Symmetry considerations are key towards our understanding of the fundamental laws of Nature. The presence of a symmetry implies that a physical system is invariant under specific transformationsand this invariance may have deep consequences. For instance, symmetry arguments state that a system will remain in its initial state if incentives to actions are equally balanced. Here, we apply this principle to a chain of qubits and show that it is possible to engineer the symmetries of its Hamiltonian in order to keep quantum information intrinsically protected from both relaxation and decoherence. We show that the coherence properties of this system are strongly enhanced relative to those of its individual components. Such a qubit chain can be realized using a simple architecture consisting of a relatively small number of superconducting Josephson junctions.
Fault tolerant quantum computing requires quantum gates with high fidelity. Incoherent errors reduce the fidelities of quantum gates when the operation time is too long. Optimal controltechniques can be used to decrease the operation time in theory, but generally do not take into account the realistic nature of uncertainty regarding the system parameters. We apply robust optimal control techniques to demonstrate that it is feasible to reduce the operation time of the cross-resonance gate in superconducting systems to under 100\,ns with two-qubit gate fidelities of F>0.99, where the gate fidelity will not be coherence limited. This is while ensuring robustness for up to 10\% uncertainty in the system, and having chosen a parameterization that aides in experimental feasibility. We find that the highest fidelity gates can be achieved in the shortest time for the transmon qubits compared with a two-level flux qubit system. This suggests that the third-level of the transmon may be useful for achieving shorter cross-resonance gate times with high fidelity. The results further indicate a speed limit for experimentally feasible pulses with the inclusion of robustness and the maximum amount of uncertainty allowable to achieve fidelities with F>0.999.
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 demonstratethat 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.
We study exact solutions of the steady state behaviour of several non-linear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planckequations 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 fields, along with the Husimi Q-function for the transmon. Second, we revisit exact solutions of quantum Duffing 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 Schroedinger cat states and the generation of squeezed states in parametric amplifiers, in addition to studying the Q-functions of the different phases of the quantum system. The field of superconducting circuits, with its strong nonlinearities and couplings, has provided access to a new parameter regime in which returning to these exact quantum optics methods can provide valuable insights.
The quasi-degenerate ground state manifold of the anisotropic Ising spin model can encode quantum information, but its degree of protection against local perturbations is known to beonly partial. We explain how the coupling between the two ground states can be used to observe signatures of Majorana zero modes in a small controlled chain of qubits. We argue that the protection against certain local perturbations persists across a range of parameters even away from the ideal point. Remarkably, when additional non-local interactions are considered the system enters a phase where the ground states are fully protected against all local field perturbations.
We propose a deterministic scheme for teleporting an unknown qubit through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-levelsystem 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 propose a dynamical scheme for deterministically amplifying photonic Schr$“o$dinger cat states based on a set of optimal state-transfers. The scheme can be implemented instrongly 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.
We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and non-classical driving. In this scenario, we show that an effective Hartree-typedecoupling yields a good approximation to the dynamics of the system. We find that the stationary states are squeezed vacuum states of the non-interacting system which are enhanced by the Q-factor of the cavity. We show that this effective interaction could be realised with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. The qubit non-linearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of parameters, enables quantum state tomography of the cavity.
Combining superconducting qubits with mesoscopic devices that carry topological states of matter may lead to compact and improved qubit devices with properties useful for fault-tolerantquantum computation. Recently, a charge qubit device based on a topological superconductor circuit has been introduced where signatures of Majorana fermions could be detected spectroscopically in the transmon regime. This device stores quantum information in coherent superpositions of fermion parity states originating from the Majorana fermions, generating a highly isolated qubit whose coherence time could be greatly enhanced. We extended the conventional semi-classical method and obtained analytical derivations for strong transmon-photon coupling. The analytical challenge is rendered tractable via a formalism based on the WKB method that allows to extract the energy eigenstates of the qubit and its dipole matrix elements. Using this formalism, we study the effect of the Majorana fermions on the quantum electrodynamics of the device embedded within an optical cavity and develop protocols to initialise, control and measure the parity states. We show that, remarkably, the parity eigenvalue can be detected via dispersive shifts of the optical cavity in the strong coupling regime and its state can be coherently manipulated via a second order sideband transition.
We analyse the transmon regime Hamiltonian of a Cooper-Pair-Box where the superconducting phase difference is coupled to the zero energy parity states that arise from Majorana quasi-particles.We investigate the level structure and properties of the transmon qubit in this regime where even a small coupling causes hybridization of different transmon-parity states without compromising the suppression of charge dispersion. We show that the microwave photon-qubit coupling is sensitive to the gate bias and all the energy scales of the Hamiltonian. As well as a probe for topological-superconductor excitations, we propose that this type of device could be used to realise a high coherence tunable four-level system in the superconducting circuits architecture.