### Publications

Bleszynski-Jayich AC, Shanks WE, Peaudecerf B, Ginossar E, von Oppen F, Glazman L, Harris JGE (2009) Persistent Currents in Normal Metal Rings, SCIENCE326(5950)pp. 272-275 AMER ASSOC ADVANCEMENT SCIENCE

Kirchmair G, Vlastakis B, Leghtas Z, Nigg SE, Paik H, Ginossar E, Mirrahimi M, Frupzio L, Girvin SM, Schoelkopf RJ (2012) Observation of quantum state collapse and revival due to the single-photon Kerr effect,NATURE495(7440)pp. 205-209 NATURE PUBLISHING GROUP

We propose a dynamical scheme for deterministically amplifying photonic
Schroedinger cat states based on a set of optimal state-transfers. The scheme
can be implemented in strongly coupled qubit-cavity systems and is well suited
to the capabilities of state of the art superconducting circuits. The ideal
analytical scheme is compared with a full simulation of the open
Jaynes-Cummings model with realistic device parameters. This amplification tool
can be utilized for practical quantum information processing in non-classical
continuous-variable states.

Schuster DI, Sears AP, Ginossar E, DiCarlo L, Frunzio L, Morton JJL, Wu H, Briggs GAD, Buckley BB, Awschalom DD, Schoelkopf RJ (2010) High-Cooperativity Coupling of Electron-Spin Ensembles to Superconducting Cavities,PHYSICAL REVIEW LETTERS105(14)ARTN 140501 AMER PHYSICAL SOC

Ginossar E, Bishop LS, Girvin SM (2012) Nonlinear oscillators and high fidelity qubit state measurement in circuit quantum electrodynamics, In: Fluctuating Nonlinear Oscillators. From nanomechanics to quantum superconducting circuits8 Oxford University Press

In this book chapter we analyze the high excitation nonlinear response of the
Jaynes-Cummings model in quantum optics when the qubit and cavity are strongly
coupled. We focus on the parameter ranges appropriate for transmon qubits in
the circuit quantum electrodynamics architecture, where the system behaves
essentially as a nonlinear quantum oscillator and we analyze the quantum and
semi-classical dynamics. One of the central motivations is that under strong
excitation tones, the nonlinear response can lead to qubit quantum state
discrimination and we present initial results for the cases when the qubit and
cavity are on resonance or far off-resonance (dispersive).

Bishop LS, Tornberg L, Price D, Ginossar E, Nunnenkamp A, Houck AA, Gambetta JM, Koch J, Johansson G, Girvin SM, Schoelkopf RJ (2009) Proposal for generating and detecting multi-qubit GHZ states in circuit QED,NEW JOURNAL OF PHYSICS11ARTN 073040 IOP PUBLISHING LTD

We present a complete classification of the electron-electron interaction in
chaotic quantum dots based on expansion in inverse powers of $1/M$, the number
of the electron states in the Thouless window, $M \simeq k_F R$. This
classification is quite universal and extends and enlarges the universal non
interacting RMT statistical ensembles. We show that existing Coulomb blockade
peak spacing data for $B=0$ and $B\ne 0$ is described quite accurately by the
interacting GSE and by its extension to $B\ne 0$. The bimodal structure
existing in the interacting GUE case is completely washed out by the combined
effect of the spin orbit, pairing and higher order residual interactions.

We propose a deterministic scheme for teleporting an unknown qubit through
continuous-variable entangled states in superconducting circuits. The qubit is
a superconducting two-level system and the bipartite quantum channel is a
photonic entangled coherent state between two cavities. A Bell-type measurement
performed on the hybrid state of solid and photonic states brings a
discrete-variable unknown electronic state to a continuous-variable photonic
cat state in a cavity mode. This scheme further enables applications for
quantum information processing in the same architecture of circuit-QED such as
verification and error-detection schemes for entangled coherent states.
Finally, a dynamical method of a self-Kerr tunability in a cavity state has
been investigated for minimizing self-Kerr distortion and all essential
ingredients are shown to be experimentally feasible with the state of the art
superconducting circuits.

We consider a semiconductor quantum-well placed in a wave guide microcavity
and interacting with the broadband squeezed vacuum radiation, which fills one
mode of the wave guide with a large average occupation. The wave guide modifies
the optical density of states so that the quantum well interacts mostly with
the squeezed vacuum. The vacuum is squeezed around the externally controlled
central frequency $\om_0$, which is tuned above the electron-hole gap $E_g$,
and induces fluctuations in the interband polarization of the quantum-well. The
power spectrum of scattered light exhibits a peak around $\om_0$, which is
moreover non-Lorentzian and is a result of both the squeezing and the
particle-hole continuum. The squeezing spectrum is qualitatively different from
the atomic case. We discuss the possibility to observe the above phenomena in
the presence of additional non-radiative (e-e, phonon) dephasing.

Johnson BR, Reed MD, Houck AA, Schuster DI, Bishop LS, Ginossar E, Gambetta JM, DiCarlo L, Frunzio L, Girvin SM, Schoelkopf RJ (2010) Quantum non-demolition detection of single microwave photons in a circuit,NATURE PHYSICS6(9)pp. 663-667 NATURE PUBLISHING GROUP

Elliott M, Ginossar E (2016) Applications of the Fokker-Planck equation in circuit quantum electrodynamics, Physical Review A: Atomic, Molecular and Optical Physics94(4) http://journals.aps.org/pra/

We study exact solutions of the steady state behaviour of several non-linear open quantum systems
which can be applied to the eld of circuit quantum electrodynamics. Using Fokker-Planck
equations in the generalised P-representation we investigate the analytical solutions of two fundamental
models. First, we solve for the steady-state response of a linear cavity that is coupled to
an approximate transmon qubit and use this solution to study both the weak and strong driving
regimes, using analytical expressions for the moments of both cavity and transmon elds, along with
the Husimi Q-function for the transmon. Second, we revisit exact solutions of quantum Du ng oscillator
which is driven both coherently and parametrically while also experiencing decoherence by the
loss of single and pairs of photons. We use this solution to discuss both stabilisation of Schrodinger
cat states and the generation of squeezed states in parametric ampli ers, in addition to studying the
Q-functions of the di erent phases of the quantum system. The eld of superconducting circuits,
with its strong nonlinearities and couplings, has provided access to new parameter regimes in which
returning to these exact quantum optics methods can provide valuable insights.

Elliott M, Ginossar E (2015) Enhancement and state tomography of a squeezed vacuum with circuit quantum electrodynamics, PHYSICAL REVIEW A92(1)ARTN 013826 AMER PHYSICAL SOC

We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and nonclassical driving. We show that this scenario could be realized with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. In the presence of dissipation, we find that an effective Hartree-type decoupling with a Fokker-Planck equation yields a good approximation. We find that the stationary state is approximately a squeezed vacuum, which is enhanced by the Q factor of the cavity but conserved by the interaction. The qubit nonlinearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of realistic parameters, enables characterization of itinerant squeezed fields.

We explore the joint activated dynamics exhibited by two quantum degrees of freedom: a cavity mode oscillator which is strongly coupled to a superconducting qubit in the strongly coherently driven dispersive regime. Dynamical simulations and complementary measurements show a range of parameters where both the cavity and the qubit exhibit sudden simultaneous switching between two metastable states. This manifests in ensemble averaged amplitudes of both the cavity and qubit exhibiting a partial coherent cancellation. Transmission measurements of driven microwave cavities coupled to transmon qubits show detailed features which agree with the theory in the regime of simultaneous switching

In this work we investigate the regime of amplitude bistability in the driven dissipative Jaynes-Cummings (JC) model. We study the semiclassical equation dynamics in contrast to entangled cavity-photon and qubit quantum trajectories, discussing our results in the context of an out-of-equilibrium first order quantum dissipative phase transition for a single JC resonator. Finally, we compare the switching process between metastable states for the two system degrees of freedom by examining a single realization of the random qubit vector in the Bloch sphere next to the intracavity amplitude quasi distributions at given time instants.

Optimization of the fidelity of control operations is of critical importance in the pursuit of fault tolerant quantum computation. We apply optimal control techniques to demonstrate that a single drive via the cavity in circuit quantum electrodynamics can implement a high fidelity two-qubit all-microwave gate that directly entangles the qubits via the mutual qubit-cavity couplings. This is performed by driving at one of the qubits? frequencies which generates a conditional two-qubit gate, but will also generate other spurious interactions. These optimal control techniques are used to find pulse shapes that can perform this two-qubit gate with high fidelity, robust against errors in the system parameters. The simulations were all performed using experimentally relevant parameters and constraints.

Solid-state Majorana fermions are generating intensive interest because of their unique properties and possible applications in fault tolerant quantum memory devices. Here we propose a method to detect signatures of Majorana fermions in hybrid devices by employing the sensitive apparatus of the superconducting charge-qubit architecture and its efficient coupling to microwave photons. In the charge and transmon regimes of this device, we find robust signatures of the underlying Majorana fermions that are, remarkably, not washed out by the smallness of the Majorana contribution to the Josephson current. It is predicted that at special gate bias points the photon-qubit coupling can be switched off via quantum interference, and in other points it is exponentially dependent on the control parameter EJ/EC. We propose that this device could be used to manipulate the quantum state of the Majorana fermion and realize a tunable high coherence four-level system in the superconducting-circuit architecture.

We propose a deterministic scheme for teleporting an unknown qubit state through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a microwave photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states transfers a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. In order to facilitate the implementation of such complex protocols we propose a design for reducing the self-Kerr nonlinearity in the cavity. The teleporation scheme enables quantum information processing operations with circuit-QED based on entangled coherent states. These include state veri?cation and single-qubit operations with entangled coherent states. These are shown to be experimentally feasible with the state of the art superconducting circuits.

Superconducting circuits provide an architecture upon which cavity quantum electrodynamics (QED) can be implemented at microwave frequencies in a highly tunable environment. Known as circuit QED, these systems can achieve larger nonlinearities, stronger coupling and greater controllability than can be achieved in cavity QED, all in a customisable, solid state device, making this technology an exciting test bed for both quantum optics and quantum information processing. These new parameter regimes open up new avenues for quantum technology, while also allowing older quantum optics results to finally be tested. In particular is is now possible to experimentally produce nonclassical states, such as squeezed and Schr\"odinger cat states, relatively simply in these devices. Using open quantum systems methods, in this thesis we investigate four problems which involve the use of nonclassical states in circuit QED. First we investigate the effects of a Kerr nonlinearity on the ability to preserve transported squeezed states in a superconducting cavity, and whether this setup permits us to generate, and perform tomography, of a highly squeezed field using a qubit, with possible applications in the characterisation of sources of squeezed microwaves. Second, we present a novel scheme for the amplification of cat states using a coupled qubit and external microwave drives, inspired by the stimulated Raman adiabatic passage. This scheme differs from similar techniques in circuit QED in that it is deterministic and therefore compatible with a protocol for stabilising cat states without the need for complex dissipation engineering. Next we use solutions of Fokker-Planck equations to study the exact steady-state response of two nonlinear systems: a transmon qubit coupled to a readout resonator, where we find good agreement with experiments and see simultaneous bistability of the cavity and transmon; and a parametrically driven nonlinear resonator, where we compare the classical and quantum phases of the system and discuss applications in the generation of squeezed states and stabilisation of cat states. Finally, we investigate the use of two different types of superconducting qubits in a single experiment, seeing that this enables engineering of the self- and cross-Kerr effects in a line of cavities. This could provide a valuable means of entangling cavity states, in addition to a resource for quantum simulation.

Arrays of dopants in silicon are promising platforms for the quantum simulation of the Fermi-Hubbard model. We show that the simplest model with only on-site interaction is insufficient to describe the physics of an array of phosphorous donors in silicon due to the strong intersite interaction in the system. We also study the resonant tunneling transport in the array at low temperature as a mean of probing the features of the Hubbard physics, such as the Hubbard bands and the Mott gap. Two mechanisms of localization which suppresses transport in the array are investigated: The first arises from the electron-ion core attraction and is significant at low filling; the second is due to the sharp oscillation in the tunnel coupling caused by the intervalley interference of the donor electron's wave function. This disorder in the tunnel coupling leads to a steep exponential decay of conductance with channel length in one-dimensional arrays, but its effect is less prominent in two-dimensional ones. Hence, it is possible to observe resonant tunneling transport in a relatively large array in two dimensions.

The engineering of Kerr interactions is of great interest for processing quantum information in multipartite quantum systems and for investigating many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schrödinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and be a useful platform for quantum simulation in circuit quantum electrodynamics.

We present evidence of metastable rare quantum-
uctuation switching for the driven dissipative
Jaynes-Cummings (JC) oscillator coupled to a zero-temperature bath in the strongly dispersive
regime. We show that single-atom complex amplitude bistability is accompanied by the appearance
of a low-amplitude long-lived transient state, hereinafter called `dark state', having a distribution
with quasi-Poissonian statistics both for the coupled qubit and cavity mode. We find that the
dark state is linked to a spontaneous
ipping of the qubit state, detuning the cavity to a low-photon
response. The appearance of the dark state is correlated with the participation of the two metastable
states in the dispersive bistability, as evidenced by the solution of the Master Equation and single
quantum trajectories.

Matmon G, Ginossar E, Villis B, Kolker A, Lim T, Solanki H, Schofield S, Curson N, Li J, Murdin B, Fisher A, Aeppli G (2018) 2D-3D crossover in a dense electron liquid in silicon,Physical Review B97155306 American Physical Society

Doping of silicon via phosphine exposures alternating with molecular beam epitaxy overgrowth is a
path to Si:P substrates for conventional microelectronics and quantum information technologies. The
technique also provides a new and well-controlled material for systematic studies of two-dimensional
lattices with a half-filled band. We show here that for a dense (ns = 2.8 × 1014 cm?2
) disordered
two-dimensional array of P atoms, the full field angle-dependent magnetostransport is remarkably
well described by classic weak localization theory with no corrections due to interaction effects.
The two- to three-dimensional cross-over seen upon warming can also be interpreted using scaling
concepts, developed for anistropic three-dimensional materials, which work remarkably except when
the applied fields are nearly parallel to the conducting planes.

Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.

Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise
for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi-
Hubbard model. We show how the topological phases at half-filling can be characterized by a
reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures
of bulk-boundary correspondence are observed in the triplon excitation of the bulk and the edge
states of uncoupled spins at the boundaries. At quarter-filling we show that owing to the presence of
the Hubbard interaction the system can undergo a transition to the topological ground state of the
non-interacting Su-Schrieffer-Heeger model with the application of a moderate-strength external
magnetic field. We propose a robust experimental realization with a chain of dopant atoms in
silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the
tunneling current through the many-body state of the chain.

We investigate the low-energy theory of a one-dimensional finite capacitance topological Josephson junction.
Charge fluctuations across the junction couple to resonant microwave fields and can be used to probe microscopic
excitations such as Majorana and Andreev bound states. This marriage between localized microscopic degrees of
freedom and macroscopic dynamics of the superconducting phase, leads to unique spectroscopic patterns which
allow us to reveal the presence of Majorana fermions among the low-lying excitations.