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arXiv:2011.13287 · Physical Review A

Magnetic noise from metal objects near qubit arrays

Jonathan Kenny, Hruday Mallubhotla, Robert Joynt

Published Jun 1, 2021• 5 citations
arXivHTMLPDF

Abstract

All metal objects support fluctuating currents that are responsible for evanescent-wave Johnson noise in their vicinity due to both thermal and quantum effects. The noise fields can decohere qubits. It is quantified by the average value of $\mathbf{B}(\mathbit{x},t)\phantom{\rule{0.28em}{0ex}}\mathbf{B}({\mathbit{x}}^{\ensuremath{'}},{t}^{\ensuremath{'}})$ and its time Fourier transform. We develop the formalism particularly for objects whose dimensions are small compared with the skin depth, which is the appropriate regime for nanoscale devices. This leads to a general and surprisingly simple formula for the two-point noise correlation function of an object of arbitrary shape. This formula has a clear physical interpretation in terms of induced currents in the object, and it can be the basis for straightforward numerical evaluation. We discuss its experimental implications. For a sphere, a solution is given in closed form in terms of a generalized multipole expansion. Plots of the solution illustrate the physical principles involved. We give examples of how the spatial pattern of noise can affect quantum information processing in nearby qubits. The theory implies that if the qubit system is miniaturized to a scale $D$, then decoherence rates of qubits scale as $1/D$.

DOI
10.1103/physreva.103.062401

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All metal objects support fluctuating currents that are responsible for evanescent-wave Johnson noise in their vicinity due to both thermal and quantum effects. The noise fields can decohere qubits. It is quantified by the average value of B(\mathbitx,t)B(\mathbitx\ensuremath′,t\ensuremath′)\mathbf{B}(\mathbit{x},t)\phantom{\rule{0.28em}{0ex}}\mathbf{B}({\mathbit{x}}^{\ensuremath{'}},{t}^{\ensuremath{'}})B(\mathbitx,t)B(\mathbitx\ensuremath′,t\ensuremath′) and its time Fourier transform. We develop the formalism particularly for objects whose dimensions are small compared with the skin depth, which is the appropriate regime for nanoscale devices. This leads to a general and surprisingly simple formula for the two-point noise correlation function of an object of arbitrary shape. This formula has a clear physical interpretation in terms of induced currents in the object, and it can be the basis for straightforward numerical evaluation. We discuss its experimental implications. For a sphere, a solution is given in closed form in terms of a generalized multipole expansion. Plots of the solution illustrate the physical principles involved. We give examples of how the spatial pattern of noise can affect quantum information processing in nearby qubits. The theory implies that if the qubit system is miniaturized to a scale DDD, then decoherence rates of qubits scale as 1/D1/D1/D.
Abstract In many quantum computer architectures, the qubits are in close proximity to metallic device elements. The fluctuating currents in the metal give rise to noisy electromagnetic fields that leak out into the surrounding region. These fields are known as evanescent-wave Johnson noise. The noise can decohere the qubits. We review and update the general theory of this effect for charge qubits subject to electric noise and for spin and magnetic qubits subject to magnetic noise. A mapping of the quantum-mechanical problem onto a problem in classical electrodynamics simplifies the calculations. The focus is on relatively simple geometries in which analytical calculations can be done. Results are presented for the local noise spectral density in the vicinity of cylindrical conductors such as small antennae, noise from objects that can be treated as dipoles, and noise correlation functions for several geometries. We summarize the current state of the comparison of theory with experimental results on decoherence times of qubits. Emphasis is placed on qualitative understanding of the basic concepts and phenomena.
In many quantum computer architectures, the qubits are in close proximity to metallic device elements. Metals have a high density of photon modes, and the fields spill out of the bulk metal because of the evanescent-wave component. Thus thermal and quantum electromagnetic Johnson-type noise from metallic device elements can decohere nearby qubits. In this Rapid Communication we use quantum electrodynamics to compute the strength of this evanescent-wave Johnson noise as a function of distance zzz from a metallic half space. Previous treatments have shown unphysical divergences at z=0z=0z=0. We remedy this by using a proper nonlocal dielectric function. Decoherence rates of local qubits are proportional to the magnitude of electric or magnetic correlation functions evaluated at the qubit position. We present formulas for the decoherence rates. These formulas serve as an important constraint on future device architectures. Comparison with single-electron spin relaxation measurements shows that evanescent-wave Johnson noise may constitute the dominant relaxation mechanism in experiments performed at low magnetic field.
Abstract : A key step in the construction of quantum computing technologies is the identification and elimination of unwanted sources of noise and its resulting quantum decoherence. In solid state devices, one important source of noise is the fluctuating electric and magnetic fields that come from the device elements themselves. The ultimate source of these fluctuations is the random electric currents that are strongest in the metallic electrodes and leads. This random motion has both thermal and quantum components, though in most devices presently under investigation, the thermal part dominates. In the past, this important physical effect has generally been modeled by picturing the device using an equivalent RC circuit and applying the Nyquist theorem to this circuit. This approach has limitations, since it depends on global quantities, rather than on the detailed geometry and the local electromagnetic properties of the components. Our aim in this research project was to compute the effect from first principles. We considered the underlying physical law (quantum electrodynamics) governing the devices in question. Given the position- and frequency-dependent dielectric function, the electromagnetic noise spectrum can be calculated, and the decohering effect can be deduced. Semiconducting quantum dot and superconducting flux qubits were investigated.
We present our study of decoherence in charge (spin) qubits due to evanescent-wave Johnson noise (EWJN) in a laterally coupled double quantum dot (single quantum dot). The high density of evanescent modes in the vicinity of metallic gates causes energy relaxation and a loss of phase coherence of electrons trapped in quantum dots. We derive expressions for the resultant energy relaxation rates of charge and spin qubits in a variety of dot geometries, and EWJN is shown to be a dominant source of decoherence for spin qubits held at low magnetic fields. Previous studies in this field approximated the charge or spin qubit as a point dipole. Ignoring the finite size of the quantum dot in this way leads to a spurious divergence in the relaxation rate as the qubit approaches the metal. Our approach goes beyond the dipole approximation and remedies this unphysical divergence by taking into account the finite size of the quantum dot. Additionally, we derive an enhancement of EWJN that occurs outside a thin metallic film, relative to the field surrounding a conducting half-space.
We compute the evanescent-wave Johnson noise (EWJN) in the vacuum half-space above a superconductor, and the resulting relaxation time (T1T_1T1​) of spin and charge qubits placed at nanometer distances from the surface. The electromagnetic response is described by a single microscopic transverse current-response kernel Q(q,ω)Q(q, ω)Q(q,ω) for a BCS superconductor. This is computed for varying densities of both non-magnetic impurities and magnetic impurities, for arbitrary frequency and temperature and for wave vectors q≪kFq \ll k_Fq≪kF​ (the Fermi wavevector). When combined with the fluctuation-dissipation theorem and the nonlocal surface impedances of the half-space, this yields the magnetic and electric field noise at any distance z≫kF−1z \gg k_F^{-1}z≫kF−1​ from the surface, from which we obtain T1T_1T1​. Just below TcT_cTc​ the magnetic noise is enhanced relative to the normal state by the coherence (Hebel-Slichter-type) peak of the dissipative conductivity and drops exponentially at lower temperatures; the electric noise shows no coherence peak. The theory predicts that there is a zero-temperature noise floor induced by magnetic impurities. In the gapless regime produced by pair breaking, the finite subgap density of states ν(0)ν(0)ν(0) yields a temperature-independent noise spectral density and a relaxation rate bounded by T1−1(T)≤[ν(0)/νF]2 T1,N−1(T)T_1^{-1}(T)\le[ν(0)/ν_F]^{2}\,T_{1,N}^{-1}(T)T1−1​(T)≤[ν(0)/νF​]2T1,N−1​(T) for T≪TcT\ll T_cT≪Tc​, with equality in the extreme nonlocal regime. Here ν(0)ν(0)ν(0) and νFν_FνF​ are the superconducting and normal-state densities of states at the Fermi energy, and T1,N(T)T_{1,N}(T)T1,N​(T) is the relaxation time the same electrode would produce in its normal state at the same temperature.
The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the individual qubits and quantum gates. 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 obtained by engineering. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, quantum devices are affected by noise decreasing with frequency fff approximately as 1/f1/f1/f. According to the present point of view, such noise is due to material- and device-specific microscopic degrees of freedom interacting with quantum variables of the nanodevice. The simplest picture is that the environment that destroys the phase coherence of the device can be thought of as a system of two-state fluctuators, which experience random hops between their states. If the hopping times are distributed in an exponentially broad domain, the resulting fluctuations have a spectrum close to 1/f1/f1/f in a large frequency range. This paper reviews the current state of the theory of decoherence due to degrees of freedom producing 1/f1/f1/f noise. Basic mechanisms of such noises in various nanodevices are discussed and several models describing the interaction of the noise sources with quantum devices are reviewed. The main focus of the review is to analyze how the 1/f1/f1/f noise destroys their coherent operation. The start is from individual qubits concentrating mostly on the devices based on superconductor circuits and then some special issues related to more complicated architectures are discussed. Finally, several strategies for minimizing the noise-induced decoherence are considered.