches, sea caves, local experts, organic food places, wine yard trails, etc. Vis Special also provide bike tools, spare parts, safe storage for your bikes, Vis organic energy bars and drinks, bike fitting, etc; don't forget we are cyclists too.
Island Vis is very special cycling destination and one of the most unknown holiday parades, located in the middle of the Adriatic Sea. Blue Cave, Stiniva bay, Green Cave and X military undermines, island famous gastronomy and wines, are only some of the highlights of Vis. Choose between professionally traced and classified islands mountain and road cycling bike trails, trails suitable for family and recreation, etc. Riding Vis inland's and costal single trails, low-traffic roads together with famous island highlights are gone make your visit of Vis an exciting and unforgettable experience.
Vis Special offer you more than 50 TREK bicycles, e-bikes, guest's transfers and bikes deliveries, bike fitting, etc. We offer large selection of different bicycle types and models. You can choose between 20", 24", 26", 27", 29" inch wheels, Mtb, City and Road bikes. All are bikes are TREK bicycles, while our e-bikes are BOSH and KARKOF hybrid bicycles.
Additional equipment included: helmets, locks, lights, water bottle cages, repair kit, baskets, beam racks.
Available additional equipment not included: child seats, Bike trailers.
We will help you to choose your bike, check the tire pressure and adapt the bike by your wishes and needs.
For guided excursions and self-guided cyclists we secure assistance and service on the spot, on every part of island Vis.
We provide transfer of guests and bikes for different points in central Dalmatia Vis, Split, Hvar, Brač, etc.
Check out our offer of guided and self-guided cycling excursions, which we can customize according to your wishes, with our without a guide, shuttle, lunch or snack followed by wine tasting, etc. We also provide shuttle service with SUV, which includes cooler with cold water and car rack or trailer. You can also wish to have your self-guided explorations and hold the car with Bike Rack on standby in case you like to us it.
We provide transfer of guests with bicycles to any spot on the islands Vis and Biševo, as well as to the other destinations in the region. Beside bicycles you can ask for a map and all the info's necessary for arriving to desired points and final destination. If you would like to learn more about the sites or you don't want to ride alone, Vis Special will provide you with a guide and/or shuttle service.
We can modify start of the tours. Minimum number of participants is 2 persons.


Superior's Annual General Meeting of Shareholders will be held at the Metropolitan Toronto Convention Centre, 255 Front Street West, Toronto, Ontario, Canada on Thursday, April 28, 2016 at 2:00 p.m. (EST).
Internet users can listen to the meeting live, or as an archived call, by using the following link.
A copy of the AGM presentation will be available at www.superiorplus.ca on April 28, 2016.


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Carrie Underwood's 'Greatest Hits: Decade #1' is Out and Jason Aldean Goes Platinum
Carrie Underwood's 'Greatest Hits: Decade #1' is out with two-discs and 25 tracks that include her #1's, two new songs and previously unreleased versions of four others. It also includes duets with Brad Paisley, Randy Travis and Vince Gill. It was 10 years ago that Carrie won American Idol.
Jason Aldean's 'Old Boots, New Dirt' has only been out 8-weeks and now we hear it's the only country album released in 2014 to sell over a million copies and be certified Platinum.
Blake Shelton says the song he sings in the shower is the theme to the TV show The Love Boat.
Miranda Lambert says Blake's the happiest person on the planet and he pulls her out of her darkness like anxiousness and worry. Miranda says she's learned everything doesn't have to be perfect and that things may even be better flawed.
Jennifer Nettles is going to announce quote "big news" on the Today Show!
Finally – Sara Evans stops by Live with Kelly and Michael today.
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The Folklore Museum in Dietenheim near Bruneck lies in the heart of the Pustertal valley. It shows the environment of the everyday life of rural population of the past – from the landed gentry and the self-sustaining peasantry to the day labourers. The centrepiece is the baroque Mair am Hof residence with its stately rooms and ethnological collections. The appendant farm building houses numerous agricultural implements and vehicles.
The open-air site containing old, original farmhouses, craft workshops, farm gardens and domestic animals invites visitors to stay and recounts the everyday life of earlier times.
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Laurence Harvey turns in an excellent performance in this sequel to the highly successful Room At The Top which follows the life of a social climber whose self-doubt tarnishes his success. With his marriage to the boss' daughter on the rocks, Harvey finds himself embroiled in an affair with a London anchorwoman.
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Encyrtus sericophilus är en stekelart som beskrevs av Conte 1912. Encyrtus sericophilus ingår i släktet Encyrtus och familjen sköldlussteklar.

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Rankings in Western Europe are dominated by the Nordic countries—Norway (1), Finland (2), Denmark (5) and Sweden (8)—as well as Switzerland (3) and Germany (6), which collectively take the region's top spots.
The Netherlands (13) and Belgium (15) rank ahead of the United Kingdom (23) and France (26) to make up the mid-range of the regional league table, while three Mediterranean countries—Portugal (43), Spain (44) and Greece (48)—take the bottom ranks.
The overall average score of the region is 71.10, the second highest after North America, and 12 out of the 20 Western European countries covered by the Index have crossed the threshold of effectively developing at least 70% of their human capital. The region shows fairly high homogeneity in human capital in contrast to regions such as East Asia and the Pacific or Middle East and North Africa.
Generally, most of the region performs below the global average with regard to the successful deployment of the human capital of its young generation, with comparatively low labour force participation and high unemployment and underemployment rates, highlighting some of the structural challenges facing the region. The Mediterranean countries in particular continue to be affected by high levels of youth unemployment—reaching 48% in Greece (48) and 43% in Spain (44)—despite some improvement compared to the recent past. More positively, across Western Europe there are well-educated older generations, with high tertiary attainment among the region's still active 55–64 age group, as well as generally solid performance on the Development subindex. Moreover, 17 of the top 30-ranked countries on the Know-how subindex are in Western Europe, indicating the depth of human capital the region may draw on as the Fourth Industrial Revolution advances.
Additional opportunities exist to realize a greater share of untapped human capital in some of the region's largest economies, including the United Kingdom (23), France (26) and Italy (35). Whereas the United Kingdom ranks in the top 10 on the Know-how subindex, with a significant high-skilled employment share (48%), it underperforms on the Capacity subindex, indicating opportunities for realizing greater human capital through targeted re- and upskilling, especially of its existing workforce and older generations. By contrast, France underperforms on the Deployment subindex with somewhat high unemployment and a 35% drop in labour force participation between the 25–54 and 55–64 age ranges. It does show a solid performance on the remaining subindexes, but could also do more to increase the skill diversity of the nation's graduates. Similarly, Italy (35) is held back by a low labour force participation rate, due to a somewhat large gender gap, and high youth unemployment. It also scores poorly on the quality of its on-the-job training. The country does, however, perform better on the Capacity subindex as well as on the skill diversity of its graduates.


text:
\section{Introduction}
\label{sec:intro}

In the field of circuit Quantum Electrodynamics (circuit QED) the combination of superconducting resonators and Josephson junctions \cite{PhysRevA.69.062320} has been used to demonstrate fundamental quantum interactions. Josphson junctions are also often combined in loops to generate Superconducting Quantum Interference Devices (SQUIDs), which allow more controllability in the systems. The interactions demonstrated in cQED are ranging from the resonant coupling between two-level systems and a harmonic oscillator \cite{Wallraff:2004oh,PhysRevLett.105.060503,PhysRevB.78.180502} over the generation of non-classical states \cite{hofheinz2008generation,vlastakis2013deterministically}, to protocols where the resonator field serves as a quantum bus to transfer quantum states and mediate interactions between different systems \cite{PhysRevLett.107.220501,PhysRevLett.110.250503,RevModPhys.85.623}. To control the interaction between the resonator mode and other physical systems, one uses the ability to tune the frequencies (and sometimes also the damping rates) of the resonator mode \cite{PhysRevLett.107.220501,PhysRevLett.110.250503,RevModPhys.85.623, PhysRevLett.90.238304}. Furthermore, periodic modulation of SQUID parameters is used in parametric amplifiers \cite{flux2008yamamoto} and parametric converters \cite{zakka2011quantum}, where interactions appear between the modes of the resonator \cite{PhysRevA.86.013814}.

\begin{figure}[b]
\flushleft (a)
\includegraphics[width=\linewidth]{modulated_sketch.pdf}

(b)
\includegraphics[width=\linewidth]{circuit_sketch.pdf}
\caption{(a) A superconducting resonator, interupted by a SQUID at $x=0$. The SQUID is modulated by an external magnetic field $\Phi(t)$ yielding a time dependent Josephson energy $E_J(t)$. (b) Circuit diagram of a resonator interrupted by an inline-SQUID. $L_T$ and $C_T$ denote the inductance and capacitance per length of the waveguide, such that each inductor (capacitor) has the inductance (capacitance) $L_T \Delta x$ ($C_T \Delta x$). The resonator is described in the limit of $\Delta x \rightarrow 0$. The inline-SQUID is characterized by the time-dependent Josephson energy, $E_J(t)$, and its capacitance, $C$.} \label{fig:sketch}
\end{figure}

While changing the frequency of a resonator allows tuning of the photon energies to match energy differences in other systems, the quantized field does not necessarily adiabatically adjust to the change in frequency and the associated change in mode function. Indeed, rapid motion of an optical mirror has been predicted to lead to the creation of photons  by the so-called dynamical Casimir effect \cite{moorequantum}, and experiments in circuit QED have addressed the microwave equivalent by rapid modulation of a SQUID, altering the boundary conditions of a waveguide with half open boundary conditions \cite{PhysRevLett.103.147003,wilson2011observation}.

In this article we study a similar situation, with a periodically modulated SQUID (see Fig. 1 (a)) in a finite size waveguide with a discrete frequency spectrum. Our goal is not to use the SQUID to drive excitations of the resonator field, and we will hence avoid driving at frequencies supported by the waveguide. Instead we will investigate how the driving leads to new, multi-frequency modes and we will characterize their frequency contents. We then determine how such modes can be used to bridge frequency gaps and coherently couple different physical systems.

Our work is inspired by \cite{flux2008yamamoto, zakka2011quantum, moorequantum, PhysRevA.86.013814, PhysRevLett.103.147003, wilson2011observation} and mechanisms used in atomic memories and light-matter interfaces \cite{RevModPhys.82.1041}, where Raman processes use a laser field to dress atomic or molecular levels such that low frequency transition of the system can be driven and probed at optical frequencies. Similarly, in opto-mechanics \cite{aspelmeyer2010quantum}, weak optical fields impinging on movable mirrors are coherently coupled to low frequency mirror vibrations via the intensity beat node with another field.  By constructing our scheme with circuit QED components, our architecture and the nature of our frequency modulation via changed boundary conditions rather than a non-linear interaction term necessitates a detailed circuit analysis, which we will build on the theory developed in \cite{devoret1995quantum,PhysRevA.86.013814,PhysRevA.89.033853}.

In Sec. \ref{sec:res} we present the physical system and we derive the spatio-temporal solutions to the wave equations for the resonator variables with time dependent boundary conditions. In Sec. \ref{sec:quant}, we present an effective, approximate parametrization of the solutions in terms of canonical conjugate variables, and we establish a quantum theory for the resonator modes and in Sec. \ref{sec:coup} we discuss the interaction across frequency gaps. In Sec. \ref{sec:ms},  we show how our driven modes can establish an effective bi-chromatic entanglement gate operation between two transmon qubits with different transitions frequencies. In Sec. \ref{sec:conc} we present a conclusion and an outlook.

\section{Multi-frequency resonance modes}
\label{sec:res}

To analyze the dynamics of a superconducting resonator modulated by an inline-SQUID we consider the circuit diagram in Fig. \ref{fig:sketch} (b). Here, we have represented the waveguide by a series of $LC$-circuits. Each waveguide segment of length $\Delta x$ is associated with an inductor with inductance $L_T \Delta x$ and a capacitor with capacitance of $C_T \Delta x$. The time-integral of the voltage potential at each node of the circuit constitutes the phase degree of freedom which, in the limit of $\Delta x \rightarrow 0$, becomes a function $\phi(x,t)$ of the continuous position variable $x$ ($L_T$  and $C_T$ are defined as the inductance and capacitance per length of the waveguide). At the center of the waveguide we introduce the inline-SQUID, which contributes a non-linear inductance set by the Josephson energy, $E_J(t)$, and a capacitance set by $C$.

The Lagrangian of the circuit is given by the expression,
\begin{align}
\mathcal{L} =& \int_{-d}^d \bigg\{ \frac{C_T}{2} \big(\partial_t \phi(x,t) \big)^2 - \frac{1}{2L_T} \big( \partial_x \phi(x,t) \big)^2 \bigg\} dx \nonumber\\
&+\frac{C}{2} (\partial_t \Delta \phi(x_J,t))^2+  E_J(t) \cos \frac{2\pi \Delta \phi(x_J,t)}{\Phi_0} , \label{eq:lagrangian}
\end{align}
where $\Delta \phi(x_J,t) = \phi(x_{J+},t) - \phi(x_{J-},t)$ denotes the change in the phase variable, $\phi(x,t)$, imposed by the discrete boundary conditions at the inline-SQUID \cite{PhysRevA.86.013814}. In the following expand the cosine term to second order in $\Delta \phi$. When needed, the higher order terms can be reintroduced, see eg. Eq. \eqref{eq:hnl}, as a pertubation at a later point in the analysis.

The Euler-Lagrange equation,
\begin{align}
\partial_x \pfrac{\mathcal{L}}{(\partial_x (\phi(x,t))} + \partial_t \pfrac{\mathcal{L}}{(\partial_t (\phi(x,t))} - \pfrac{\mathcal{L}}{\phi(x,t)} = 0,
\end{align}
yields the wave-equation for the phase variable along the waveguide
\begin{align}
-v^2 \partial_x^2 \phi(x,t) + \partial_t^2 \phi(x,t) = 0, \label{eq:wavext}
\end{align}
where $v$ denotes the propagation speed of the wave.
We assume that our resonator obeys open boundary conditions at its ends at $x=\pm d$, while at $x_J=0$ the SQUID defines boundary conditions, parametrized by the time-dependent Josephson energy, $E_J(t)$, and the capacitance, $C$, of the SQUID,
\begin{align}
&\pfrac{\phi(x,t)}{x}\Big|_{x=\pm d} = 0 \\
&\frac{1}{L_T} \pfrac{\phi(x,t)}{x}\Big|_{x=0\pm} = C \pfrac{^2 \Delta \phi(0,t)}{t^2} + \frac{(2\pi)^2 E_J(t)}{\Phi_0}  \Delta \phi(0,t). \label{eq:bcxt}
\end{align}
Equations \eqref{eq:wavext}--\eqref{eq:bcxt} define the time-dependent mode functions of the circuit that we shall first calculate and then use as basis for the quantum interaction with additional circuit elements.

In this article we consider a periodically modulated magnetic flux, $\Phi(t)$, through the SQUID leading to a harmonically varying Josephson energy,
\begin{align}
E_J(t) = E_{J,0} + \delta E_J \cos \omega_d t.
\end{align}
If the modulation were not too fast {($\omega_d \ll \omega$), we could have treated the SQUID as a quasi-static component and found the eigenmodes of the system for each value of $E_J(t)$. For not too strong driving ($\delta E_J \ll E_{J,0}$) this would give rise to a variation in the eigenmode frequencies $\omega(t) = \omega'+\delta\omega' \cos \omega_d t$, equivalent to the formation of a central frequency component with sidebands at multiples of the modulation frequency $\omega_d$. A natural \emph{ansatz} for the quadrature operator associated with excitation of the quantized resonator circuit would then be given by
\begin{align}
\hat{q} \approx q_{zpf} (1 + \frac{\delta\omega'}{2\omega'} \cos \omega_d t)(\hat{a}\dag + \hat{a}), \label{eq:qah}
\end{align}
where $\hat{a}$ and $\hat{a}^\dagger$ are the corresponding annihilation and creation operators and $q_{zpf}$ denotes the zero point fluctuations of the corresponding physical observable. While this approach may constitute a good approximation if $\omega_d$ and the modulation amplitude $\delta E_J$ were small, we also expect to find resonances in the system with a central frequency and sideband components when we modulate the SQUID more strongly and with high frequency. A more careful approach is therefore needed to calculate the modes and their frequencies for a larger range of driving parameters and to subsequently quantize the system dynamics.

We thus return to the original, linearized problem with the time-dependent boundary condition and to exploit the periodicity of the driving, we transform our fields into frequency space,
\begin{align}
\phi(x,\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} \phi(x,t)\, e^{-i\omega t} dt.
\end{align}
We rewrite the wave-equation as
\begin{align}
v^2 \partial_x^2 \phi(x,\omega) + \omega^2 \phi(x,\omega) = 0. \label{eq:wave}
\end{align}
while the boundary conditions in frequency space become:
\begin{align}
\pfrac{\phi(x,\omega)}{x}\Big|_{x=0\pm} &= L_T C \omega^2 \Delta \phi(0,\omega) \nonumber\\&\quad + L_T \frac{(2\pi)^2}{\Phi_0} \frac{E_J(\omega) \otimes \Delta \phi(0,\omega)}{\sqrt{2\pi}}, \label{eq:ftbc}\\
\pfrac{\phi(x,\omega)}{x}\Big|_{x=\pm d} &= 0. \label{eq:openbc}
\end{align}
In Eq. \eqref{eq:ftbc}, $E_J(\omega) \otimes \Delta\phi(0,\omega)$ denotes the convolution product, which is readily calculated since  $E_J(\omega) = E_{J,0} \delta(\omega) + \frac{\delta E_J}{2} (\delta(\omega + \omega_d) + \delta(\omega - \omega_d))$,
\begin{align}
&E_J(\omega) \otimes \Delta\phi(0,\omega) = \nonumber\\&\;\, E_{J,0}\Delta \phi(0,\omega) + \frac{\delta E_J}{2} (\Delta\phi(0,\omega + \omega_d) + \Delta\phi(0,\omega - \omega_d)).
\end{align}
Since the coupling to the SQUID in Eq. \eqref{eq:lagrangian} cancels for even modes ($\Delta\phi(x_J,t)=0$), we consider only odd solutions to Eqs. \eqref{eq:wave} and \eqref{eq:openbc}, i.e., solutions in the form
\begin{align}
\phi(x,\omega) = \begin{cases}\phi(\omega) \cos \big( \omega/v \;(d-x) \big) & \text{for } x > 0, \\ - \phi(\omega)\cos \big( \omega/v \;(-d-x) \big) & \text{for } x < 0. \end{cases}
\end{align}

These functions display the discrete jump at $x=x_J=0$ necessary to fulfil the boundary condition (\ref{eq:ftbc}), which leads to the equation
\begin{align}
 \frac{\omega }{v}d \,\sin \Big(\frac{\omega}{v}d\Big) \phi(\omega) =
2\frac{L_T d}{ L_J}  \cos \Big(\frac{\omega}{v}d\Big)\phi(\omega) \nonumber \\ +\, 2 \frac{L_T d}{\delta L_J} \cos \Big(\frac{\omega + \omega_d}{v}d\Big) \phi(\omega + \omega_d) \nonumber \\ +\, 2 \frac{L_T d}{\delta L_J} \cos \Big(\frac{\omega - \omega_d}{v}d\Big) \phi(\omega - \omega_d), \label{eq:newbc}
\end{align}
 where we have defined $L_J = \sqrt{2\pi} \Phi_0 / (4\pi^2 E_J)$ and $\delta L_J = 2 \sqrt{2\pi} \Phi_0 / (4\pi^2 \delta E_J)$. We have neglected contributions from the Josephson capacitance, assuming typical values obeying $C \omega^2 \ll L_T / L_J$ \cite{PhysRevLett.103.147003}.

Equation \eqref{eq:newbc} can be solved numerically for the allowed discrete values of $\omega$ and the corresponding vector of amplitude strengths $\phi(\omega+m\omega_d)$. For our purpose it is sufficient to approximate the system and restrict ourselves to a dominant frequency component, $\omega$, and two sidebands, $\omega\pm\omega_d$, and ignore coupling to further frequency components $\omega \pm 2 \omega_d, ... $. With this approximation the carrier and sideband components of the system eigenmodes have wave numbers that obey
\begin{align}
kd =& \frac{2L_Td}{L_J} \frac{\cos kd}{\sin kd} + \frac{\big(\frac{2L_Td}{\delta L_J}\big)^2 \frac{\cos kd}{\sin kd}\cos k_-d}{\frac{2L_Td}{ L_J} \cos k_-d + k_-d\sin k_-d} \nonumber \\&+ \frac{\big(\frac{2L_Td}{\delta L_J}\big)^2 \frac{\cos kd}{\sin kd}\cos k_+d}{\frac{2L_Td}{L_J} \cos k_+d + k_+d\sin k_+d}. \label{eq:hard1}
\end{align}
where $k = \omega/v$ and  $k_\pm = (\omega \pm \omega_d)/v$.  The amplitudes of the sidebands are given by
\begin{align}
\phi(\omega \pm \omega_d) = \frac{ \frac{2L_Td}{\delta L_J} \cos k d}{\frac{2L_Td}{L_J} \cos k_\pm d + k_\pm d\sin k_\pm d} \phi(\omega) = A_\pm \phi(\omega). \label{eq:subpm}
\end{align}
We notice that to first order,  the amplitude of the sidebands are inversely proportional to $\delta L_J$ and hence proportional to the driving amplitude $\delta E_J$. This is reminiscent of the important role played by the classical (pump) field amplitude in atom-light interfaces \cite{RevModPhys.82.1041} and in optomechanics \cite{aspelmeyer2010quantum}.

\begin{figure}
\includegraphics[width=\linewidth]{Figure-phi.pdf}
\vspace*{-1cm}
\caption{The mode-functions when we modulate the SQUID with a frequency $\omega_d = 2\pi \times 2.0$ GHz and $\delta E_J / E_{J,0} = 0.4$ for a mode with $kd = 4.614$ ($\omega = 2\pi \times 7.343$ GHz). The green solid line shows the central frequency component $u_\omega(x)$ while the red dashed and the blue dash-dotted lines show the sideband components $u_-(x)$ and $u_+(x)$ respectively. The parameters of the resonator are $d=1.2$ cm, $E_{J,0}/\hbar = 2\pi \times 715$ GHz, $v = 1.2 \times 10^8$ m/s and $L_T = 50\, \Omega / v$.} \label{fig:mode}
\end{figure}

Now we transform our solution back into the time-domain where the solution to the wave equation attains the form:
\begin{align}
\phi(x,t) &= \text{sign}(x) \cos \big(k(\text{sign}(x)d-x)\big)\cos (\omega t) \phi_{\omega} \nonumber \\
 &\,+ \text{sign}(x) \cos \big(k_+(\text{sign}(x)d-x)\big) \cos(\omega_+  t) \phi_+ \nonumber \\
 &\,+  \text{sign}(x) \cos \big(k_-(\text{sign}(x)d-x)\big) \cos(\omega_-  t) \phi_- \\
 &= u_\omega(x) \phi_\omega(t) + u_+(x) \phi_+(t) + u_-(x) \phi_-(t). \label{eq:three-fr}
\end{align}
In the last line we have separated the terms into space-dependent $u_j(x)$ with values exploring the range $[-1,1]$, while the amplitudes governed by (\ref{eq:subpm}) are included in the time-dependent functions $\phi_j(t) = \cos (\omega_j t) \phi_j$.

We show an example of the mode-structure in Fig. \ref{fig:mode}, where the solid line shows the carrier function $u_\omega(x)$ and the dashed curves show the two associated side band mode functions $u_\pm(x)$. The solutions have three nodes and correspond to the 3rd mode of the resonator. Only odd modes acquire sidebands due to the coupling to the SQUID, and in Fig. \ref{fig:E} we show how the solution of Eq. \eqref{eq:hard1} for the 1st, 3rd and 5th mode leads to eigenfrequencies that vary with the modulation strength, $\delta E_J / E_{J,0}$. In Fig. \ref{fig:E} we notice a frequency shift of the order of 10 MHz, which is much larger than typical bandwidths of superconducting resonators and cannot be predicted without taking the full dynamics into account.

To reach the solution (\ref{eq:three-fr}), we assumed that the sidebands at $\omega \pm \omega_d$ in \eqref{eq:newbc} are present and that the coupling to further components at $\omega\pm 2\omega_d$ is negligible. This assumption is fulfilled for applications in this article, where we deal with $A_{\pm}\sim 10^{-2}$, significantly limiting higher sideband exitation. When the system is externally driven on resonance with the values of $\omega$ shown, or at the sidebands $\omega\pm \omega_d$, the modulation of the SQUID  at $\omega_d$ causes the effective excitation of the multi-frequency solution (\ref{eq:three-fr}). While (\ref{eq:three-fr}) is derived under the assumption of periodic driving, it also holds during transient excitation of the system or coupling to other systems, as long as the resulting evolution is slow with respect to the natural frequencies.

\begin{figure}
\includegraphics[width=\linewidth]{Figure-E.pdf}
\vspace*{-1cm}

\caption{Classical resonances for the odd modes of a resonator calculated by Eq. \eqref{eq:hard1} with the same parameters as in Fig. \ref{fig:mode}. We modulate the SQUID with varying strengths at a frequency $\omega_d = 2\pi \times 2.0$ GHz . In (a) we show the variation of the central frequency of the 1st mode, in (b) the 3rd mode and in (c) the 5th mode. The even modes are not considered, since they do not experience the modulation of the SQUID.} \label{fig:E}
\end{figure}

\section{Quantization of the multi-frequency modes}
\label{sec:quant}

Following the normal procedures of second quantization we would have first expanded a general solution $\phi(x,t)$ on stationary eigenmodes of the unmodulated system, and we would have replaced the mode amplitudes by operators satisfying canonical commutation relations. The time-varying SQUID would then be introduced as a driving term which transfers excitation among the quantized modes and which parametrically drives pair-excitation of the modes, cf. \cite{PhysRevA.89.063606, PhysRevLett.113.093602, zhang2014dynamical}. We have deviated from that procedure here because the time varying SQUID modifies the boundary conditions for the resonator modes, and it is clear from Fig. 2. that a large number of the eigenmodes calculated in the absence of the SQUID would be needed to represent the discontinuous jumps in the function $\phi(x,t)$ across the SQUID. Our time dependent mode functions already obey the boundary condition in the presence of the driving. For the finite waveguide, these modes have discrete and well separated frequencies, and we may disregard coupling between them and restrict our analysis to their individual excitation dynamics and their resonant coupling to other systems with transition frequencies at $\omega$ or $\omega\pm \omega_d$. To treat the time dependent mode quantum mechanically, we observe that the central frequency amplitude $\phi_\omega(t)$ oscillates at frequency $\omega$, consistent with the quadratic Lagrangian,
\begin{align}
\mathcal{L} =& \frac{C_\omega}{2} \dot{\phi}_\omega(t)^2 - \frac{1}{2L_\omega} \phi_\omega(t)^2 \label{eq:linlag}
\end{align}
where  $C_\omega$ is conveniently represented by the parts of \eqref{eq:lagrangian} that depend on $\dot{\phi}_\omega(t)$
\begin{align}
C_\omega =&\, 2\int_0^d C_T \cos^2 k (d{-}x) \, dx + C \cos^2 kd \nonumber \\ =&\, C_T d \Big( 1 + \frac{\sin 2kd}{2kd} \Big) + C \cos^2 kd.
\end{align}
The full Lagrangian, indeed, depends on $\dot{\phi}_\omega(t)$ also via the sideband components, but by setting $L_\omega = 1/(C_\omega\omega^2)$ in (\ref{eq:linlag}), we ensure the right evolution frequency of the amplitude variable. The error that we make by assigning the approximate values of $C_\omega$ and $L_\omega$ will only cause relative changes of order $A_{\pm}$ or $A_{\pm}^2$ in the coupling strengths used later in the article.

Introducing the canonical conjugate pair of variables, $\phi = \phi_\omega(t)$, $q = \partial\mathcal{L}/\partial \dot{\phi}_\omega(t) = C_\omega  \dot{\phi}_\omega(t)$, we obtain the effective harmonic oscillator Hamiltonian for the mode
\begin{align}
H = \frac{1}{2C_\omega} q^2 + \frac{1}{2L_\omega} \phi^2.
\end{align}
Applying usual canonical quantization, we impose $[q,\phi]=i\hbar$, and define annihilation and creation operators,
\begin{align}
q = \sqrt{\frac{\hbar C_\omega \omega}{2}} (a\dag + a), \label{eq:qquant} \\
\phi = i\sqrt{\frac{\hbar }{2C_\omega \omega}} (a\dag - a), \label{eq:phiquant}
\end{align}
which obey $[a,a\dag]=1$ and allow rewriting of the quantum mechanical Hamiltonian in the well known form
\begin{align}
H = \hbar \omega (a\dag a + \frac{1}{2}). \label{eq:Hmode}
\end{align}
By construction, this Hamiltonian yields the dynamics of the amplitude of the central frequency component of the driven $\omega$-mode, and Eqs. (\ref{eq:subpm},\ref{eq:three-fr}) account for the physical circuit observables that oscillate at $\omega$ and $\omega_\pm$.

Our  Eqs. \eqref{eq:qquant} and \eqref{eq:phiquant} differ from similar expansions in \cite{PhysRevA.86.013814,PhysRevA.80.032109} where the mode function $u(x)$, and thus the canonical quantum variables, are normalized in terms of the total capacitance $C_\Sigma = 2C_Td + C$ instead of $C_\omega$. Our approach, similar to that of \cite{PhysRevA.89.033853,eichler2014controlling}, gives simpler expressions for our applications.

The validity of the quantization of individual time dependent modes with no mutual couplings relies on the same assumption as we applied to justify the expansion of the classical circuit variables on the multi-frequency eigenmodes. In particular, changes in the excitation of the mode must be slow compared to the frequency separation to other modes.

\subsection{Coupling physical systems across frequency gaps}
\label{sec:coup}

Our quantization of the multi-frequency mode suggests the operator form of the positive and negative frequency parts,
\begin{align}
\hat{\phi}(x,t) = -\frac{i}{2}\sqrt{\frac{\hbar}{2C_{\omega}\omega}} \, a(t)\, \Big(u_\omega(x) + A_+ e^{-i\omega_d t}u_+(x) \nonumber \\ + A_- e^{i\omega_d t}u_-(x) \Big) + \text{h.c.}, \label{eq:qmode}
\end{align}
where $a(t)$ is given in the Heisenberg picture, and therefore $\hat{\phi}(x,t)$, due to (\ref{eq:Hmode}), acquires oscillations at the frequencies $\omega$ and $\omega\pm\omega_d$. From $\hat{\phi}(x,t)$ we can express all other variable of interest like the voltage, charge distribution etc. As an example we can consider the voltage operator
\begin{align}
\hat{V}(x,t) &= \pfrac{\hat{\phi}(x,t)}{t} \\&= \frac{1}{2}\sqrt{\frac{\hbar}{2C_{\omega}\omega}} \, a(t)\, \Big( \omega u_\omega(x) + \omega_+ A_+ e^{-i\omega_d t}u_+(x) \nonumber \\ &\quad + \omega_- A_- e^{i\omega_d t}u_-(x) \Big) + \text{h.c.}.\label{eq:voltage}
\end{align}

Electric charges and dipoles couple to the voltage along the waveguide, and the expression (\ref{eq:voltage}) implies that the driving of the in-line SQUID allows to bridge the frequency gap between the quantized circuit degrees of freedom and auxiliary quantum systems if they have transition frequencies equal to any one of the frequencies $\omega$ and $\omega\pm\omega_d$  - in the same way as a pump laser field may assist a quantized optical probe in the driving of atomic Raman transitions and optomechanical motion.

The coupling may have different forms, but if a quantum system $\mathcal{S}$ is detuned by a small amount $\delta$, from one of the multimode frequency components, the joint system dynamics is given by a Hamiltonian, which in the interaction picture takes the form,
\begin{align}
H = \hbar \delta\, a\dag a + \hbar G (a\dag b + b\dag a), \label{eq:HI}
\end{align}
where the coupling strength $G$ depends on the physical coupling mechanism and $b$ ($b\dag$) is the lowering (raising) operator of excitations in $\mathcal{S}$. This Hamiltonian is known as a beam-splitter interaction, which adiabatically transfers the quantum state of $\mathcal{S}$ to the resonator. For the application of the resonator as a quantum bus this is the desired interaction. For a physical component with excitation frequency $\omega_S \sim \omega \pm \omega_d$, situated at $x=x_t$ and coupled to the local value of $\hat{V}(x,t)$, we obtain $G_{\pm} \propto (\omega\pm \omega_d) A_{\pm}u_{\pm}(x_t)$, while the value $G \propto \omega u_\omega(x_t)$ is obtained when $\omega_S \sim \omega$. We will write this coupling for the former case as
\begin{align}
G_{\pm} = \frac{g\,\omega_\pm A_\pm}{4 \sqrt{\hbar C_\omega \omega}} u_\pm (x_t), \label{eq:G}
\end{align}
where $g$ is determined by the auxiliary system observables.

As a simple example we consider a transmon capacitively coupled to the resonator \cite{PhysRevA.76.042319} at position $x_t$. The transmon has quantized charge and phase variables $\hat{n}$ and $\hat{\psi}$, such that its Hamiltonian is given by $H_t = 4E_C (\hat{n} - n_g)^2 - E_{J,t} \cos \hat\psi$, while it couples to the resonator with
\begin{align}
H_I = 2e \beta \hat{n}\, \hat{V}(x_t)
\end{align}
where $\beta = C_c / C_\Sigma$ denotes the ratio between the coupling capacitor and the total capacitance of the transmon. In the limit of $E_{J,t} \ll E_C$, the transmon can be approximated as a two-level system, and the charge operator is given by Pauli transition operators between its eigenstates
\begin{align}
\hat{n} = i\Big(\frac{E_{J,t}}{8E_C} \Big)^{1/4} \frac{1}{\sqrt{2}} (\sigma\dag - \sigma).
\end{align}
The coupling constant $g$ between the system states in (\ref{eq:G}) thus becomes \cite{PhysRevA.76.042319}
\begin{align}
g = 2e \beta \bra{1}\hat{n}\ket{0}= \sqrt{2}ie\beta\Big(\frac{E_{J,t}}{8E_C} \Big)^{1/4}.
\end{align}
For realistic transmon and resonator parameters, the coupling strength $G_-$ to the lower sideband of the first mode of a short resonator is shown in Fig. \ref{fig:G} for different values of $\omega_d$. Characteristic resonant coupling strengths of transmon qubits to coplanar waveguides are a few hundred MHz \cite{PhysRevB.77.180502}, and we expect, within the validity of our approximations, to obtain few MHz coupling strengths between transmons and waveguides when an GHz frequency separation between them is bridged by the modulated SQUID. We, indeed, observe such values in the figure, and we also observe the expected increase of the coupling strength with the modulation amplitude $\delta E_J$. Due to the factor of $\omega_-$ in the expression for $G$ we obtain a lower value when we modulate with a higher frequency. In the figure we have also included a calculation using the simplified approach presented in the beginning of Sec. \ref{sec:res}. This quasi-static approach yields a coupling that is independent of the modulation frequency and in the regime of small modulation frequency and amplitude it matches our more precise calculation.

 We have chosen parameters to ensure a large free spectral range for the transmon qubits, since close to a resonance a cross-Kerr effect between the transmon and the resonator mode of strength
\begin{align}
\chi = G_\omega^2 \frac{\alpha}{\hbar \Delta (\hbar \Delta + \alpha)}, \label{eq:kerr}
\end{align}
may alter the dynamics. In Eq.(\ref{eq:kerr}), $\Delta = \omega_{10} - \omega$, $G_\omega$ is the coupling strength to the center frequency and $\alpha = -E_C$ is the anharmonicity of the transmon \cite{PhysRevA.76.042319}. For the parameters used for the thick green line in Fig. \ref{fig:G} $\chi \approx 2\pi \times 0.2$ MHz, and it is independent of the modulation frequency amplitude.

Since the same mode may be simultaneously coupled to different systems via its different frequency components, it may serve to transfer quantum states coherently between systems whose frequencies differ by $\omega_d$ or $2\omega_d$. Since we may apply a more complicated signal to the inline-SQUID, we may also modulate it at different frequencies and thus establish sidebands, which can interact selectively with different systems.  In the next section we shall couple the multi-frequency mode to two different transmon qubits and obtain a bichromatic two-qubit entangling gate, similar to gates applied in ion traps.

\begin{figure}
\includegraphics[width=\linewidth]{Figure-G.pdf}
\vspace*{-1cm}

\caption{Coupling strength of the two lowest states of a transmon to the resonator mode. The frequencies are such that $\omega_{10} = \omega_- = \omega - \omega_d$, where $\omega$ is the frequency of the 1st mode in a resonator with $d=0.25$ cm and $\omega=2\pi \times 10.82$ GHz in the absence of modulation. The transmon is located at $x_t=0.1d$ and it has $E_J / E_C = 80$ and $\beta = 2/3$. The thick (green) line is calculated by Eq. \eqref{eq:G} for the modulation frequency set to $\omega_d = 2\pi\times 6$ GHz while the thin (blue) line shows  Eq. \eqref{eq:G} for $\omega_d = 2\pi\times 0.5$ GHz. The dashed (red) line shows the result of the quasi-static aspproximation, Eq. \eqref{eq:qah}, which is independent of the modulation frequency.} \label{fig:G}
\end{figure}

\section{Multi-frequency modulation and Multi-Qubit gates}
\label{sec:ms}

\begin{figure}[t]
\flushleft (a)
\includegraphics[width=\linewidth]{twoqubit_sketch.pdf}

(b)
\includegraphics[width=\linewidth]{Figure-ms.pdf}
\caption{(a) Setup with two transmon qubits placed at $x_I=0.1d$ and $x_I=-0.1d$. (b) Time evolution of two-qubit density matrix elements obtained by a simulation of the master-equation with the Hamiltonian in Eq. \eqref{eq:ms}, a resonator decay-rate of $\kappa = 2\pi \times 0.2$ MHz, and transmon decay and dephasing lifetimes $T_1 = 10$ $\mu$s and $T_2 = 5$ $\mu$s. The transmon qubits have different excitation frequencies $\Omega_{1} = 2\pi \times 6.0$ GHz and $\Omega_2 = 2\pi \times 6.5$ GHz and the resonator frequency is $2\pi\times10.82$GHz. For parameters described in the text we obtain the Hamiltonian \eqref{eq:ms} with $G = 2\pi \times 2.5$ MHz and $\delta = 2\pi \times 10$ MHz. In the simulation we have also included a kerr-term with magnitude given in Eq. \eqref{eq:kerr}.} \label{fig:ms}
\end{figure}

Trapped ions can be excited by laser fields at a frequency sideband that excites their collective vibrational motion, and a bichromatic scheme, using laser frequencies detuned symmetrically around the internal state transition frequency, can be used to entangle the internal state of two or more ions \cite{PhysRevLett.82.1971,sackett2000experimental,PhysRevA.62.022311}. In this section we will develop a scheme that uses the multi-frequency resonator modes to accomplish a similar entangling operation among transmon qubits. If the central frequency component of the quantized field has frequency $\omega$, and the qubits have frequency $\Omega$, driving the SQUID at $\omega_t=\omega-\Omega$  makes the transfer of excitation between the qubits and the lower multi-frequency sideband  almost resonant. If, at the same time, the SQUID is driven at
$\omega_p=\omega+\Omega$, a parametric interaction, leading to the joint excitation (and deexcitation) of the resonator mode and the transmons becomes resonant. Detuning of these two driving terms by a small amount $\delta$ leads in the interaction picture with respect to the transmon and single mode Hamiltonian to the near resonant coupling of the transmons and resonator field operators,
\begin{align}
H_I =& \,\hbar G \sum_{n=1,2} (  a e^{-i\delta t} + a\dag e^{i\delta t} )( \sigma_{+,n} + \sigma_{-,n}). \label{eq:ms}
\end{align}
Unlike the ion trap implementation, where laser frequencies differing by a relatively small amount are applied to the ion qubits, our driving fields are applied to the resonator system and their frequencies differ strongly (by twice the qubit transition frequency, $\omega_p-\omega_t \sim 2\Omega$). The interaction Hamiltonian, however, is the same, and the analysis in \cite{PhysRevA.62.022311} applies for both the trapped ions and for the superconducting qubit system. We can hence use the scheme  to accomplish a two-qubit entangling gate as part of a universal gate set and with more transmon qubits, we may also prepare multi-qubit entangled states.

Before passing to an example with realistic interaction and damping parameters, we note that transmon qubits are likely to have different transition frequencies. If these are well separated, we merely have to modulate the in-line SQUID by separate pairs of modulation frequencies, $\omega_{t,n}=\omega-\delta-\Omega_n$, $\omega_{p,n}=\omega-\delta+\Omega_n$ and strengths, in which case we can recover Eq. (\ref{eq:ms}). In Fig. 5 we illustrate a coplanar waveguide resonator coupled to two transmon qubits with different transition frequencies, $\Omega_{1} = 2\pi \times 6.0$ GHz and $\Omega_2 = 2\pi \times 6.5$ GHz. We modulate the SQUID at frequencies $\lbrace \omega_{t,1}, \omega_{p,1}, \omega_{t,2}, \omega_{p,2} \rbrace = 2\pi \times  \lbrace 4.366, 17.366, 4.866, 16.866 \rbrace$ GHz and with the amplitudes $\lbrace \delta E_{J,t1}, \delta E_{J,p1}, \delta E_{J,t2}, \delta E_{J,p2} \rbrace / E_{J,0} = \lbrace 0.1581, -0.1584, 0.1682, -0.1687\rbrace$, leading to the Hamiltonian (\ref{eq:ms}), with $G = 2\pi \times 2.5$ MHz and $\delta = 2\pi \times 10$ MHz. With these parameters, an entangling gate has the duration $\tau=2\pi/\delta = 100$  ns \cite{PhysRevA.62.022311}, as indicated in Fig. 5 (b) by the time evolution of the two-qubit density matrix elements. The three matrix elements shown in Fig. \ref{fig:ms} are, in the ideal case, the only non-zero matrix elements of the two-qubit density matrix and thus the concurrence can be expressed as $2\, \text{Im}(\rho_{ee,gg})$. In the calculation, we have taken the finite coherence and excitation lifetimes of the qubit and of the resonator into account, and we obtain a maximally entangled state with a fidelity $F=95 \%$.

Our proposal is competitive with the achievements of other entanglement-gates in circuit QED \cite{dicarlo2009demonstration, PhysRevLett.107.080502, PhysRevLett.109.060501, PhysRevA.88.032317, PhysRevA.87.022309} and it may offers some advantages: (i) Using the SQUID to modulate the resonator frequency, there is no need for additional control lines to the qubits and we avoid the dephasing associated with the conventional frequency tuning of qubits. (ii) When our qubits are idle, they are far detuned with respect to each other and to the resonator, and hence they are immune to cross talk and Purcell-enhanced decay.

\section{Conclusion and outlook}
\label{sec:conc}

In conclusion, we have identified the resonant modes of a superconducting resonator with periodically modulated boundary conditions. The resulting modes consist of a carrier and two weak sideband components at frequencies which are separated by the modulation frequency, see Eq. \eqref{eq:three-fr} and Fig. \ref{fig:mode}. The classical sideband amplitudes are proportional to the carrier amplitude, and assuming that this proportionality is maintained, the dynamics is described by a simple harmonic oscillator Hamiltonian, which we take as the starting point for our quantum analysis. Elementary excitations of the system thus contain three frequency components and can exploit the sidebands to couple different physical system separated by large frequency gaps. Our sideband mediated transfer of excitation between two systems with very different frequencies can also be viewed as a transition between two energy eigenstates of the joint system, driven resonantly by the oscillating magnetic flux applied to the inline-SQUID. The rapid modification of SQUID parameters is already routinely accomplished for rapid tuning in laboratories and the harmonic driving is used in parametric amplifiers \cite{flux2008yamamoto} and parametric converters \cite{zakka2011quantum}. We hence believe that our proposal can be implemented with devices that can be readily constructed, while modulation of tuning elements to form sidebands rather than static frequency shifts may be employed in resonators that are already in use.

The multi-frequency modes were calculated using a linearized Lagrangian. Treating the non-linearity of the Josephson Hamiltonian as a perturbation on the single mode Hamiltonian, we obtain the Kerr-nonlinearity \cite{PhysRevA.86.013814,eichler2014controlling},
\begin{align}
H_{NL} = -\frac{E_{J,0}}{4} \Bigg( \frac{2\pi \sqrt{\hbar/2C_\omega \omega}}{\Phi_0} \Bigg) \cos^4 kd\; a\dag a\dag a a. \label{eq:hnl}
\end{align}
This term is small for the parameters used  in this paper, but in combination with the ability to couple systems at very different frequencies, its application, e.g., for the generation of non-classical states of the oscillator mode may be useful.

Finally, we discussed the application of the quantized multi-frequency oscillator mode to mediate an entangling gate between two transmon qubits, and by simulation we showed that a Bell-state with a fidelity of 95\% may be achieved using realistic parameters. This  analysis readily generalizes to multi-qubit systems, where the frequency control of the SQUID modulation may be used to control one and two-qubit gates as well as multi-qubit entanglement operations on any qubits in the resonator.

A bulk acoustic wave-modulator has been recently proposed to modulate the capacitance of a superconducting $LC$-circuit \cite{PhysRevLett.108.130504} and hence mediate the frequency difference between the quantized high frequency excitations of the circuit and the slow motion of a trapped atomic ion. That proposal relies in a similar way as ours on the frequency modulation of a quantized field degree of freedom, and due to the modulated capacitance it couples more strongly to low frequency motion than our oscillating voltage (\ref{eq:voltage}), which carries prefactors proportional to the low frequency.

\section*{Acknowledgements}
We thank P. Haikka, A.C.J. Wade, M.C. Tichy and Q. Xu for feedback on the manuscript. We furthermore acknowledge support from the Villum Foundation Center of Excellence, QUSCOPE, and the EU 7th Framework Programme collaborative project iQIT.

redpajama_set_name: RedPajamaArXiv


text:
Pose: Never knew love like this before
July 11, 2019 7:10 AM - Season 2, Episode 4 - Subscribe
"In "Never Knew Love Like This Before," Pose held up a mirror to the continued violence perpetrated against transgender women of color in our society and asked us not to look away."
Recaps:
- them.
"Since murder is the reality for so many trans women — particularly those involved in sex work — it's only fair that Pose would eventually reckon with it in a major way. But just as it's done since its first season, the show continues to use traumatic plot developments to make profound statements. Rather than ending Candy's arc with a disturbing close-up of her battered body, Ryan Murphy and the Pose creative team — utilizing the medium of television to right some of the wrongs frequently experienced by Candy's real-world counterparts — instead chose to give her the opportunity to say goodbye to her loved ones."
- Billboard
- AV Club
"It's a devastating loss for the characters of Pose, made even more devastating by the fact that it's an epidemic that persists. Angel is distraught throughout the episode and notes right away that it's only May and already eleven girls have been killed. Decades later, and already at least eleven Black trans women have been killed in 2019. Pose is fiercely committed to portraying the lived experiences of queer and trans people of color, and that includes the reality of violence, loss, and grief."
- Vox
"Beyond its flash and sizzle, Pose is also a poignant drama about a found family of people who've come together to support each other in a world that otherwise might not care. It is frequently moving, often beautiful, and sometimes corny. But it is a show where the lives of trans people of color are shown to matter. And in its latest episode, Pose killed off one of its characters, a black trans woman on the extreme edges of its story. Is her death an exploitative example of every story about black trans women becoming a story about violence at its core? Or is it a necessary depiction of the world as it is? Or is it both?"
Commentary and Interviews
- Esquire
"For thirty days a year, corporate brands voice their support for LGBTQ people. Publications push out stories about brave gay and lesbian and trans people. Straight people rally at parades with signs and rainbow headbands with fists thrust into the air. Pose's powerful fourth episode dares to ask if anyone cares once those days are up. After all, much like Pose, the story continues once the show is over. Are you still watching?"
- Out: Angelica Ross Opens Up About That Explosive Episode of Pose
I would definitely imagine in a different world for Candy in the same way I imagine that for trans women of color. I had plans for Candy to not only pull her look together, but to pull her life together with the connections at her retail job or develop her career like I did by starting at the beauty counters. So, I saw that there might've been an opportunity for Candy to live her dreams too, just like Angel was able to live hers. But when it comes to statistics, not just with HIV, but with trying to make it as a trans woman, one of us has got to go. It's sad the way that it is, but I kind of took that responsibility on willingly and said, "If this is to be what it is, I will make this the most glorious episode."
- Shondaland: Angelica Ross Opens Up About Her Powerful 'Pose' Episode
KT: Looking at the first three episodes of this season, you could sense that Candy was evolving, which was clearly intentional, right?
AR: Exactly. And I couldn't tell anyone in the cast either that she was going to die either! So I was playing Candy in those earlier episodes with this fever pitch, as if she knew that death was around the corner. And it took a toll on me.
One day the press was on set, and Candy was dressed up as Madonna, and in between takes, I went to the bathroom and just broke down in tears. Mind you, those scenes weren't at all emotional. It was just knowing what was coming down for Candy, holding all that in and knowing I would be saying goodbye to a cast and crew I had been building a relationship with for over a year.
- NY Times interview with Ryan Murphy, Janet Mock, and Angelica Ross
ANGELICA ROSS As we were acting, I felt like everyone crying in the pews, and everyone that was just crying along, was crying because every single word felt like words you've heard before. And that everything Candy was saying to her parents was everything you wish you had the opportunity to say. And so I was riding this wave of shared experience. I could feel it in the room. There were so many times where I had to excuse myself because I was trying to keep myself in ready mode.
When the parents came in [to the funeral home], I almost started crying, seeing them looking around the space. Because I just thought about my parents not knowing anything about the L.G.B.T.Q. community, nothing, especially back in the early '90s. So all of this context was flying at me on set and it was just there to use. I didn't rehearse any of those scenes.
- Tine: "The Tears were Real." Ryan Murphy and Janet Mock on Pose's Most Emotional Episode Yet
Janet Mock: "Why Candy?" was a fight we had in the writers' room. None of us wanted to give up any of these five trans women who are at the center of our show. So we had a difficult conversation. We had to lose someone who was beloved so that everyone could truly go through the grieving process. And Candy is our most rambunctious, aggressive fighter of a character. She's the one who takes risks. She's the one who storms the ballroom floor with a hammer. A lot of people's first reaction when they see Candy in that closet is: "It's not real. This show doesn't do that." But it's like, "No, we're going there and you have to watch and you have to deal. Because that's what people deal with every day when they lose their trans sisters."
- EW: Angelica Ross discusses Candy's fate on Pose: "I was devastated."
I honestly feel like the phoenix that is sort of rising out of Candy's ashes. I am Candy. Candy is me, and so the reality is that walking out of my house today, the possibility is that my story could end the same way. My story can end in violence, too. But to see the possibility which I think that people are going to get to see because I'm already working on some amazing projects is that they're going to see a black trans woman get her life. I feel like in the same similar ways that Candy got her life in the afterlife, you just want to think that somewhere they're living their life.
- Twitter thread from Indya Moore (Angel)
I didn't watch episode 4 with y'all, bc it was triggering and way to close to home for triggering layers of reasons. It was the day we filmed it we found that muhlaysia Brooker was murdered. Angelica was the first trans body I ever seen in a casket. Layleen Polonco was the second. During set we cried, were angry and tried to maintaining, "professionality", stay focused on the job... but Seeing Angelica in the casket, crying was too close to home. Her tears mirrored our black trans ancestors before they were murdered.The spiritual, emotional & psychological LABOR Angelica held for this scene, I hope is noticed. This scene was so close to home for all of us, the monthly string of trans murders already had me emotionally distraught and broke into my work.
posted by ChuraChura (4 comments total) 1 user marked this as a favorite
Candy's death was pretty well foreshadowed/spoiled beforehand so I was ... as prepared as I could be. I cried through the whole episode. It was heavyhanded, but I appreciate that the funeral home/ballroom scenes tried to take care of the audience and help us process this and that Janet Mock and Murphy apparently never even considered showing any of the actual violence. Reading Angelica and Indya's reactions, watching the episode, I was thinking I hope they took care of the actresses through shooting this, too.
Have been seeing that Candy's storyline is based on Venus Xtravanganza, like Elektra's man in the suitcase is based on Dorian Corey and Angel this season possibly on Octavia St. Laurent.
I liked Blanca supporting Candy in the opening ballroom scene, because season one was hard with Blanca's desire for the community to be kind to each other next to the obviously meant to be satisfying tear downs of Candy and Lulu. And it was beautiful that her moment with Candy was just...solemn humming together, holding hands, like a motherly comfort for Candy as much as it was for her.
posted by gaybobbie at 11:49 AM on July 11, 2019 [2 favorites]
This is the second time we've seen Blanca face down some extremely harsh trans-bashing on the show with dignity and grace. (First time was at her own mother's funeral, and now from Candy's parents.)
I do appreciate that they don't shy away from showing this, but it's painful to watch. And I can't imagine that it's easy for these actors to hear the same words they've likely had used against them in real life while calmly acting through each scene. Praying they at least have some mental health professionals available to deal with hearing what must be some very triggering shit during the course of their workdays.
This is an important show, and yeah, it's hella corny sometimes. You put in all the entertaining reasons to watch (great soundtrack, eye-catching costumes, beautiful actors), then you sneak in the hard-hitting issues and hope to God America keeps tuning in. Get people to connect with and relate to these characters.
As many times as Ryan Murphy's gone off the rails with his shows, this one seems slightly more reined in and consistent. It's been spottier this season than the first one, but the writing team is literally just re-telling stories that have already happened IRL.
That said, I'm really sorry to see Candy/Angelica go. I hope I get to see her again in future roles! It made sense and was somewhat foreshadowed; I just hate to see any trans woman have a good, high-profile role like that snatched away so soon.
Poor Lulu has to care for a whole house now as a single mother. I honestly get so stressed worrying about all these young people having enough money for rent and food, it feels too real!
posted by Unicorn on the cob at 4:44 PM on July 11, 2019 [2 favorites]
I hope I get to see her again in future roles!
Angelica Ross has been cast in American Horror Story: 1984.
I love this show so much. It's beautifully told, and provides so much necessary visibility and representation for trans actors of color. This episode was hard to watch. I appreciate that the violence was not sensationalized but was very present, and I am stunned to learn the funeral home scenes were not rehearsed.
posted by donnagirl at 6:01 PM on July 11, 2019 [6 favorites]
I've never cried so hard through any movie or tv program as I did with this episode. It really caught me off guard. It tore my heart apart. I love that I'm alive at a time when I can experience such a show, and I'm grateful to have watched it with you all!
posted by el gran combo at 12:05 AM on September 30, 2019
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Join the Young Promoters Group!
Scotland's largest rural performing arts festival is looking for talented individuals to join its board.
Now in its 38th year, the Dumfries and Galloway Arts Festival has built a reputation of excellence in bringing world-class theatre, music, dance, comedy and the spoken word to venues throughout the region. This is delivered via its 10-day festival at the end of May each year and year-round through its successful touring project, Dumfries and Galloway Arts Live, which piloted in 2016.
Last year's festival was the most successful, extensive and diverse to date with 85 performances in 48 venues across the entire region: from the grand setting of the Easterbrook Hall, to one of Scotland's smallest rural stages, the Swallow Theatre. Many 2016 shows sold out and more venues and local performing artists were involved than ever before.
An important aspect of the festival's work involves nurturing young performing artists and audiences and young people are encouraged to take an active part in the performing arts across the region as well as supporting the development of emerging local talent.
Last year, five events in the festival staged and promoted by young people and 1,038 young people attended 27 workshops led by visiting professional performing artists.
Helping to continue the year-on-year success of the organisation, the festival board comprises a diverse group of skilled and experienced individuals who all have a keen interest in performing arts and a vision to carry on delivering the best quality experience to every part of the region.
Ken said: "We are fortunate enough to have an excellent group of festival board members who, combined, cover a wide range of skills and most parts of the region.
"That said, we should be delighted to widen our scope and welcome more people on board who will represent their corner of Dumfries and Galloway and bring their good ideas to the table.
"Wherever you live in Dumfries and Galloway, your contribution of skill and knowledge would make a difference, particularly at a local level.
For information on how to contribute to the development of the festival and Arts Live, visit www.dgartsfestival.org.uk or contact chair@dgartsfestival.org.uk.