Quantum noise operators for theN-level system

Ch. Schmid, H. Risken

Dibyendu Chatterjee, Arijit Roy

A four-level qubit system is applied to realize quantum half-adder operation.The half-adder circuit is obtained in terms of a quantum CPHASE gate realized by the qubits comprised of four energy levels [C.P. Yang, Prog.Theor.Phys.128, 587 (2012)], and such a CPHASE gate is demonstrated using the transmon.Commonly, higher energy levels are very sensitive and are easily perturbed by the noise sources.Compared to other qubit systems, the higher energy levels of the transmon are less prone to noise such as charge noise, flux noise and other noises.Further, the order of the dephasing time of the higher energy levels (third and fourth energy levels) is nearly the same as that of the lower energy levels of the transmon when the ratio between the Josephson energy and the charging energy 1.A system of three transmons coupled to a single high quality-factor superconducting coplanar resonator is demonstrated to obtain two-and three-qubit CPHASE gates which are in turn used to obtain the quantum half-adder operation.The main advantage of this quantum half-adder scheme is the reduction in the number of required elementary gates, leading to a significant increase in operational speed and robustness compared to the other existing half-adder schemes.The operational time of a complete half-adder operation is ∼37 ns.The methods presented in this article can also be implemented for more complicated quantum circuits.. . . . .

Marek Sawerwain, Joanna Wiśniewska

The quantum entanglement is considered as one of the most important notions of quantum computing. The entanglement is a feature of quantum systems and it is used as a basis for many quantum algorithms and protocols. In this paper we analyze the level of entanglement for the quantum switch, during its work. The level of entanglement during the correct operating may be compared with the situation when a noise is present in the analyzed system. The noise changes the level of quantum entanglement and we utilize this observation to evaluate if the switch works properly. We present the formulae describing the value of entanglement with use of the Concurrence measure and also the value of entropy. Both mentioned values may be utilized to detect the noise during the operating of quantum switch.

François Chapeau-Blondeau

Malin Premaratne, Govind P. Agrawal

Andrew J. Kerman, William D. Oliver

We present a scheme for implementing quantum operations with superconducting qubits. Our approach uses a "coupler" qubit to mediate a controllable interaction between data qubits, pulse sequences which strongly mitigate the effects of 1/f flux noise, and a high-Q resonator-based local memory. We develop a Monte Carlo simulation technique capable of describing arbitrary noise-induced dephasing and decay, and demonstrate in this system a set of universal gate operations with O(10(-5)) error probabilities in the presence of experimentally measured levels of 1/f noise. We then add relaxation and quantify the decay times required to maintain this error level.