Noise-induced looping on the Bloch sphere: Oscillatory effects in dephasing of qubits subject to broad-spectrum noise

Abstract

For many implementations of quantum computing, 1/f and other types of broad-spectrum noise are an important source of decoherence. An important step forward would be the ability to back out the characteristics of this noise from qubit measurements and to see if it leads to new physical effects. For certain types of qubits, the working point of the qubit can be varied. Using a new mathematical method that is suited to treat all working points, we present theoretical results that show how this degree of freedom can be used to extract noise parameters and to predict a new effect: noise-induced looping on the Bloch sphere. We analyze data on superconducting qubits to show that they are very near the parameter regime where this looping should be observed.PACS numbers: 85.25. Cp, 03.65.Yz, 75.10.Jm Motivated by the prospect of quantum computation and communication, coherent quantum operation and control of small systems has become a central area of physics research. The isolation of these systems from external noise is a key problem, as noise produces decoherence. In solid-state systems, some level of 1/f or other broad-spectrum noise (BSN) is almost always present, and is typically difficult to eliminate [1]. Indeed, in superconducting qubits, single-electron and other tunneling devices, this type of noise is recognized as the factor chiefly responsible for dephasing [2,3,4,5].One interesting question is the extent to which the characteristics of the BSN can be determined by measurements on the qubit itself. This has been considered by several authors [6,7,8,9]. For the most part, these authors considered the case of pure dephasing noise. Some theoretical work has been done for "mixed" noise, which causes both relaxation and dephasing, but this has usually been limited to Gaussian approximations [10], asymptotic analysis, or small numbers of RTNs [11].In this Letter, we show how to treat mixed noise analytically for all times, fully taking into account the nonGaussian effects. This will enable us to show how to back out the characteristics of the noise from qubit measurements. A new physical effect is predicted: noise-induced looping on the Bloch sphere. We shall analyze data on superconducting flux qubits to show that they are close to the regime in which this effect comes into play. However, we stress that this effect can occur in any two-level system that is subject to BSN, which can include qubit implementation from atomic and molecular physics as well as solid-state ones.The effective Hamiltonian of a qubit is often written, where ε and ∆ are the energy difference and tunneling splitting between the two physical states. For example, in a flux qubit ε is proportional to the applied flux through the superconducting loop and ∆ is the Josephson coupling. h ′ (t) is the noise, a random function. We shall be interested in the case where h ′ (t) comes from K random telegraph noise sources (RTNs) with a wide range of switching frequencies, giving rise to BSN. The coordinate system will be rotated by the angle θ = tan...

Disentanglement and decoherence from classical non-Markovian noise: random telegraph noise

“…There are thus two time scales set by the RTN's characteristics: the correlation time of the environment τ e ∼ 1/γ and the noise induced looping time of the qubit τ l ∼ 1/ (g cos θ ), where θ is the angle between the energy axisẑ and the noise coupling directionĝ [37]. The relative lengths of these two time scales are critical for the qubit decoherence and disentanglement.…”

“…The time evolution of the single qubit Bloch vector is simply a precession along theẑ direction with Larmor frequency B 0 . If the qubit is subject to a RTN, the transfer matrix can be calculated by known methods [36,37] and we have…”

“…Four issues are addressed. Firstly, it is known that RTNs can be put into two categories according to the ratio of their switching rates and coupling strengths to the qubit, namely the weakly-coupled (fast, Markovian) ones and strongly-coupled (slow, non-Markovian) ones [36][37][38]. We thus seek for qualitative differences in the disentanglement caused by these two types of RTNs.…”

“…In these architectures, it is found that 1/ f noise is the dominant source of decoherence. Thus a thorough understanding of those experiments requires models that (a) deal with non-Markovian noises, especially random telegraph noises (RTN) [15] which are the basic building blocks of 1/ f noise; (b) treat dephasing together with relaxation [35][36][37][38][39][40][41].…”

“…In this paper we use the quasi-Hamiltonian method [35][36][37] to investigate bipartite disentanglement of two independent qubits caused by uncorrelated sources of classical RTN. This method is extremely powerful for these types of problems and we will be able to obtain many analytic results, in an area of research dominated by numerical studies.…”