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Physical Review A

Decoherence of coupled Josephson charge qubits due to partially correlated low-frequency noise

Yong Hu, Zheng-Wei Zhou, Jianming Cai, Guang‐Can Guo

Published May 21, 2007• 9 citations
Publisher

Abstract

Josephson charge qubits are promising candidates for scalable quantum computing. However, their performances are strongly degraded by decoherence due to low-frequency background noise, typically with a $1∕f$ spectrum. In this paper, we investigate the decoherence process of two Cooper pair boxes (CPBs) coupled via a capacitor. Going beyond the common and uncorrelated noise models and the Bloch-Redfield formalism of previous works, we study the coupled system's quadratic dephasing under the condition of partially correlated noise sources. Based on reported experiments and generally accepted noise mechanisms, we introduce a reasonable assumption for the noise correlation, with which the calculation of multiqubit decoherence can be simplified to a problem on the single-qubit level. For the conventional Gaussian $1∕f$ noise case, our results demonstrate that the quadratic dephasing rates are not very sensitive to the spatial correlation of the noises. Furthermore, we discuss the feasibility and efficiency of dynamical decoupling in the coupled CPBs.

DOI
10.1103/physreva.75.052327

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Josephson charge qubits are promising candidates for scalable quantum computing. However, their performances are strongly degraded by decoherence due to low-frequency background noise, typically with a 1∕f1∕f1∕f spectrum. In this paper, we investigate the decoherence process of two Cooper pair boxes (CPBs) coupled via a capacitor. Going beyond the common and uncorrelated noise models and the Bloch-Redfield formalism of previous works, we study the coupled system's quadratic dephasing under the condition of partially correlated noise sources. Based on reported experiments and generally accepted noise mechanisms, we introduce a reasonable assumption for the noise correlation, with which the calculation of multiqubit decoherence can be simplified to a problem on the single-qubit level. For the conventional Gaussian 1∕f1∕f1∕f noise case, our results demonstrate that the quadratic dephasing rates are not very sensitive to the spatial correlation of the noises. Furthermore, we discuss the feasibility and efficiency of dynamical decoupling in the coupled CPBs.
Charge fluctuations from gate bias and background traps severely limit the performance of a charge qubit in a Cooper-pair box (CPB). Here we present an experimentally realizable method to control the decoherence effects of these charge fluctuations using two strongly capacitively coupled CPBs. This coupled-box system has a low-decoherence subspace of two states. Our results show that the interbox Coulomb correlation can help significantly suppress decoherence of this two-level system, making it a promising candidate as a logical qubit, encoded using two CPBs.
Many solid-state qubit systems are afflicted by low-frequency noise mechanisms that operate along two perpendicular axes of the Bloch sphere. Depending on the qubit control fields, either noise can be longitudinal or transverse to the quantization axis of the qubit, thus affecting its dynamics in distinct ways, generally contributing to decoherence that goes beyond pure dephasing. Here, we present a theory that provides a unified platform to study dynamics of a qubit subjected to two perpendicular low-frequency noises (assumed to be Gaussian and uncorrelated) under dynamical decoupling pulse sequences. The theory is demonstrated by the commonly encountered case of power law noise spectra, where approximate analytical results can be obtained.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
Quantum computing provides significantly more efficient methods than classical computers for doing rigorous calculations such as encryption, search algorithms, and physical simulations. This is accomplished through the use of qubits which exist in a superposition of multiple states at once allowing for both complex and fast calculations. Environmental fluctuations interfere with these states and resulting in decoherence and dephasing and the break down of the algorithm. One type of qubit is the fluxonium: a superconducting artificial atom derived from the Cooper pair box. The purpose of this project was to analyze the effect of charge noise on the fluxonium qubit which, in the past, has never systematically been done before. Charge noise enters the qubit in the form of 1/f noise resulting in interference with the Cooper pairs, two loosely bound electrons, hopping between the superconducting island and reservoir. A program was developed to simulate the qubit's state over time by solving a stochastic differential Schrodinger equation numerically. The program simulated the noise by using its 1/f power spectrum. Looking into the both its wavefunction and density matrix, its dephasing and decoherence rates were determined for different inductive, capacitive, and Josephson energies. Results will be presented.
In quantum computation, quantum coherence must be maintained during gate operation. However, in physical implementations, various couplings with the environment are unavoidable and can lead to a dephasing of a quantum bit (qubit). The background charge fluctuations are an important dephasing process, especially in a charge qubit system. We examined the dephasing rate of a qubit due to random telegraph noise. Solving stochastic differential equations, we obtained the dephasing rate of a qubit constructed of a coupled-dot system; we applied our results to the charge Josephson qubit system. We examined the dephasing rates due to two types of couplings between the coupled-dot system and the background charge, namely, fluctuation in the tunnel coupling constant and fluctuation in the asymmetric bias. For a strong-coupling condition, the dephasing rate was inversely proportional to the time constant of the telegraph noise. When there is fluctuation in the tunnel coupling constant, Gaussian decay occurs in the initial regime. We also examined the rate of dephasing due to many impurity sites. For a weak-coupling condition with fluctuation in the asymmetric bias, the obtained dephasing rate coincided with that obtained by the perturbation method using the spectral weight of a boson thermal bath, which is proportional to the inverse of the frequency.
Electrical engineers and physicists are naturally very interested in noise in circuits, amplifiers and detectors. With the advent of quantum computation and other high frequency electronics operating at low temperatures, we have entered a regime where quantum noise and quantum-limited detectors are important. In this paper we describe the general concept of a two-level system as a quantum spectrum analyzer and apply it to a simple superconducting qubit, the Cooper-pair box. We derive and discuss the quantum noise associated with both a resistor and a classical tunnel junction, and study the effect these noise sources will have on a Cooper-pair box. Finally, we describe a theoretical technique for calculating quantum noise which involves studying the noisy system of interest coupled to a two-level system. We use this technique to calculate and give a heuristic explanation of the quantum charge noise of a normal metal single electron transistor.