Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities

In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level structure. We also show how this physics can account for the high-fidelity avalanchelike measurement recently reported by Reed {\it et al.} [arXiv:1004.4323v1].Comment: 4 pages, 5 figure

The interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory

Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function $z(t)$ appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value $z(t)$ even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system ``conditioned'' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.Comment: 9 page

Pure-state quantum trajectories for general non-Markovian systems do not exist

Since the first derivation of non-Markovian stochastic Schr\"odinger equations, their interpretation has been contentious. In a recent Letter [Phys. Rev. Lett. 100, 080401 (2008)], Di\'osi claimed to prove that they generate "true single system trajectories [conditioned on] continuous measurement". In this Letter we show that his proof is fundamentally flawed: the solution to his non-Markovian stochastic Schr\"odinger equation at any particular time can be interpreted as a conditioned state, but joining up these solutions as a trajectory creates a fiction.Comment: 4 page

Implementing optimal control pulse shaping for improved single-qubit gates

We employ pulse shaping to abate single-qubit gate errors arising from the weak anharmonicity of transmon superconducting qubits. By applying shaped pulses to both quadratures of rotation, a phase error induced by the presence of higher levels is corrected. Using a derivative of the control on the quadrature channel, we are able to remove the effect of the anharmonic levels for multiple qubits coupled to a microwave resonator. Randomized benchmarking is used to quantify the average error per gate, achieving a minimum of 0.007+/-0.005 using 4 ns-wide pulse.Comment: 4 pages, 4 figure

Oil Presses.

1. Introduction; 2. Processes for obtaining vegetable oils; 3. Detailing the continuous mechanical pressing; 4. Examples on the application of pressing for obtaining oil from cotton, peanut and sunflower; 5. Conclusion

A perturbative approach to non-Markovian stochastic Schr\"odinger equations

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two level atom immersed in a environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensembled average state $\rho_{\rm red}(t)$ approach the exact reduced state found via Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure

Randomized benchmarking and process tomography for gate errors in a solid-state qubit

We present measurements of single-qubit gate errors for a superconducting qubit. Results from quantum process tomography and randomized benchmarking are compared with gate errors obtained from a double pi pulse experiment. Randomized benchmarking reveals a minimum average gate error of 1.1+/-0.3% and a simple exponential dependence of fidelity on the number of gates. It shows that the limits on gate fidelity are primarily imposed by qubit decoherence, in agreement with theory.Comment: 4 pages, 4 figures, plus supplementary materia