We introduce a general protocol for obtaining the charge basis density matrix of a superconducting quantum circuit. Inspired by cavity state tomography, our protocol combines Josephson-energypulse sequences and projective charge-basis readout to access the off-diagonal elements of the density matrix, a scheme we thus dub charge basis tomography. We simulate the reconstruction of the ground state of a target transmon using the Aharonov-Casher effect in a probe qubit to realise projective readout and show the Hilbert-Schmidt distance can detect deviations from the correct model Hamiltonian. Unlocking this ability to validate models using the ground state sets the stage for using transmons to detect interacting and topological phases, particularly in materials where time-domain and spectroscopic probes can be limited by intrinsic noise.
Semiconductor-based Josephson junctions embedded within a Cooper-pair-box can host complex many-body states, such as interacting Andreev states and potentially other quasi-particlesof topological origin. Here, we study the insights that could be revealed from a tomographic reconstruction of the Cooper-pair charge distribution of the junction prepared in its ground state. We posit that interacting and topological states can be identified from distinct signatures within the probability distribution of the charge states. Furthermore, the comprehensive dataset provides direct access to information theory metrics elucidating the entanglement between the charge sector of the superconductor and the microscopic degrees of freedom in the junction. We demonstrate how these metrics serve to further classify differences between the types of excitations in the junction.
In the era of Noisy Intermediate-Scale Quantum computing as well as in error correcting circuits, physical qubits coherence time and high fidelity gates are essential to the functioningof quantum computers. In this paper, we demonstrate theoretically and experimentally, that pulses designed by optimization can be used to counteract the loss of fidelity due to a control amplitude error of the transmon qubit. We analyze the control landscape obtained by robust optimal control and find it to depend on the error range, namely the solutions can get trapped in the basin of attraction of sub-optimal solutions. Robust controls are found for different error values and are compared to an incoherent loss of fidelity mechanism due to a finite relaxation rate. The controls are tested on the IBMQ’s qubit and found to demonstrate resilience against significant ∼10% errors.
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.