Loss-tolerant parity measurement for distant quantum bits

We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that for a probe electromagnetic field in a particular quantum state, namely a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary back-action on the probe state. This leads to a parity measurement protocol where the main effect of the transmission losses is a decrease in the measurement strength. By repeating the non-destructive (weak) parity measurement, one achieves a high-fidelity entanglement in spite of a significant transmission loss

General phase spaces: from discrete variables to rotor and continuum limits

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.Comment: 22 pages, 3 figures; part of special issue on Rabi model; v2 minor change

Planar Superconducting Whispering Gallery Mode Resonators

We introduce a microwave circuit architecture for quantum signal processing combining design principles borrowed from high-Q 3D resonators in the quantum regime and from planar structures fabricated with standard lithography. The resulting '2.5D' whispering-gallery mode resonators store 98% of their energy in vacuum. We have measured internal quality factors above 3 million at the single photon level and have used the device as a materials characterization platform to place an upper bound on the surface resistance of thin film aluminum of less than 250nOhms.Comment: 3 Pages, 3 Figure

Circuit QED and engineering charge based superconducting qubits

The last two decades have seen tremendous advances in our ability to generate and manipulate quantum coherence in mesoscopic superconducting circuits. These advances have opened up the study of quantum optics of microwave photons in superconducting circuits as well as providing important hardware for the manipulation of quantum information. Focusing primarily on charge-based qubits, we provide a brief overview of these developments and discuss the present state of the art. We also survey the remarkable progress that has been made in realizing circuit quantum electrodynamics (QED) in which superconducting artificial atoms are strongly coupled to individual microwave photons.Comment: Proceedings of Nobel Symposium 141: Qubits for Future Quantum Informatio

Josephson Amplifier for Qubit Readout

We report on measurements of a Josephson amplifier (J-amp) suitable for quantum-state qubit readout in the microwave domain. It consists of two microstrip resonators which intersect at a Josephson ring modulator. A maximum gain of about 20 dB, a bandwidth of 9 MHz, and a center-frequency tunability of about 60 MHz with gain in excess of 10 dB have been attained for idler and signal of frequencies 6.4 GHz and 8.1 GHz, in accordance with theory. Maximum input power measurements of the J-amp show a relatively good agreement with theoretical prediction. We discuss how the amplifier characteristics can be improved.Comment: 9 pages, 4 figure

Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array

Quantum fluctuations in an anharmonic superconducting circuit enable frequency conversion of individual incoming photons. This effect, linear in the photon beam intensity, leads to ramifications for the standard input-output circuit theory. We consider an extreme case of anharmonicity in which photons scatter off a small set of weak links within a Josephson junction array. We show that this quantum impurity displays Kondo physics and evaluate the elastic and inelastic photon scattering cross sections. These cross sections reveal many-body properties of the Kondo problem that are hard to access in its traditional fermionic version.Comment: 18 pages, 5 figures; v2: published versio

Detecting charge noise with a Josephson junction: A problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the fundamental problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyse experimental data and to optimize detection circuits.Comment: 4 pages, 1 figure; minor typos corrected, some revisions in the tex

Measuring the Decoherence of a Quantronium Qubit with the Cavity Bifurcation Amplifier

Dispersive readouts for superconducting qubits have the advantage of speed and minimal invasiveness. We have developed such an amplifier, the Cavity Bifurcation Amplifier (CBA) [10], and applied it to the readout of the quantronium qubit [2]. It consists of a Josephson junction embedded in a microwave on-chip resonator. In contrast with the Josephson bifurcation amplifier [17], which has an on-chip capacitor shunting a junction, the resonator is based on a simple coplanar waveguide imposing a pre-determined frequency and whose other RF characteristics like the quality factor are easily controlled and optimized. Under proper microwave irradiation conditions, the CBA has two metastable states. Which state is adopted by the CBA depends on the state of a quantronium qubit coupled to the CBA's junction. Due to the MHz repetition rate and large signal to noise ratio we can show directly that the coherence is limited by 1/f gate charge noise when biased at the sweet spot - a point insensitive to first order gate charge fluctuations. This architecture lends itself to scalable quantum computing using a multi-resonator chip with multiplexed readouts.Comment: 6 pages, 5 figures To be published in Physical Review