Decoherence and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi>/</mml:mi><mml:mi mathvariant="italic">f</mml:mi></mml:math>Noise in Josephson Qubits

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...

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“…This has been considered by several authors [6,7,8,9]. For the most part, these authors considered the case of pure dephasing noise.…”

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

Zhou

Joynt

2010

Phys. Rev. A

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“…In addition, stochastic modeling allows us to perform a detailed analysis for relevant kinds of noise, which are usually difficult to describe within a full quantum treatment, e.g., Gaussian noise with and without a Lorentzian spectral density. For qubit systems, description of environment-induced decoherence by the interaction with classical fluctuating field has been successfully carried out [73][74][75][76][77][78][79][80][81][82] and this approach has provided insights into the decoherence process for systems of interest in quantum technology.…”

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Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment

et al. 2015

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We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a maximally nonclassical state, e.g., a Fock number state or a Schrödinger-cat-like state, and then coupled to either a resonant or a nonresonant external field. Stochastic modeling allows us to describe the decoherence dynamics without resorting to approximated quantum master equations and to introduce non-Markovian effects in a controlled way. A detailed comparison among different nonclassicality criteria and a thorough analysis of the decoherence time reveal a rich phenomenology whose main features may be summarized as follows: (i) Classical memory effects increase the survival time of quantum coherence and (ii) a detuning between the natural frequency of the system and the central frequency of the classical field induces revivals of quantum coherence.

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“…Since these noise perturb the voltage bias of the CB, the interaction Hamiltonian H int has the form H int = σ zÊZ + σ zÊB , whereÊ Z and E B are environment operators (with the coupling strengths included). Here we focus on the fluctuations in the voltage bias, the dominating source of decoherence and neglect noise in the B x field (the critical current), as practised customarily [5,18,19]. This is because charge qubits are insensitive to flux noise and the effect of the fluctuation in the I c suppression field is secondary to the bias voltage variations discussed above.…”

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“…This is because charge qubits are insensitive to flux noise and the effect of the fluctuation in the I c suppression field is secondary to the bias voltage variations discussed above. Detailed treatment of the two voltage noise sources and their influence on the charge qubit system can be found in the literature [18,19]. For our purpose, the nature of the environment and specific form ofÊ Z andÊ B are not essential, therefore we do not go into detail here.…”

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“…In order to control B x = E J , we use a flux biased small dc-SQUID to replace the junction, whose critical current is maximal (I c = I 0 c ) when the flux bias is off and vanishes (I c = 0) when it is Φ 0 /2 = h 4e . The dominating decoherence sources in this system are circuit noise in the voltage bias [1] and charge fluctuations in the background (known as "charge noise") [17,18], as indicated in Fig. 1 (a).…”

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Dispersive manipulation of paired superconducting qubits

et al. 2004

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We combine the ideas of qubit encoding and dispersive dynamics to enable robust and easy quantum information processing (QIP) on paired superconducting charge boxes sharing a common bias lead. We establish a decoherence free subspace on these and introduce universal gates by dispersive interaction with a LC resonator and inductive couplings between the encoded qubits. These gates preserve the code space and only require the established local symmetry and the control of the voltage bias.PACS numbers: 03.67. Lx, 74.50.+r Superconducting nano-circuits consisting of charge boxes (CB) [1] are among the most promising candidates for a quantum computer. Coherent control of a single charge qubit [2], long decoherence time [3] and, more recently, coupled two qubit systems [4] have been demonstrated. But despite this encouraging experimental progress, there are serious difficulties with superconducting QIP which may appear insurmountable. The first is the severe decoherence experienced by these macroscopic qubits, which are coupled to a large number of degrees of freedom in their environment including control circuitry [5]. A few methods have been employed to reduce the decoherence [6,7], but they usually require sophisticated manipulation or significant overhead in the control circuitry. The second major difficulty comes from the imperfect control realizable in solid state systems. Specifically, one finds it difficult to achieve controllable couplings between superconducting qubits, since the commonly used hard-wired inductive or capacitive couplings are untunable. Great effort has been exercised to realize controllable couplings [8,9,10]. Schemes allowing to compute with invariable couplings were also studied [11,12]. Others have recently discussed to use an LC circuit to actively mediate the interaction between superconducting qubits [13,14].The requirement to reduce decoherence and the desire for the easiest manipulation apply to all QIP implementations. Unfortunately, it is not always easy to accomplish both -actually the goals are often contradictory -since reducing decoherence may require extra complication in the manipulation.In this work we show how to achieve both goals. Using a closely placed pair of charge boxes (PCB) sharing a common bias lead as the logic qubit, we can encode information in a fashion immune to collective noise, which is the dominating decoherence source in our setting. We introduce LC resonators inductively coupled to the PCBs whose virtual excitations allow us to manipulate the PCB dispersively; all interactions will be off resonance, without energy transfer [15,16], and thus a logical qubit stays within its encoding space even during manipulation. By inductively coupling the * Electronic address: mikewulf@pas.rochester.edu CBs and taking advantage of dispersive dynamics again, controlled phases can be induced between logical qubits.Combining dispersive dynamics and encoding offers a new method for QIP. It overcomes the major difficulties of superconducting CBs in a realistic and very si...

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Decoherence and1/fNoise in Josephson Qubits

Cited by 310 publications

References 24 publications

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

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

Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment

Dispersive manipulation of paired superconducting qubits

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